Related papers: Asymptotics of the partition function for $\beta$-…
We calculate explicitly the variation $\delta T_c$ of the Bose-Einstein condensation temperature $T_c$ induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments,…
It is "conventional wisdom" that the uncertainty of local temperature measurements on equilibrium systems diverges exponentially fast as their temperature $T$ drops to zero. In contrast, some exactly solvable models showcase a more benign…
We study the high temperature (or small inverse temperature $\beta$) expansion of the free energy of double scaled SYK model. We find that this expansion is a convergent series with a finite radius of convergence. It turns out that the…
The Debye-H\"uckel theory describes rigorously the thermal equilibrium of classical Coulomb fluids in the high-temperature $\beta\to 0$ regime ($\beta$ denotes the inverse temperature). It is generally believed that the Debye-H\"uckel…
Although partition functions of finite-size systems are always analytic, and hence have no poles, they can be expressed in many cases as series containing terms with poles. Here we show that such poles can be related to linear branches of…
The partition function and specific heat of a system consisting of a finite number of bosons confined in an external potential are calculated in canonical ensemble. Using the grand partition function as the generating function of the…
We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas…
We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density,…
The circular $\beta$ ensemble for $\beta =1,2$ and 4 corresponds to circular orthogonal, unitary and symplectic ensemble respectively as introduced by Dyson. The statistical state of the eigenvalues is then a determinantal point process…
Conformational transitions of a single macromolecule of finite size $N$ cannot be described within standard thermodynamic framework. Taking as a basis a simple model of homopolymer exhibiting a coil-globule transition, we show that a…
Among the statistical mechanical frameworks able to describe systems in non-equilibrium steady states such as collisionless plasmas, self-gravitating systems and other complex systems, superstatistics have gained recent attention.…
We study the extreme point process associated to the off-diagonal components in the matrix representation of the Gaussian $\beta$-Ensemble and prove its convergence to Poisson point process as $n\to +\infty$ when the inverse temperature…
The author gave the sharp asymptotic behavior of the free energy of $1+1$ dimensional directed polymers in random environment(DPRE) as the inverse temperature $\beta\to 0$ under the assumption that random environment satisfies a certain…
An asymptotic expansions for the grand partition function of ideal Bose gas in the canonical ensemble with arbitrary number of particles is obtained. It is shown that the expressions found are valid in the whole temperature region, the…
We compute the full probability distribution of the moment of inertia $I \propto \sum_{i=1}^N \vec{r}_i^{\,2}$ of a gas of $N$ noninteracting bosons trapped in a harmonic potential $V(r) = (1/2)\, m\, \omega^2 r^2$, in all dimensions and at…
I show that for two inverse temperatures $\beta_1$ and $\beta_2$, the von Neumann entropy $S(\rho_\beta)$ of the Gibbs state $\rho_\beta$ for a given Hamiltonian $H$ satisfies $S(\rho_{\beta_1}) \geq S(\rho_{\beta_2}) \iff \beta_{1} \leq…
Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics…
We develop exact, simple closed form expressions for partition functions associated with relativistic bosons and fermions in odd spatial dimensions. These expressions, valid at high temperature, include the effects of a non-trivial Polyakov…
We consider the probability measure minimizing a free energy functional equal to the sum of a Coulomb interaction, a confinement potential and an entropy term, which arises in the statistical mechanics of Coulomb gases. In the limit where…
We analyze the thermodynamic limit - modeled as the open-trap limit of an isotropic harmonic potential - of an ideal, non-relativistic Bose gas with a special emphasis on the phenomenon of Bose-Einstein condensation. This is accomplished by…