Related papers: Coordinates in the relativistic Boltzmann theory
Collective coordinates provide a powerful tool for separating collective and elementary excitations, allowing both to be treated in the full quantum theory. The price is a canonical transformation which leads to a complicated starting point…
We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for…
Starting with the relativistic Boltzmann equation where the collision term was generalized to include gradients of the phase-space distribution function, we recently presented a new derivation of the equations for the relativistic…
We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no…
In this paper we solve the Boltzmann transport equation using AI libraries. The reason why this is attractive is because it enables one to use the highly optimised software within AI libraries, enabling one to run on different computer…
We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical…
We consider the numbers arising in the problem of normal ordering of expressions in canonical boson creation and annihilation operators. We treat a general form of a boson string which is shown to be associated with generalizations of…
In this paper, first we give the notion of a representation of a relative Rota-Baxter Lie algebra and introduce the cohomologies of a relative Rota-Baxter Lie algebra with coefficients in a representation. Then we classify abelian…
A great number of problems of relativistic position in quantum mechanics are due to the use of coordinates which are not inherent objects of spacetime, cause unnecessary complications and can lead to misconceptions. We apply a…
A general iterative method proposed some years ago for the description of relativistic collapse, is presented here in comoving coordinates. For doing that we redefine the basic concepts required for the implementation of the method for…
Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three…
We connect two different generalizations of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities…