Related papers: Interrelations between different canonical descrip…

Over recent years, a lot of progress has been achieved in understanding of the relationship between localization and transport of energy in essentially nonlinear oscillatory systems. In this paper we are going to demonstrate that the…

The von Neumann entropy of various quantum dissipative models is calculated in order to discuss the entanglement properties of these systems. First, integrable quantum dissipative models are discussed, i.e., the quantum Brownian motion and…

A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…

A typical linear open system is often defined as a component of a larger conservative one. For instance, a dielectric medium, defined by its frequency dependent electric permittivity and magnetic permeability is a part of a conservative…

The energy and time variables of the elementary classical dynamical systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group…

In this work, we develop a mathematical framework to model a quantum system whose Hamiltonian may depend on the state of changing environment, that evolves according to a Markovian process. When the environment changes its state, the…

The Hamilton principle is a variation principle describing the isolated and conservative systems, its Lagrange function is the difference between kinetic energy and potential energy. By Feynman path integration, we can obtain the Hermitian…

Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

Estimation of physical parameters is a must in almost any part of science and technology. The enhancement of the performances in this task, e.g., beating the standard classical shot-noise limit, using available physical resources is a major…

We examine two exactly solvable models of decoherence -- a central spin-system, (i) with and (ii) without a self--Hamiltonian, interacting with a collection of environment spins. In the absence of a self--Hamiltonian we show that in this…

We generalize the oscillator model of a particle interacting with a thermal reservoir by introducing arbitrary nonlinear couplings in the particle coordinates.The equilibrium positions of the heat bath oscillators are promoted to space-time…

The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…

We consider the case when decoherence is due to the fluctuations of some classical variable or parameter of a system and not to its entanglement with the environment. Under few and quite general assumptions, we derive a model-independent…

Macroscopic field quantization is presented for a nondispersive photonic dielectric environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivatives shows…

Using numerically exact diagonalization, we study the correlated Haldane-Hubbard model in the presence of dissipation. Such dissipation can be modeled at short times by the dynamics governed by an effective non-Hermitian Hamiltonian, of…

A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of…

The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex…

We quantify the total, quantum, and classical correlations with entropic measures, and quantitatively compare these correlations in a quantum system, as exemplified by a Heisenberg dimer which is subjected to the change of environmental…