Related papers: Asymptotics of partition functions in a fermionic …
We study a model of quantum mechanical fermions with matrix-like index structure (with indices $N$ and $L$) and quartic interactions, recently introduced by Anninos and Silva. We compute the partition function exactly with $q$-deformed…
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…
With a view towards higher-spin applications, we study the partition function of a free complex fermion in 2d CFT, restricted to the neutral (zero fermion number) sector. This restriction leads to a partial theta function with a…
We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…
We consider the asymptotics of the partition function of the extended Gross-Witten-Wadia unitary matrix model by introducing an extra logarithmic term in the potential. The partition function can be written as a Toeplitz determinant with…
We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…
We obtain large N asymptotics for the Hermitian random matrix partition function \[Z_N(V)=\int_{\mathbb R^N}\prod_{i<j}(x_i-x_j)^2 \prod_{j=1}^N e^{-N V(x_j)}dx_j,\] in the case where the external potential $V$ is a polynomials such that…
We explore systems with a large number of fermionic degrees of freedom subject to non-local interactions. We study both vector and matrix-like models with quartic interactions. The exact thermal partition function is expressed in terms of…
Andrews-Dyson-Hickerson, Cohen build a striking relation between q-hypergeometric series, real quadratic fields, and Maass forms. Thanks to the works of Lewis-Zagier and Zwegers we have a complete understanding on the part of these…
In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various…
The eigenstate thermalization hypothesis provides to date the most successful description of thermalization in isolated quantum systems by conjecturing statistical properties of matrix elements of typical operators in the (quasi-)energy…
We offer new Tauberian theorems for a generalized partition function as our main result. Our analysis provides insight into asymptotic behavior of power series with arithmetic functions as coefficients.
We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to…
We consider equilibrium level occupation numbers in a Fermi gas with a fixed number of particles, n, and finite level spacing. Using the method of generating functions and the cumulant expansion we derive a recurrence relation for canonical…
We give asymptotic analysis of power series associated with lacunary partition functions. New partition theoretic interpretations of some basic hypergeometric series are offered as examples.
This paper investigates the thermodynamics of a large class of non-Hermitian, $PT$-symmetric oscillators, whose energy spectrum is entirely real. The spectrum is estimated by second-order WKB approximation, which turns out to be very…
We derive the dominant asymptotic form and the order of the correction terms of the finite-perimeter partition function of self-avoiding polygons on the square lattice, which are weighted according to their area A as q^A, in the inflated…
Let $f \in \mathbb{Z}[y]$ be a polynomial such that $f(\mathbb{N}) \subseteq \mathbb{N}$, and let $p_{\mathcal{A}_{f}}(n)$ denote number of partitions of $n$ whose parts lie in the set $\mathcal{A}_f:=\{f(n):n \in \mathbb{N}\}$. Under…
In this work, we present a compact analytical approximation for the quantum partition function of systems composed of quantum oscillators. The proposed formula is general and applicable to an arbitrary number of oscillators described by a…
We establish Tracy-Widom asymptotics for the partition function of a random polymer model with gamma-distributed weights recently introduced by Sepp\"al\"ainen. We show that the partition function of this random polymer can be represented…