Related papers: Canonical quantization of nonlinear many body syst…
An analysis of the Dicke model, N two-level atoms interacting with a single radiation mode, is done using the Holstein-Primakoff transformation. The main aim of the paper is to show that, changing the quantization axis with respect to the…
We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked…
We develop a framework for identifying nonclassical speedups in systems with polarization, likewise spin degrees of freedom. By confining the dynamics to the manifold of angular momentum coherent states, which act as the classical reference…
We consider the Nelson model which describes a quantum system of nonrelativistic identical particles coupled to a possibly massless scalar Bose field through a Yukawa type interaction. We study the limiting behaviour of that model in a…
In this paper, we study a general class of inhomogeneous kinetic models that unifies fundamental models in both the statistical physics of particles and of waves, namely the kinetic Boltzmann equations and the kinetic wave equations, in…
In this article we present a full description of the quantum Kerr Ising model---a linear optical network of parametrically pumped Kerr non-linearities. We consider the non-dissapative Kerr Ising model and, using variational techniques, show…
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…
Canonical quantization has served wonderfully for the quantization of a vast number of classical systems. That includes single classical variables, such as $p$ and $q$, and numerous classical Hamiltonians $H(p,q)$, as well as field…
We study the quantum mechanics of the derivative nonlinear Schrodinger equation which has appeared in many areas of physics and is known to be classically integrable. We find that the N-body quantum problem is exactly solvable with both…
For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…
Identical particle correlations at fixed multiplicity are considered by means of quantum canonical ensemble of finite systems. We calculate one-particle momentum spectra and two-particle Bose-Einstein correlation functions in the ideal gas…
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
In the present effort we consider the most general non linear particle kinetics within the framework of the Fokker-Planck picture. We show that the kinetics imposes the form of the generalized entropy and subsequently we demonstrate the…
A generalized canonical form of multi-time dynamical theories is proposed. This form is a starting point for a modified canonical quantization procedure of theories based on a quantum version of the action principle. As an example, the…
For classical discrete systems under constant composition (specifically substitutional alloys), canonical average acts as a map from a set of many-body interatomic interactions to a set of configuration in thermodynamic equilibrium, which…
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…
In this paper we achieve the quantization of a particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using group-theoretical methods. For this purpose, a fundamental role is played by contact,…
A mathematically well-defined, manifestly covariant theory of classical and quantum field is given, based on Euclidean Poisson algebras and a generalization of the Ehrenfest equation, which implies the stationary action principle. The…
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is…