Related papers: Numerical Approximation to the Thermodynamic Integ…
In this article, we would like to pay tribute to Gabor Kalman, outlining his contribution to a model widely used in dense plasma physics: the high-temperature Thomas-Fermi model. The approach of Ruoxian Ying and Kalman relies on the…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
We recently derived the Hamiltonian of fermionic composites by an exact procedure of bosonization. In the present paper expand this Hamiltonian in the inverse of the number of fermionic states in the composite wave function and give the…
This report presents the application of polynomial regression for estimating free energy differences using thermodynamic integration. We employ linear regression to construct a polynomial that optimally fits the thermodynamic integration…
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…
The knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic ``perturbative'' equation of state of a homogeneous ultracold gas we make predictions…
The partition function and free energy of a quantum many-body system determine its physical properties in thermal equilibrium. Here we study the computational complexity of approximating these quantities for $n$-qubit local Hamiltonians.…
Ensuring a satisfactory statistical convergence of anharmonic thermodynamic properties requires sampling of many atomic configurations, however the methods to obtain those necessarily produce correlated samples, thereby reducing the…
We present numerical studies of fermion and boson models with random all-to-all interactions (the SYK models). The high temperature expansion and exact diagonalization of the $N$-site fermion model are used to compute the entropy density:…
The number-theoretical problem of partition of an integer corresponds to $D=2$. This problem obeys the Bose--Eeinstein statistics, where repeated terms are admissible in the partition, and to the Fermi--Dirac statistics, where they are…
We analyze a system of fermions in a one-dimensional harmonic trap with attractive delta-interactions between different fermions species, as an approximate description of experiments involving atomic dimers. We solve the problem of two…
This Thesis concentrates on the analysis of coupled RTA (relaxation time approximation) kinetic equations for bosons and fermions. Bosons are treated as massless particles, while fermions have a finite mass. Using analytic and numerical…
We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the…
An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free…
After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…
Using a field-theoretic approach, we systematically generalize the usual semiclassical approximation for a harmonically trapped ideal Bose gas in such a way that its range of applicability is essentially extended. With this we can…
We investigate the fundamental and practical precision limits of thermometry in bosonic and fermionic environments by coupling an $N$-level probe to them and continuously monitoring it. Our findings show that the ultimate precision limit,…
Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional…
We consider thermodynamics of the excluded volume particles at finite temperature and chemical potential, in the low density approximation. We assume Boltzmann statistics and study the influence of the excluded volume on an ideal gas…