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searching for Partition function (mathematics) 171 found (204 total)

alternate case: partition function (mathematics)

Integer partition (3,405 words) [view diff] no match in snippet view article find links to article

partition is called a part. The number of partitions of n is given by the partition function p(n). So p(4) = 5. The notation λ ⊢ n means that λ is a partition

Partition function (number theory) (4,357 words) [view diff] no match in snippet view article

In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because

List of partition topics (237 words) [view diff] no match in snippet view article find links to article

Partition calculus Partition function (quantum field theory) Partition function (statistical mechanics) Derivation of the partition function Partition of an

Symmetry number (255 words) [view diff] no match in snippet view article find links to article

molecular conformations in the partition function. In this sense, the symmetry number depends upon how the partition function is formulated. For example,

Ramanujan's congruences (954 words) [view diff] no match in snippet view article find links to article

In mathematics, Ramanujan's congruences are the congruences for the partition function p(n) discovered by Srinivasa Ramanujan: p ( 5 k + 4 ) ≡ 0 ( mod

Kostant partition function (1,711 words) [view diff] no match in snippet view article find links to article

In representation theory, a branch of mathematics, the Kostant partition function, introduced by Bertram Kostant (1958, 1959), of a root system Δ {\displaystyle

Arf invariant of a knot (739 words) [view diff] no match in snippet view article find links to article

Jones showed that the Arf invariant can be obtained by taking the partition function of a signed planar graph associated to a knot diagram. This approach

Newman's conjecture (774 words) [view diff] no match in snippet view article find links to article

Unsolved problem in mathematics Given arbitrary m, r, are there infinitely values of n such that the partition function at n is congruent to r mod m?

Bosonic string theory (1,596 words) [view diff] no match in snippet view article find links to article

26. Physical quantities are then constructed from the (Euclidean) partition function and N-point function: Z = ∑ h = 0 ∞ ∫ D g m n D X μ N exp ⁡ ( − I

Bost–Connes system (203 words) [view diff] no match in snippet view article find links to article

In mathematics, a Bost–Connes system is a quantum statistical dynamical system related to an algebraic number field, whose partition function is related

Bruria Kaufman (873 words) [view diff] no match in snippet view article find links to article

applied spinor analysis to rederive the result of Lars Onsager on the partition function of the two-dimensional Ising model, and to the study of the Mössbauer

Mathukumalli V. Subbarao (580 words) [view diff] no match in snippet view article find links to article

the partition function". American Mathematical Monthly. 73 (8): 851–854. doi:10.2307/2314179. JSTOR 2314179. Ono, K. (1996). "Parity of the partition function

A. O. L. Atkin (372 words) [view diff] no match in snippet view article find links to article

properties of the integer partition function and the monster module. He was a vocal fan of using computers in mathematics, so long as the end goal was

Free entropy (1,386 words) [view diff] no match in snippet view article find links to article

logarithm of a partition function. The Onsager reciprocal relations in particular, are developed in terms of entropic potentials. In mathematics, free entropy

Corner transfer matrix (2,357 words) [view diff] no match in snippet view article find links to article

k and l are arranged as follows: For a lattice with N sites, the partition function is Z N = ∑ a l l s p i n s ∏ a l l f a c e s w ( σ i , σ j , σ k

Chern–Simons theory (3,591 words) [view diff] no match in snippet view article find links to article

multiplies the action. The action is gauge dependent, however the partition function of the quantum theory is well-defined when the level is an integer

Boltzmann distribution (2,496 words) [view diff] no match in snippet view article find links to article

The partition function can be calculated if we know the energies of the states accessible to the system of interest. For atoms the partition function values

Hansraj Gupta (375 words) [view diff] no match in snippet view article find links to article

mathematician specialising in number theory, in particular the study of the partition function. Gupta was born 9 October 1902 in Rawalpindi, then part of British

Bertram Kostant (1,209 words) [view diff] no match in snippet view article find links to article

prequantization has led to the theory of quantum Toda lattices. The Kostant partition function is named after him. With Gerhard Hochschild and Alex F. T. W. Rosenberg

Witten conjecture (1,167 words) [view diff] no match in snippet view article find links to article

of 2-dimensional quantum gravity should have the same partition function. The partition function for one of these models can be described in terms of intersection

Hardy–Ramanujan–Littlewood circle method (1,522 words) [view diff] no match in snippet view article find links to article

"On the expansion of the partition function in a series", Annals of Mathematics, Second Series, 44 (3), The Annals of Mathematics, Vol. 44, No. 3: 416–422

Zeta function regularization (2,125 words) [view diff] no match in snippet view article find links to article

eigenvalues of Laplacians are known, the zeta function corresponding to the partition function can be computed explicitly. Consider a scalar field φ contained in

Topological quantum field theory (3,764 words) [view diff] no match in snippet view article find links to article

value. In analogy with statistical mechanics it is also called the partition function. The reason why a theory with a zero Hamiltonian can be sensibly formulated

Marginal likelihood (992 words) [view diff] no match in snippet view article find links to article

that the posterior is a proper probability. It is related to the partition function in statistical mechanics. Given a set of independent identically distributed

Square lattice Ising model (1,792 words) [view diff] no match in snippet view article find links to article

{\displaystyle T} and the Boltzmann constant k {\displaystyle k} , the partition function Z N ( K ≡ β J , L ≡ β J ∗ ) = ∑ { σ } exp ⁡ ( K ∑ ⟨ i j ⟩ H σ i σ

Asano contraction (1,012 words) [view diff] no match in snippet view article find links to article

have used this theorem to relate the zeroes of the partition function to zeroes of the partition function of its subsystems. Asano contractions can be used

Asymptotic analysis (2,803 words) [view diff] no match in snippet view article find links to article

{n}{e}}\right)^{n}} —this is Stirling's approximation Partition function For a positive integer n, the partition function, p(n), gives the number of ways of writing

Steinberg formula (225 words) [view diff] no match in snippet view article find links to article

element of the Weyl group, ρ is the Weyl vector, and P is the Kostant partition function giving the number of ways of writing a vector as a sum of positive

Canonical ensemble (2,828 words) [view diff] no match in snippet view article find links to article

free energy) may be restated in terms of the canonical partition function by simple mathematical manipulations. Historically, the canonical ensemble was

Lee–Yang theorem (1,027 words) [view diff] no match in snippet view article find links to article

M. (1974), "Zeros of the partition function for generalized Ising systems", Communications on Pure and Applied Mathematics, 27 (2): 143–159, doi:10.1002/cpa

Rank of a partition (1,359 words) [view diff] no match in snippet view article find links to article

study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. A different concept

Gopakumar–Vafa invariant (633 words) [view diff] no match in snippet view article find links to article

invariants can be viewed as a partition function in topological quantum field theory. They are proposed to be the partition function in Gopakumar–Vafa form:

List of number theory topics (938 words) [view diff] no match in snippet view article find links to article

function Möbius inversion formula Divisor function Liouville function Partition function (number theory) Integer partition Bell numbers Landau's function Pentagonal

Hans Rademacher (724 words) [view diff] no match in snippet view article find links to article

In 1937 Rademacher discovered an exact convergent series for the partition function P(n), the number of integer partitions of a number, improving upon

Xi (letter) (1,154 words) [view diff] no match in snippet view article

complex analysis The "cascade particles" in particle physics The partition function under the grand canonical ensemble in statistical mechanics Indicating

Neutral network (evolution) (2,832 words) [view diff] no match in snippet view article

a polynomial time DP algorithm for computing the full equilibrium partition function of an RNA secondary structure. This changed the dominant calculation

List of mathematical functions (1,065 words) [view diff] no match in snippet view article find links to article

function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer

Chern–Simons form (611 words) [view diff] no match in snippet view article find links to article

Schwartz, A. S. (1978). "The partition function of degenerate quadratic functional and Ray-Singer invariants". Letters in Mathematical Physics. 2 (3): 247–252

Tutte polynomial (5,377 words) [view diff] no match in snippet view article find links to article

Independently of the work in algebraic graph theory, Potts began studying the partition function of certain models in statistical mechanics in 1952. The work by Fortuin

Jordan Ellenberg (1,225 words) [view diff] no match in snippet view article find links to article

made a cameo appearance in the film as a professor lecturing on the partition function and Ramanujan's congruences. This gives him a Erdős-Bacon number of

Al-Salam–Chihara polynomials (403 words) [view diff] no match in snippet view article find links to article

Zeng, J. (2009). The Andrews–Stanley partition function and Al-Salam–Chihara polynomials. Discrete Mathematics, 309(1), 151-175. Atakishiyeva, M. K.

Euler function (789 words) [view diff] no match in snippet view article find links to article

(q)}}=\sum _{k=0}^{\infty }p(k)q^{k}} where p {\displaystyle p} is the partition function. The Euler identity, also known as the Pentagonal number theorem,

Supersymmetric theory of stochastic dynamics (6,105 words) [view diff] no match in snippet view article find links to article

the finite-time GTO is larger than unity. Under this condition, the partition function, Z t t ′ = T r M ^ t t ′ = ∑ α e − ( t − t ′ ) H α , {\displaystyle

Path integral formulation (14,277 words) [view diff] no match in snippet view article find links to article

these functional integrals mathematically precise. Such a functional integral is extremely similar to the partition function in statistical mechanics.

Analytic Combinatorics (book) (748 words) [view diff] no match in snippet view article

at least to the work of G. H. Hardy and Srinivasa Ramanujan on the partition function, the citation also quoted a review by Robin Pemantle stating that

Jennifer Tour Chayes (1,216 words) [view diff] no match in snippet view article find links to article

Kleinwaks; Kotecky (2004), "Partition function zeros at first-order phase transitions: A general analysis", Communications in Mathematical Physics, 251 (1): 79–131

Atle Selberg (1,788 words) [view diff] no match in snippet view article find links to article

Srinivasa Ramanujan and he found an exact analytical formula for the partition function as suggested by the works of Ramanujan; however, this result was first

Nikita Nekrasov (580 words) [view diff] no match in snippet view article find links to article

gauge theory, quantum integrability, and string theory. The Nekrasov partition function, which he introduced in his 2002 paper, relates in an intricate way

Selberg integral (1,012 words) [view diff] no match in snippet view article find links to article

Dyson (1963), who were unaware of Selberg's earlier work. It is the partition function for a gas of point charges moving on a line that are attracted to

Euler numbers (2,049 words) [view diff] no match in snippet view article find links to article

A1. Malenfant, J. (2011). "Finite, Closed-form Expressions for the Partition Function and for Euler, Bernoulli, and Stirling Numbers". arXiv:1103.1585 [math

Albert Schwarz (625 words) [view diff] no match in snippet view article find links to article

A12(7):1405–1429, 1997. V. Kac, A. Schwarz, Geometric interpretation of the partition function of 2D gravity, Phys. Lett. B257 (1991), nos. 3–4, 329–334. A. A. Belavin

Arithmetic function (7,555 words) [view diff] no match in snippet view article find links to article

\dots \;\;\;\;{\text{ is not a prime power}}.\end{cases}}} p(n), the partition function, is the number of ways of representing n as a sum of positive integers

Amanda Folsom (670 words) [view diff] no match in snippet view article find links to article

Folsom participated in the discovery of a fractal structure in the partition function that allows any particular value of the function to be computed exactly

Rudin–Shapiro sequence (2,732 words) [view diff] no match in snippet view article find links to article

S(N,x)=\sum _{0\leq n<2^{N}}\exp(2\pi ixu(n,N)).} Recall that the partition function of the one-dimensional Ising model can be defined as follows. Fix

Pamela E. Harris (990 words) [view diff] no match in snippet view article find links to article

representation she studies vector partition functions, in particular Kostant's partition function. She is also interested in graph theory and number theory. In 2016

Stuart Samuel (physicist) (1,455 words) [view diff] no match in snippet view article

fermionic-like particles. This allowed a rapid computation of the partition function and correlation functions. Samuel went on to treat certain interacting

Effective field theory (1,526 words) [view diff] no match in snippet view article find links to article

value Feynman diagram Lattice field theory LSZ reduction formula Partition function Path Integral Formulation Propagator Quantization Regularization Renormalization

Timeline of number theory (742 words) [view diff] no match in snippet view article find links to article

3000 theorems, including properties of highly composite numbers, the partition function and its asymptotics, and mock theta functions. He also makes major

Quicksort (9,925 words) [view diff] no match in snippet view article find links to article

gets swapped with other elements in the partition function. Therefore, the index returned in the partition function isn't necessarily where the actual pivot

Ising model (20,177 words) [view diff] no match in snippet view article find links to article

{\displaystyle Z_{\beta }=\sum _{\sigma }e^{-\beta H(\sigma )}} is the partition function. For a function f {\displaystyle f} of the spins ("observable"), one

Knot polynomial (416 words) [view diff] no match in snippet view article find links to article

Kauffman noticed the Jones polynomial could be computed by means of a partition function (state-sum model), which involved the bracket polynomial, an invariant

Griffiths inequality (2,239 words) [view diff] no match in snippet view article find links to article

( σ ) {\displaystyle Z=\int d\mu (\sigma )e^{-H(\sigma )}} be the partition function. As usual, ⟨ f ⟩ = 1 Z ∑ σ f ( σ ) e − H ( σ ) {\displaystyle \langle

Wheeler–DeWitt equation (1,632 words) [view diff] no match in snippet view article find links to article

and applied mathematics, is a field equation attributed to John Archibald Wheeler and Bryce DeWitt. The equation attempts to mathematically combine the

Ice-type model (2,935 words) [view diff] no match in snippet view article find links to article

Eulerian orientations of an underlying 4-regular undirected graph. The partition function also counts the number of nowhere-zero 3-flows. For two-dimensional

History of mathematics (16,226 words) [view diff] no match in snippet view article find links to article

of the American Mathematical Society. 56: 448–469. doi:10.1090/S0002-9947-1944-0011087-2. Murty, M. Ram (2013). "The Partition Function Revisited". The

Entropy (statistical thermodynamics) (2,621 words) [view diff] no match in snippet view article

_{\text{mic}}} is the microcanonical partition function Z can {\displaystyle Z_{\text{can}}} is the canonical partition function Z gr {\displaystyle {\mathcal

George Stanley Rushbrooke (755 words) [view diff] no match in snippet view article find links to article

(1962). "High-temperature partition function and refated noncrossing polygons for the simple cubic lattice". Journal of Mathematical Physics. 3: 185–189. doi:10

Robert Churchhouse (867 words) [view diff] no match in snippet view article find links to article

computational mathematics". Singapore: World Scientific. Churchhouse, Robet F. (1969). "Congruence properties of the binary partition function". Mathematical Proceedings

Gifted (2017 film) (2,061 words) [view diff] no match in snippet view article

experiences. Ellenberg also cameos as a professor lecturing on the partition function and Ramanujan's congruences. The film was scheduled to be released

Renormalization group (7,044 words) [view diff] no match in snippet view article find links to article

constants { J k } {\displaystyle \{J_{k}\}} . This function may be a partition function, an action, a Hamiltonian, etc. It must contain the whole description

Ken Ono (1,774 words) [view diff] no match in snippet view article find links to article

congruences for the partition function with all prime moduli greater than 3. His paper was published in the Annals of Mathematics. In a joint work with

Gaussian integral (4,351 words) [view diff] no match in snippet view article find links to article

the harmonic oscillator, and in statistical mechanics, to find its partition function. Although no elementary function exists for the error function, as

Goldbach's conjecture (3,720 words) [view diff] no match in snippet view article find links to article

are believed to be of roughly comparable difficulty. The Goldbach partition function is the function that associates to each even integer the number of

Crank of a partition (1,282 words) [view diff] no match in snippet view article find links to article

published in 1918 stated and proved the following congruences for the partition function p(n), since known as Ramanujan congruences. p(5n + 4) ≡ 0 (mod 5)

Functional integration (1,801 words) [view diff] no match in snippet view article find links to article

Lévy process Fractional statistical mechanics Feynman path integral Partition function (quantum field theory) Saddle point approximation Daniell, P. J. (July

Connective constant (2,354 words) [view diff] no match in snippet view article find links to article

to b {\displaystyle b} . The aim of the proof is to show that the partition function Z ( x ) = ∑ γ : a → H x ℓ ( γ ) = ∑ n = 0 ∞ c n x n {\displaystyle

Index of physics articles (V) (674 words) [view diff] no match in snippet view article

scanning probe microscopy Vibrational energy relaxation Vibrational partition function Vibrational transition Vibronic coupling Vickers hardness test Victor

Bethe lattice (1,948 words) [view diff] no match in snippet view article find links to article

magnetic field. The Ising model on the Bethe lattice is defined by the partition function Z = ∑ { σ } exp ⁡ ( K ∑ ( i , j ) σ i σ j + h ∑ i σ i ) . {\displaystyle

Itô diffusion (4,657 words) [view diff] no match in snippet view article find links to article

{\displaystyle \rho _{\infty }(x)=Z^{-1}\exp(-\beta \Psi (x)),} where the partition function Z is given by Z = ∫ R n exp ⁡ ( − β Ψ ( x ) ) d x . {\displaystyle

Modular form (4,651 words) [view diff] no match in snippet view article find links to article

theory, such as representation of integers by quadratic forms and the partition function. The crucial conceptual link between modular forms and number theory

Jan Hendrik Bruinier (115 words) [view diff] no match in snippet view article find links to article

formula for the values of the partition function. He was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to

Freeman Dyson (8,580 words) [view diff] no match in snippet view article find links to article

in the context of a study of certain congruence properties of the partition function discovered by the mathematician Srinivasa Ramanujan. In number theory

Robert Dirks (1,886 words) [view diff] no match in snippet view article find links to article

base pairing probabilities through calculation of the statistical partition function. Unlike other structure prediction tools, NUPACK is capable of handling

Srinivasa Ramanujan (11,705 words) [view diff] no match in snippet view article find links to article

for the hyperbolic secant. In 1918, Hardy and Ramanujan studied the partition function P(n) extensively. They gave a non-convergent asymptotic series that

Branches of physics (1,889 words) [view diff] no match in snippet view article find links to article

classical mechanics. The theory is based on two postulates: (1) that the mathematical forms of the laws of physics are invariant in all inertial systems; and

Renormalization (7,763 words) [view diff] no match in snippet view article find links to article

constants { J k } {\displaystyle \{J_{k}\}} . This function may be a partition function, an action, a Hamiltonian, etc. It must contain the whole description

Robert Penner (1,273 words) [view diff] no match in snippet view article find links to article

punctured surfaces including the so-called Penner matrix model, the basic partition function for Riemann's moduli space. Extending the foregoing to orientation-preserving

Dedekind eta function (3,057 words) [view diff] no match in snippet view article find links to article

formula Ramanujan–Sato series q-series Weierstrass elliptic function Partition function Kronecker limit formula Affine Lie algebra Siegel, C. L. (1954). "A

Vertex operator algebra (8,938 words) [view diff] no match in snippet view article find links to article

–z−n–1∂z as n ranges over integers greater than 1. The module then has partition function T r V q L 0 = ∑ n ∈ R dim ⁡ V n q n = ∏ n ≥ 2 ( 1 − q n ) − 1 {\displaystyle

List of unsolved problems in mathematics (20,026 words) [view diff] no match in snippet view article find links to article

C(\varepsilon )\cdot f^{6+\varepsilon }} . Newman's conjecture: the partition function satisfies any arbitrary congruence infinitely often. Piltz divisor

Differential poset (1,601 words) [view diff] no match in snippet view article find links to article

every differential poset and some constant a. By comparison, the partition function has asymptotics p ( n ) ∼ 1 4 n 3 exp ⁡ ( π 2 n 3 ) . {\displaystyle

Atiyah–Singer index theorem (7,553 words) [view diff] no match in snippet view article find links to article

displaying short descriptions of redirect targets Witten index – Modified partition function Atiyah & Singer 1963. Kayani 2020. Hamilton 2020, p. 11. Gel'fand

Equipartition theorem (11,997 words) [view diff] no match in snippet view article find links to article

the same results can be obtained by an alternative method using the partition function. A diatomic gas can be modelled as two masses, m1 and m2, joined by

Laplace transform (9,453 words) [view diff] no match in snippet view article find links to article

states g ( E ) {\displaystyle g(E)} defines the partition function. That is, the canonical partition function Z ( β ) {\displaystyle Z(\beta )} is given by

Instanton (6,385 words) [view diff] no match in snippet view article find links to article

{\text{Im}}Z_{k}} whereby Z k {\displaystyle Z_{k}} is the canonical partition function, which is calculated by taking the trace of the Boltzmann operator

Gauge theory (6,822 words) [view diff] no match in snippet view article find links to article

under these transformations. The term "gauge" refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian

Möbius function (3,121 words) [view diff] no match in snippet view article find links to article

interesting connections to number theory, including the fact that the partition function is the Riemann zeta function. This idea underlies Alain Connes's attempted

Virasoro algebra (4,140 words) [view diff] no match in snippet view article find links to article

s}(c){\big )}^{p(N-rs)},} where p ( N ) {\displaystyle p(N)} is the partition function, and A N {\displaystyle A_{N}} is a positive constant that does not

Cumulant (8,877 words) [view diff] no match in snippet view article find links to article

drawn from a distribution E ∼ p ( E ) {\textstyle E\sim p(E)} . The partition function of the system is Z ( β ) = ∑ i e − β E i , {\displaystyle Z(\beta

Yang–Mills theory (4,217 words) [view diff] no match in snippet view article find links to article

experimental observation. This shows why QCD confinement at low energy is a mathematical problem of great relevance, and why the Yang–Mills existence and mass

UBASIC (2,089 words) [view diff] no match in snippet view article find links to article

identical terms, stop at the previous term. UBASIC can calculate the partition function to over p(1330521). (In 8.74 up to p(1361911) and the 4000 digit versions

Pentagonal number theorem (2,118 words) [view diff] no match in snippet view article find links to article

\ldots \geq \lambda _{\ell }>0} . The number of partitions of n is the partition function p(n) having generating function: ∑ n = 0 ∞ p ( n ) x n = ∏ k = 1 ∞

Numerical sign problem (2,260 words) [view diff] no match in snippet view article find links to article

fermion chemical potential μ {\displaystyle \mu } . One evaluates the partition function Z {\displaystyle Z} by summing over all classical field configurations

Hideki Yukawa (1,313 words) [view diff] no match in snippet view article find links to article

middle school principal, the principal praised his "high potential" in mathematics and offered to adopt Ogawa himself in order to keep him on a scholarly

Game theory (15,399 words) [view diff] no match in snippet view article find links to article

Lucas, William F. (1963), " n {\displaystyle n} -person games in partition function form", Naval Research Logistics Quarterly, 10 (4): 281–298, doi:10

John Hubbard (physicist) (1,242 words) [view diff] no match in snippet view article

popularizing a method first derived by Ruslan Stratonovich for computing the partition function of many-body systems, now called the Hubbard–Stratonovich transformation

List of prime numbers (5,814 words) [view diff] no match in snippet view article find links to article

111181111, 111191111, 777767777, 77777677777, 99999199999 (OEIS: A077798) Partition function values that are prime. 2, 3, 5, 7, 11, 101, 17977, 10619863, 6620830889

Lambert series (3,873 words) [view diff] no match in snippet view article find links to article

products whose lower triangular entries are given in terms of the partition function and the Möbius function by the divisor sums s n , k ( − 1 ) = ∑ d

Entropic gravity (3,736 words) [view diff] no match in snippet view article find links to article

C.; Jeynes, C. (21 April 2021). "Entropic uncertainty principle, partition function and holographic principle derived from Liouville's Theorem". Physics

Permutation (11,671 words) [view diff] no match in snippet view article find links to article

number of cycle types of a set with n elements equals the value of the partition function p ( n ) {\displaystyle p(n)} . Polya's cycle index polynomial is a

Feynman diagram (15,967 words) [view diff] no match in snippet view article find links to article

The field's partition function is the normalization factor on the bottom, which coincides with the statistical mechanical partition function at zero temperature

Redheffer matrix (6,249 words) [view diff] no match in snippet view article find links to article

0}\ell (k-j)[q^{j}](q;q)_{\infty }\right],} where p(n) denotes the partition function, μ ( n ) {\displaystyle \mu (n)} is the Moebius function, and the

Spin glass (4,923 words) [view diff] no match in snippet view article find links to article

interactions are called bond or link variables. In order to determine the partition function for this system, one needs to average the free energy f [ J i j ]

Spin structure (4,373 words) [view diff] no match in snippet view article find links to article

wavefunction, and one often needs to sum over these choices in the partition function. In many physical theories E is the tangent bundle, but for the fermions

Outline of physics (3,331 words) [view diff] no match in snippet view article find links to article

mediated by magnetic field. Mathematical physics – application of mathematics to problems in physics and the development of mathematical methods for such applications

Gluon field strength tensor (2,107 words) [view diff] no match in snippet view article find links to article

{A}}}} which represent the non-abelian character of the SU(3). A more mathematically formal derivation of these same ideas (but a slightly altered setting)

Brillouin and Langevin functions (2,896 words) [view diff] no match in snippet view article find links to article

(2018). "A comprehensive study of the mathematical methods used to approximate the inverse Langevin function". Mathematics and Mechanics of Solids. 24 (7):

Likelihood function (8,546 words) [view diff] no match in snippet view article find links to article

{\displaystyle \mathbf {T} (x)} ⁠, minus the normalization factor (log-partition function) ⁠ A ( η ) {\displaystyle A({\boldsymbol {\eta }})} ⁠. Thus for example

Pauli–Lubanski pseudovector (2,102 words) [view diff] no match in snippet view article find links to article

and Representations: An Elementary Introduction, Graduate Texts in Mathematics, vol. 222 (2nd ed.), Springer, doi:10.1007/978-3-319-13467-3, ISBN 978-3319134666

Stirling numbers of the first kind (7,262 words) [view diff] no match in snippet view article find links to article

the NIST Handbook of Mathematical Functions. Malenfant, Jerome (2011). "Finite, closed-form expressions for the partition function and for Euler, Bernoulli

Bernoulli number (13,056 words) [view diff] no match in snippet view article find links to article

Malenfant, Jerome (2011), "Finite, closed-form expressions for the partition function and for Euler, Bernoulli, and Stirling numbers", arXiv:1103.1585 [math

Chiral anomaly (3,271 words) [view diff] no match in snippet view article find links to article

transformation. Wess and Zumino developed a set of conditions on how the partition function ought to behave under gauge transformations called the Wess–Zumino

Verma module (4,330 words) [view diff] no match in snippet view article find links to article

positive roots (this is closely related to the so-called Kostant partition function). This assertion follows from the earlier claim that the Verma module

Pfaffian (3,929 words) [view diff] no match in snippet view article find links to article

used to calculate the number of domino tilings of a rectangle, the partition function of Ising models in physics, or of Markov random fields in machine

Ralph Kenna (3,225 words) [view diff] no match in snippet view article find links to article

R.; Lang, C.B. (1991). "Finite-Size Scaling and the Zeroes of the Partition Function in the φ 4 4 {\displaystyle \varphi _{4}^{4}} Model". Physics Letters

Quantum field theory in curved spacetime (1,938 words) [view diff] no match in snippet view article find links to article

theory in curved spacetime (Lecture Note 39/2008 Max Planck Institute for Mathematics in the Natural Sciences (2008))" (PDF). Khavkine, Igor; Moretti, Valter

Q-Pochhammer symbol (2,654 words) [view diff] no match in snippet view article find links to article

}:=(q;q)_{\infty }} similarly arises as the generating function for the partition function, p ( n ) {\displaystyle p(n)} , which is also expanded by the second

Density matrix (5,446 words) [view diff] no match in snippet view article find links to article

that the trace of ρ {\displaystyle \rho } be equal to 1 defines the partition function to be Z ( β ) = t r exp ⁡ ( − β H ) {\displaystyle Z(\beta )=\mathrm

Quantum electrodynamics (6,577 words) [view diff] no match in snippet view article find links to article

agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting

Source field (9,512 words) [view diff] no match in snippet view article find links to article

N ≡ Z [ J = 0 ] {\displaystyle {\mathcal {N}}\equiv Z[J=0]} , the partition function is given by Z [ J ] = N ∫ D ϕ exp ⁡ [ − i ( ∫ d t L ( t ; ϕ , ϕ

Network entropy (3,470 words) [view diff] no match in snippet view article find links to article

)=Tr[e^{-\beta L}]} is a normalizing factor which plays the role of the partition function, and β {\displaystyle \beta } is a tunable parameter which allows

Wightman axioms (2,719 words) [view diff] no match in snippet view article find links to article

In mathematical physics, the Wightman axioms (also called Gårding–Wightman axioms), named after Arthur Wightman, are an attempt at a mathematically rigorous

Uncertainty principle (19,263 words) [view diff] no match in snippet view article find links to article

typical infinitesimal phase space volume used in the calculation of a partition function. The inequality is also strict and not saturated. Efforts to improve

Index of physics articles (T) (2,020 words) [view diff] no match in snippet view article

Transition rule Translation (physics) Translational lift Translational partition function Translational symmetry Transmission-line Transmission (mechanics)

Lagrangian (field theory) (6,708 words) [view diff] no match in snippet view article

they only provide an irrelevant overall multiplicative term to the partition function, so again play no role. Physically this is because in these theories

Cyclometer (3,070 words) [view diff] no match in snippet view article find links to article

partitions of n (the partition numbers)" https://oeis.org/A000041; "Partition Function P(n)", stating "gives the number of ways of writing the integer n

Glossary of engineering: M–Z (31,177 words) [view diff] no match in snippet view article find links to article

based in statistical thermodynamics, the latter of which provides the partition function of the system and allows thermodynamic functions to be specified.

Grand canonical ensemble (5,285 words) [view diff] no match in snippet view article find links to article

grand potential) may be restated in terms of the grand partition function by simple mathematical manipulations. The grand canonical ensemble is the ensemble

Martin H. Krieger (1,858 words) [view diff] no match in snippet view article find links to article

Mathematical Physics: Structure, Tricks, and Lacunae in Derivations of the Partition Function of the Two-Dimensional Ising Model and in Proofs of The Stability

Quantum vacuum state (2,755 words) [view diff] no match in snippet view article find links to article

23) C: Canonical commutation relations". Encyclopedic dictionary of mathematics (2nd ed.). MIT Press. p. 1303. ISBN 978-0-262-59020-4. Paul Busch; Marian

Bargmann–Wigner equations (2,501 words) [view diff] no match in snippet view article find links to article

1⁄2, 3⁄2, 5⁄2 ...). The solutions to the equations are wavefunctions, mathematically in the form of multi-component spinor fields. They are named after Valentine

Fundamental thermodynamic relation (2,676 words) [view diff] no match in snippet view article find links to article

{\textstyle \Pr(i)\propto f(E_{i},T)} . The normalization factor (partition function) is therefore Z = ∑ i f ( E i , T ) . {\displaystyle Z=\sum _{i}f(E_{i}

Theta function (14,667 words) [view diff] no match in snippet view article find links to article

"Partition Function P". Eric W. Weisstein (2022-03-11). "Partition Function Q". Abramowitz, Milton; Stegun, Irene A. (1964). Handbook of Mathematical Functions

Von Neumann entropy (5,061 words) [view diff] no match in snippet view article find links to article

k B {\displaystyle k_{B}} is the Boltzmann constant, and Z is the partition function. The von Neumann entropy of a Gibbs state is, up to a factor k B {\displaystyle

Mathematical formulation of the Standard Model (7,734 words) [view diff] no match in snippet view article find links to article

This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the

Tsung-Dao Lee (2,161 words) [view diff] no match in snippet view article find links to article

value Feynman diagram Lattice field theory LSZ reduction formula Partition function Path Integral Formulation Propagator Quantization Regularization Renormalization

Particle physics (4,287 words) [view diff] no match in snippet view article find links to article

particle physics attempts to develop the models, theoretical framework, and mathematical tools to understand current experiments and make predictions for future

Nested sampling algorithm (2,266 words) [view diff] no match in snippet view article find links to article

used in the field of materials modeling. It can be used to learn the partition function from statistical mechanics and derive thermodynamic properties. Dynamic

Coherent state (7,370 words) [view diff] no match in snippet view article find links to article

} , and β = 1 / ( k B T ) {\displaystyle \beta =1/(k_{B}T)} . The partition function is equal to Z = tr { e − ℏ β ω a † a } = ∑ n = 0 ∞ e − n β ℏ ω = 1

Nucleic acid structure prediction (3,715 words) [view diff] no match in snippet view article find links to article

PMC 514697. PMID 15294028. McCaskill JS (1990). "The equilibrium partition function and base pair binding probabilities for RNA secondary structure".

Wilcoxon signed-rank test (6,443 words) [view diff] no match in snippet view article find links to article

function u n {\displaystyle u_{n}} is closely related to the integer partition function. If p n ( t + ) {\displaystyle p_{n}(t^{+})} is the probability that

Radial distribution function (4,541 words) [view diff] no match in snippet view article find links to article

\mathbf {r} _{N})=\sum _{i=1}^{N}U_{1}(\mathbf {r} _{i})} , then the partition function factorizes, and the probability of an elementary configuration decomposes

Casimir effect (8,099 words) [view diff] no match in snippet view article find links to article

French naval analogy.) Downling, J. P. (1989). "The Mathematics of the Casimir Effect". Mathematics Magazine. 62 (5): 324–331. doi:10.1080/0025570X.1989

Laplace's method (7,181 words) [view diff] no match in snippet view article find links to article

2019 by D. Makogon and C. Morais Smith primarily in the context of partition function evaluation for a system of interacting fermions. For complex integrals

Quantum field theory (14,903 words) [view diff] no match in snippet view article find links to article

without mutual contact".: 4 It was not until the 18th century that mathematical physicists discovered a convenient description of gravity based on fields—a

Second law of thermodynamics (15,472 words) [view diff] no match in snippet view article find links to article

sum of all the probabilities to 1, this function is known as the partition function. We now consider an infinitesimal reversible change in the temperature

Yang–Baxter equation (3,340 words) [view diff] no match in snippet view article find links to article

Bibcode:1944PhRv...65..117O. doi:10.1103/PhysRev.65.117. Baxter, R. J. (1972). "Partition function of the Eight-Vertex lattice model". Annals of Physics. 70 (1). Elsevier:

Dynamic programming (9,283 words) [view diff] no match in snippet view article find links to article

"Cooperative phenomena in homopolymers: An alternative formulation of the partition function", Biopolymers, 13 (7): 1511–1512, doi:10.1002/bip.1974.360130719 Gurskiĭ

Fine-structure constant (7,099 words) [view diff] no match in snippet view article find links to article

of Mathematics. Vol. 2. Simon & Schuster. pp. 1074–1093. Whittaker, Edmund (1945). "Eddington's theory of the constants of nature". The Mathematical Gazette

Functional derivative (5,102 words) [view diff] no match in snippet view article find links to article

particularly useful in calculating the correlation functions from the partition function in quantum field theory. A function can be written in the form of

Canonical quantization (4,736 words) [view diff] no match in snippet view article find links to article

Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158

Propagator (6,183 words) [view diff] no match in snippet view article find links to article

refers to G as well, this article will use the term to refer to K. The mathematics of PDEs and the wave equation, p 32., Michael P. Lamoureux, University

Probabilistic context-free grammar (5,242 words) [view diff] no match in snippet view article find links to article

AAAI Press. pp. 143–153. McCaskill J. S. (1990). "The Equilibrium Partition Function and Base Pair Binding Probabilities for RNA Secondary Structure".

Symmetry in quantum mechanics (7,915 words) [view diff] no match in snippet view article find links to article

quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physics. In general

Introduction to gauge theory (4,360 words) [view diff] no match in snippet view article find links to article

it successfully to electromagnetism. Gauge symmetry was generalized mathematically in 1954 by Chen Ning Yang and Robert Mills in an attempt to describe

Higgs mechanism (6,691 words) [view diff] no match in snippet view article find links to article

the phase of the field from point to point costs very little energy. Mathematically, if ϕ ( x ) = Φ e i θ ( x ) {\displaystyle \ \phi (x)=\Phi e^{i\theta

Planck's law (18,054 words) [view diff] no match in snippet view article find links to article

}{=}}\ {\frac {1}{k_{\mathrm {B} }T}}.} The denominator Z(β), is the partition function of a single mode. It makes Pr properly normalized, and can be evaluated

Tau function (integrable systems) (6,689 words) [view diff] no match in snippet view article

abelian subgroup of the general linear group. It typically arises as a partition function, in the sense of statistical mechanics, many-body quantum mechanics

Frank A. Weinhold (1,956 words) [view diff] no match in snippet view article find links to article

water and other pure substances. QCE predictions are based on a model partition function composed from an equilibrium mixture of molecular clusters {Mn}, each

Zero-point energy (26,815 words) [view diff] no match in snippet view article find links to article

practical calculations zero-point energy is dismissed by fiat in the mathematical model as a term that has no physical effect. Such treatment causes problems

Light front quantization (12,723 words) [view diff] no match in snippet view article find links to article

Develop numerical methods/computer codes to directly evaluate the partition function (viz. thermodynamic potential) as the basic thermodynamic quantity