Related papers: The Canonical Partition Function for Quons
We address problems arising in supersaturated systems of small atomic particles in solids. Nucleation processes in such systems do not seem to follow the classical interpretation but may be indicative of quantal nucleation partucularly at…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary…
A new kind of quantum statistics which interpolates between Bose and Fermi statistics is proposed beginning with the assumption that the quantum state of a many-particle system is a functional on the internal space of the particles. The…
In this paper we present a method to obtain a possible self-adjoint Hamiltonian operator so its energies satisfy Z(1/2+iE_n)=0, which is an statement equivalent to Riemann Hypothesis, first we use the explicit formula for the Chebyshev…
The probability distribution of a function of a subsystem conditioned on the value of the function of the whole, in the limit when the ratio of their values goes to zero, has a limit law: It equals the unconditioned marginal probability…
A great many observables seen in intermediate energy heavy ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble (energy and…
It is shown that in adiabatic approximation for nuclei the many-component Coulomb system cannot be described on the basis of the grand canonical ensemble. Using the variational Bogolyubov's procedure for the free energy, the Hohenberg-Kohn…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
We calculate the susceptibility of a canonical ensemble of quantum oscillators to the singular random metric. If the covariance of the metric is $\vert {\bf x}-{\bf x}^{\prime}\vert^{-4\alpha}$ $0< \alpha<\frac{1}{2}$ then the expansion of…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
Quantum thermodynamics can be cast as a resource theory by considering free access to a heat bath, thereby viewing the Gibbs state at a fixed temperature as a free state and hence any other state as a resource. Here, we consider a…
We suggest the existence of systems in which the statistics of a particle changes with the quantum level it occupies. The occupation numbers in thermal equilibrium depend on a continuous statistical parameter that interpolates between…
An equation of state for an ideal gas with a small number of particles is studied. The resulting equation is found to differ from that expected in conventional thermodynamics, which is strikingly illustrated when considering the traditional…
We summarize recent results on positive temperature equilibrium states of large bosonic systems. The emphasis will be on the connection between bosonic grand-canonical thermal states and the (semi-) classical Gibbs measures on one-body…
The quantum Maxwell theory at finite temperature at equilibrium is studied on compact and closed manifolds in both the functional integral- and Hamiltonian formalism. The aim is to shed some light onto the interrelation between the topology…
We discuss the quantum statistical fluctuations of energy in subsystems of hot relativistic gas for both spin-zero and spin half particles. We explicitly show the system size dependence of the quantum statistical fluctuation of energy. Our…
Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for…
We calculate the baryon chemical potential ($\mu_B$) dependence of thermodynamic observables, i.e., pressure, baryon number density and susceptibility by lattice QCD using the canonical approach. We compare the results with those by the…
The quantum partition function for dissolving Abelian Higgs vortices is calculated explicitly, using spectral data for the Beltrami Laplacian on the $N$-vortex moduli space $\mathbb{CP}^N$ with a scaled Fubini--Study metric. From the…