Related papers: Quantum Systems Obeying to Generalized Exclusion-I…
We study the electrodynamics of generic charged particles (bosons, fermions, relativistic or not) constrained to move on an infinite plane. An effective gauge theory in 2+1 dimensional spacetime which describes the real electromagnetic…
A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum…
The dynamics of quantum systems strongly depends on the local structure of the Hamiltonian. For short-range interacting systems, the well-known Lieb-Robinson bound defines the effective light cone with an exponentially small error with…
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
The aim of the article is to develop the stochastic interpretation of quantum mechanics by E. Nelson on the basis of balancing the intra-systemic contradiction (i.e., antisymmetry) between "order" and "chaos". For the set task, it is…
With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…
The celebrated problem of a non-homogeneous sphere rolling over a horizontal plane was proved to be integrable and was reduced to quadratures by Chaplygin. Applying the formalism of variational integrators (discrete Lagrangian systems) with…
We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…
We study the properties of a quantum particle interacting with a one dimensional structure of equidistant scattering centres. We derive an analytical expression for the dispersion relation and for the Bloch functions in the presence of both…
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…
Einstein`s equivalence principle states the complete physical equivalence of a gravitational field and corresponding inertial field in an accelerated reference frame. However, to what extent the equivalence principle remains valid in…
We first survey some open questions concerning stochastic interacting particle systems with open boundaries. Then an asymmetric exclusion process with open boundaries that generalizes the lattice gas model of Katz, Lebowitz, and Spohn (KLS)…
The paper studies the physical-constraints-preserving (PCP) schemes for multi-dimensional special relativistic magnetohydrodynamics with a general equation of state (EOS) on more general meshes. It is an extension of the work [Math. Models…
The ideal CGL plasma equations, including the double adiabatic conservation laws for the parallel ($p_\parallel$) and perpendicular pressure ($p_\perp$), are investigated using a Lagrangian variational principle. An Euler-Poincar\'e…
We describe the Lie group and the group representations associated to the nonlinear Thermodynamic Coordinate Transformations (TCT). The TCT guarantee the validity of the Thermodynamic Covariance Principle (TCP) : {\it The nonlinear closure…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
Transformations performing on the dependent and/or the independent variables are an useful method used to classify PDE in class of equivalence. In this paper we consider a large class of U(1)-invariant nonlinear Schr\"odinger equations…