Related papers: Properties of Tensor Hermite Polynomials
We present a formula for thermal transport in the bulk of Bose systems based on the quantum Boltzmann equation (QBE). First, starting from the quantum kinetic equation and using the Born approximation for impurity scattering, we derive the…
In previous work we provided the explicit form of the nonlinear PDEs, subjected to the appropriate boundary conditions, which have to be satisfied by transport coefficients for systems out of Onsager's region. Since the proposed PDEs are…
The electronic and transport properties of the half-Heusler compound LaPtSb are investigated by performing first-principles calculations combined with semi-classical Boltzmann theory and deformation potential theory. Compared with many…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
We construct a new class of charged rotating solutions of $(n+1)$-dimensional Einstein-Born-Infeld gravity with cylindrical or toroidal horizons in the presence of cosmological constant and investigate their properties. These solutions are…
Orthogonal polynomials with respect to the hypergeometric distribution on lattices in polyhedral domains in ${\mathbb R}^d$, which include hexagons in ${\mathbb R}^2$ and truncated tetrahedrons in ${\mathbb R}^3$, are defined and studied.…
We study black-hole thermodynamics in theories that contain dimensionful constants such as the cosmological constant or coupling constants in Wald's formalism. The most natural way to deal with these constants is to promote them to scalar…
We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Pad\'e table. We give some properties of…
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…
The q-Hermite I-Sobolev type polynomials of higher order are consider for their study. Their hypergeometric representation is provided together with further useful properties such as several structure relations which give rise to a…
One considers the motion of a test particle in an homogeneous fluid in equilibrium at temperature $T$, undergoing dissipative collisions with the fluid particles. It is shown that the corresponding linear Boltzmann equation still posseses a…
Finite-temperature calculations are relevant for rationalizing material properties yet they are computationally expensive because large system sizes or long simulation times are typically required. Circumventing the need for performing many…
A classical result from 1861 due to Hermite says that every separable equation of degree 5 can be transformed into an equation of the form x^5 + b x^3 + c x + d = 0. Later this was generalized to equations of degree 6 by Joubert. We show…
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…
Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…
Rosseland equation is one of the most popular models of the conduction-radiation coupled heat transfer in the thermal protection system. The well-posedness, the corresponding mathematical theory and the Multi-scale analysis method for the…
We study heat conduction in a one-dimensional chain of particles with longitudinal as well as transverse motions. The particles are connected by two-dimensional harmonic springs together with bending angle interactions. Using equilibrium…
We study a Brownian Carnot cycle introduced by T. Schmiedl and U. Seifert [Europhys. Lett. \textbf{81}, 20003 (2008)] from a viewpoint of the linear irreversible thermodynamics. By considering the entropy production rate of this cycle, we…
In this paper, we show generation and propagation of polynomial and exponential moments, as well as global well-posedness of the homogeneous binary-ternary Boltzmann equation. We also show that the co-existence of binary and ternary…