Related papers: Interrelations between different canonical descrip…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
We investigate the competition of coherent and dissipative dynamics in many-body systems at continuous quantum transitions. We consider dissipative mechanisms that can be effectively described by Lindblad equations for the density matrix of…
Information on quantum systems can be obtained only when they are open (or opened) in relation to a certain environment. As a matter of fact, realistic open quantum systems appear in very different shape. We sketch the theoretical…
We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match with that of physical degrees of freedom…
Although conservative Hamiltonian systems with constraints can be formulated in terms of Dirac structures, a more general framework is necessary to cover also dissipative systems such as gradient and metriplectic systems with constraints.…
Dirac's method of classical analogy is employed to incorporate quantum degrees of freedom into modern nonequilibrium thermodynamics. The proposed formulation of dissipative quantum mechanics builds entirely upon the geometric structures…
We investigate a two-level system in resonant contact with a larger environment. The environment typically is in a canonical state with a given temperature initially. Depending on the precise spectral structure of the environment and the…
The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
We address the multiplicity of solutions to the time-energy canonical commutation relation for a given Hamiltonian. Specifically, we consider a particle spatially confined in a potential free interval, where it is known that two distinct…
The model of dynamical noncommutativity is proposed. The system consists of two interrelated parts. The first of them describes the physical degrees of freedom with coordinates q^1, q^2, the second one corresponds to the noncommutativity r…
The exchange of energy between a classical open system and its environment can be analysed for a single run of an experiment using the phase space trajectory of the system. By contrast, in the quantum regime such energy exchange processes…
We consider a particularly simple exactly solvable model for a qubit coupled to sequentially nested environments. The purpose is to exemplify the coherence conserving effect of a central system, that has been reported as a result of…
It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
Using a minimal-coupling-scheme we investigate the quantum Brownian motion of a particle in an anisotropic-dissipative-medium under the influence of an arbitrary potential in both relativistic and non-relativistic regimes. A general quantum…
The state of a thermodynamic system being characterized by its set of extensive variables $q^{i}(i=1,...,n) ,$ we write the associated intensive variables $\gamma_{i},$ the partial derivatives of the entropy $ S(q^{1},...,q^{n}) \equiv…