Related papers: Properties of Tensor Hermite Polynomials
The statistical mechanics of a two dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby…
This work extends the seminal work of Gottfried on the two-body quantum physics of particles interacting through a delta-shell potential to many-body physics by studying a system of non-relativistic particles when the thermal De-Broglie…
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…
We introduce the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system under consideration is a Lorentz gas with fixed…
The Ehrhart polynomial and the reciprocity theorems by Ehrhart \& Macdonald are extended to tensor valuations on lattice polytopes. A complete classification is established of tensor valuations of rank up to eight that are equivariant with…
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium. Two time…
In order to describe a nonuniform equilibrium mixture with an interface between two coexisting phases it is necessary to consider contributions to the Helmholtz energy which depend on the gradients of for instance the density. Van der Waals…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
We find a near detailed balance solution to the relativistic Boltzmann equation under the relaxation time approximation with a collision term which differs from the Anderson-Witting model and is dependent on the stationary observer. Using…
We present a tensor-decomposition method to solve the Boltzmann transport equation (BTE) in the Bhatnagar-Gross-Krook approximation. The method represents the six-dimensional BTE as a set of six one-dimensional problems, which are solved…
A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal…
Transport phenomena-describing the movement of particles, energy, or other physical quantities-are fundamental in various scientific disciplines, including nuclear physics, plasma physics, astrophysics, engineering, and the natural…
It is well-known that two-dimensional Coulomb gases at a special inverse temperature $\beta = 2$ can be analyzed by using the orthogonal polynomial method borrowed from the theory of random matrices. In this paper, such Coulomb gas…
The relation between thermal transport and gravity was highlighted in the seminal work by Luttinger in 1964, and has been extensively developed to understand thermal transport, most notably the thermal Hall effect. Here we review the novel…
The paper considers a coupled system of linear Boltzmann transport equations (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in…
In condensed matter physics, transport measurements are essential not only for the characterization of materials, but also to discern between quantum phases and identify new ones. The extension of these measurements into atomic quantum…
A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of…
Consistent descriptions of the equation of states, and information about transport coefficients of deuterium-tritium mixture are demonstrated through quantum molecular dynamic (QMD) simulations (up to a density of 600 g/cm$^{3}$ and a…
We present a more refined version of rational extended thermodynamics of rarefied polyatomic gases in which molecular rotational and vibrational relaxation processes are treated individually. In this case we need a triple hierarchy of the…
The geometric theory of additive separation of variables is applied to the search for multiplicative separated solutions of the bi-Helmholtz equation. It is shown that the equation does not admit regular separation in any coordinate system…