Related papers: Dynamical Semigroups for Unbounded Repeated Pertur…
Hyperbolic partial differential equations on a one-dimensional spatial domain are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of non-homogeneous transmission lines. The…
A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature $T>0$. We show that for fixed, small values of the coupling constant $\lambda$, the true reduced dynamics of the system is…
A subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is…
It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of…
Despite considerable progress during the last decades in devising a semiclassical theory for classically chaotic quantum systems a quantitative semiclassical understanding of their dynamics at late times (beyond the so-called Heisenberg…
This is a continuation of the study of the theory of quantum stochastic dilation of completely positive semigroups on a von Neumann or $C^*$ algebra, here with unbounded generators. The additional assumption of symmetry with respect to a…
Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on…
In this paper, we study Random Dynamical Systems (RDSs) of homeomorphisms on the circle without a finite orbit. We characterize the topological dynamics of the associated semigroup by identifying the existence of invariant sets which are…
A simple collision model is employed to introduce elementary concepts of open system dynamics of quantum systems. In particular, within the framework of collision models we introduce the quantum analogue of thermalization process called…
Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the Fractional Quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich…
We introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we…
We study the geometry and dynamics of discrete subgroups $\Gamma$ of $\PSL(3,\mathbb{C})$ with an open invariant set $\Omega \subset \PC^2$ where the action is properly discontinuous and the quotient $\Omega/\Gamma$ contains a connected…
Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups…
We investigate the stability properties of strongly continuous semigroups generated by operators of the form $A-BB^\ast$, where $A$ is a generator of a contraction semigroup and $B$ is a possibly unbounded operator. Such systems arise…
We study the nonlinear, semiclassical dynamics of an open spin-1 (three-level) variant of the traditional Dicke model. In particular, we focus on V-type energy-level configurations with varying degrees of energy-level asymmetry. We also…
The Lindblad equation embodies a fundamental paradigm of the quantum theory of open systems, and the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generation theorem says precisely which superoperators can appear on its right-hand side.…
We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments - one a continuous bosonic environment leading to a unitary system-environment evolution…
We obtain slow dynamics for self-adjoint semigroups and unitary evolution groups. For semigroups, the slow dynamics is for orbits, and for the average return probability in the case of unitary evolution groups. We present an application to…
We introduce a class of quantum Markov semigroups describing the evolution of interacting quantum lattice systems, specified either as generic qudits or as fermions. The corresponding generators, which include both conservative and…
In this paper, we construct a semigroup associated to an action of countable discrete group on a compact Hausdorff space, that can be regarded as a higher dimensional generalization of the type semigroup. Using this generalized type…