Related papers: Statistics and Nos\'e formalism for Ehrenfest dyna…
We consider the dynamics of interacting quantum and classical systems in the Heisenberg representation. Unlike the usual construction in standard quantum mechanics, mixed quantum-classical systems involve the interplay of unitary operators…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
Following Ehrenfest's approach, the problem of quantum-classical correspondence can be treated in the class of trajectory-coherent functions that approximate as $\h\to 0$ a quantum-mechanical state. This idea leads to a family of systems of…
The dynamical evolution of squeezing correlations in an ultracold Bose-Einstein distributed across two modes is investigated theoretically in the framework of the Bose-Hubbard model. It is shown that the eigenstates of the Hamiltonian do…
We discuss a generalization of the Ehrenfest theorem to the recently proposed precanonical quantization of vielbein gravity which proceeds from a space-time symmetric generalization of the Hamiltonian formalism to field theory. Classical…
Mixed quantum-classical spin systems have been proposed in spin chain theory and, more recently, in magnon spintronics. However, current models of quantum-classical dynamics beyond mean-field approximations typically suffer from…
Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…
A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…
The Ehrenfest urn process, also known as the dogs and fleas model, is realistically simulated by molecular dynamics of the Lennard-Jones fluid. The key variable is Delta z, i.e. the absolute value of the difference between the number of…
We study the semiclassical Ehrenfest trajectories in open quantum systems. We first derive in explicit form the Fokker-Planck equation that governs the time evolution of the mixing measure for a Gaussian mixture. Then, we embed the…
We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in…
Ehrenfest urns with interaction that are connected in a ring is considered as a paradigm model for non-equilibrium thermodynamics and is shown to exhibit two distinct non-equilibrium steady states (NESS) of uniform and non-uniform particle…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
By examining both the divergence of the velocity vector in orthogonal Cartesian coordinate space $\mathbf{\Gamma} $ of dimension $\R^{\textrm {2fN}}$ and the structure of the Hamiltonian determining a system trajectory, it is shown that the…
Newtonian and Scrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
The symplectic structure of quantum commutators is first unveiled and then exploited to introduce generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantum-classical systems are described by a…
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
In this paper we presented an overview on our works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type's…
The correspondence principle is investigated in the framework of deterministic predictions for individual systems. Exact analytical results are obtained for the quantum and the Liouvillian dynamics of a nonlinear oscillator coupled to a…