Related papers: Eigenvalue statistics in quantum ideal gases
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large…
Recently is was shown that the imaginary part of the canonical partition function of Schwarzschild black holes with an energy spectrum E_n = \sigma \sqrt{n} E_P, n= 1,2, ..., has properties which - naively interpreted - leads to the…
We study a one-dimensional gas of $N$ Brownian particles that diffuse independently but are simultaneously reset whenever any of them reaches a fixed threshold located at $L > 0$. For any $N > 2$, the system reaches a non-equilibrium…
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…
We study the classical and quantum mechanics of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. The quasi-energy spectral properties of the model are obtained from…
We give a method for obtaining states of massive particle representations of the two-parameter deformation of the Poincar\'e algebra proposed in q-alg/9601010, q-alg/9505030 and q-alg/9501026. We discuss four procedures to generate…
Eigenstates in finite systems such as nuclei, atoms, atomic clusters and quantum dots with few excited particles are chaotic superpositions of shell model basis states. We study criterion for the equilibrium distribution of basis components…
Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a…
Consider a bound state (an eigenfunction) $\psi$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $\gamma$ and of the one-particle kinetic energy density matrix $\tau$ associated with $\psi$. The paper…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
The explicit solution to the spectral problem of quantum graphs is used to obtain the exact distributions of several spectral statistics, such as the oscillations of the quantum momentum eigenvalues around the average, $\delta…
In this paper we find a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules, composing an ideal gas. In such a gas, the motion of each individual molecule can be considered…
Analytic expressions for the energy eigenvalues and eigenfunctions of a one-dimensional harmonic crystal are obtained. The average energy and density profiles are obtained numerically as a function of temperature. A surprisingly large…
An equilibrium theory of classical fluids based on the space distribution among the particles is derived in the framework of the energy minimization method. This study is motivated by current difficulties of evaluation of optical properties…
The fluctuations in the ideal quantum gases are studied using the strongly intensive measures $\Delta[A,B]$ and $\Sigma[A,B]$ defined in terms of two extensive quantities $A$ and $B$. In the present paper, these extensive quantities are…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…
I discuss ideal and interacting quantum gases obeying general fractional exclusion statistics. For systems with constant density of single-particle states, described in the mean field approximation, the entropy depends neither on the…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…