Related papers: Generalized Invariants and Quantum Evolution of Op…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
According to standard quantum theory, the time evolution operator of a quantum system is independent of the state of the system. One can, however, consider systems in which this is not the case: the evolution operator may depend on the…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…
The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and…
We consider stochastic and open quantum systems with a finite number of states, where a stochastic transition between two specific states is monitored by a detector. The long-time counting statistics of the observed realizations of the…
We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the…
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
We describe fermions in terms of a classical statistical ensemble. The states $\tau$ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability…
We use the free evolution propagator to determine the quantum probability representation (i.e., the general expression of the tomogram) of any one-dimensional system described by a density state. The evolution operator for the considered…
We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a…
In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another…
We consider the quantum evolution of a fermion-hole pair in a d-dimensional gas of non-interacting fermions in the presence of random phase scattering. This system is mapped onto an effective Ising model, which enables us to show rigorously…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
Dynamical Lie-algebraic method for the construction of local quantum invariants of motion in non-integrable many-body systems is proposed and applied to a simple but generic toy model, namely an infinite kicked $t-V$ chain of spinless…
The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the…
The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches. Starting from the appropriate…
We show that generalizations of classical and quantum dynamics with two times lead to fundamentally constrained evolution. At the level of classical physics, Newton's second law is extended and exactly integrated in $1+2$ dimensional space,…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators.With a time-dependent metric, the pseudo-Hermitian invariant operator is…
We introduce a `proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical…