相关论文: From Random Matrix Theory to Statistical Mechanics…
The one-body density matrix (OBDM) of a strongly interacting spinor quantum gas in one dimension can be written as a summation of products of spatial and spin parts. We find that there is a remarkable connection between the spatial part and…
The statistical mechanics of an anyon gas in a magnetic field is addressed. An harmonic regulator is used to define a proper thermodynamic limit. When the magnetic field is sufficiently strong, only exact $N$-anyon groundstates, where…
Recent measurements on 2d materials tuning between fractional quantum anomalous Hall phases and a plethora of correlated electronic states call for a detailed understanding of the dynamics of anyons. Here we develop a general theory of the…
Using the exact $N$-particle ground state wave function for a one-dimensional gas of hard-core bosons in a harmonic trap we develop an algorithm to compute the reduced single-particle density matrix and corresponding momentum distribution.…
We investigate the strongly interacting hard-core anyon gases in a one dimensional harmonic potential at finite temperature by extending thermal Bose-Fermi mapping method to thermal anyon-ferimon mapping method. With thermal anyon-fermion…
The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied…
The equilibrium distribution function of a relativistic ideal gas has been derived to include the effect of angular momentum. The result agrees with the one obtained from kinetic theory, and consistent with relativistic thermodynamics. The…
The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal…
We analyze the quantum mechanics of anyons on the sphere in the presence of a constant magnetic field. We introduce an operator method for diagonalizing the Hamiltonian and derive a set of exact anyon energy eigenstates, in partial…
We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy…
The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an…
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…
In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two…
Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…