Related papers: Convergence to equilibrium for many particle syste…
For a quantum system to be captured by a stationary statistical ensemble, as is common in thermodynamics and statistical mechanics, it is necessary that it reaches some apparently stationary state in the first place. In this book chapter,…
A reexamination of the semiclassical approach of the relativistic electron indicates a possible variation of its helicity for electric and magnetic static fields applied along its global motion due to zitterbewegung effects, proportional to…
In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the…
We consider a Hamiltonian describing three quantum particles in dimension one interacting through two-body short-range potentials. We prove that, as a suitable scale parameter in the potential terms goes to zero, such Hamiltonian converges…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy.…
How many particles are necessary to make a quantum system many-body? To answer this question, we take as reference for the many-body limit a quantum system at half-filling and compare its properties with those of a system with $N$…
This paper can be seen as an exercise in how to adapt quantum mechanics from a strict relativistic perspective while being respectful and critical towards the experimental achievements of the contemporary theory. The result is a fully…
This article reviews and extends recent results concerning entanglement and frustration in multipartite systems which have some symmetry with respect to the ordering of the particles. Starting point of the discussion are Bell inequalities:…
We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their…
The low-lying bound states of a microscopic quantum many-body system of $n$ particles and the related physical observables can be worked out in a truncated $n$--particle Hilbert space. We present here a non-perturbative analysis of this…
The paper is devoted to further development of the new approach in equilibrium statistical mechanics the basis of which was worked out in a series of articles by the author. The approach proceeds on the use of a hierarchy of equations for…
Correlated classical and quantum many-particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging…
We derive the approximate solution for the pairing Hamiltonian in the Berggren ensemble of single particle states including bound, resonance and non-resonant scattering states. We show that this solution is reliable in the limit of a weak…
This paper concerns the absolute versus relative motion debate. The Barbour and Bertotti 1982 work may be viewed as an indirectly set up relational formulation of a portion of Newtonian mechanics. I consider further direct formulations of…
We prove a strong/weak stability estimate for the 3D homogeneous Boltzmann equation with moderately soft potentials ($\gamma\in(-1,0)$) using the Wasserstein distance with quadratic cost. This in particular implies the uniqueness in the…
The amount of correlation attainable between the components of a quantum system is constrained if the system is closed. We provide some examples, largely from the field of quantum thermodynamics, where knowing the maximal possible variation…
Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a…
Quantum ergordic theorem for a large class of quantum systems was proved by von Neumann [Z. Phys. {\bf 57}, 30 (1929)] and again by Reimann [Phys. Rev. Lett. {\bf 101}, 190403 (2008)] in a more practical and well-defined form. However, it…
A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion,…