13,983 research outputs found
Open Quantum Systems. An Introduction
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 methods traditionally employed by different communities. We
present in some detail the mathematical structure and the general properties of
the dynamical maps underlying open system dynamics. We also discuss the
microscopic derivation of dynamical equations, including both Markovian and
non-Markovian evolutions.Comment: 100 pages, 3 figures. Updated version with typos corrected. Preprint
version of the published boo
Current in open quantum systems
We show that a dissipative current component is present in the dynamics
generated by a Liouville-master equation, in addition to the usual component
associated with Hamiltonian evolution. The dissipative component originates
from coarse graining in time, implicit in a master equation, and needs to be
included to preserve current continuity. We derive an explicit expression for
the dissipative current in the context of the Markov approximation. Finally, we
illustrate our approach with a simple numerical example, in which a quantum
particle is coupled to a harmonic phonon bath and dissipation is described by
the Pauli master equation.Comment: To appear in Phys. Rev. Let
Resonances in open quantum systems
The Hamilton operator of an open quantum system is non-Hermitian. Its
eigenvalues are, generally, complex and provide not only the energies but also
the lifetimes of the states of the system. The states may couple via the common
environment of scattering wavefunctions into which the system is embedded. This
causes an {\it external mixing} (EM) of the states. Mathematically, EM is
related to the existence of singular (the so-called exceptional) points (EPs).
The eigenfunctions of a non-Hermitian operator are biorthogonal, in contrast to
the orthogonal eigenfunctions of a Hermitian operator. A quantitative measure
for the ratio between biorthogonality and orthogonality is the phase rigidity
of the wavefunctions. At and near an EP, the phase rigidity takes its minimum
value. The lifetimes of two nearby eigenstates of a quantum system bifurcate
under the influence of an EP. At the parameter value of maximum width
bifurcation, the phase rigidity approaches the value one, meaning that the two
eigenfunctions become orthogonal. However, the eigenfunctions are externally
mixed at this parameter value. The S-matrix and therewith the cross section do
contain, in the one-channel case, almost no information on the EM of the
states. The situation is completely different in the case with two (or more)
channels where the resonance structure is strongly influenced by the EM of the
states and interesting features of non-Hermitian quantum physics are revealed.
We provide numerical results for two and three nearby eigenstates of a
non-Hermitian Hamilton operator which are embedded in one common continuum and
influenced by two adjoining EPs. The results are discussed. They are of
interest for an experimental test of the non-Hermitian quantum physics as well
as for applications.Comment: Title of the paper is changed. The Introduction is broaden. The
difference of the non-Hermitian formalism for the description of open quantum
systems in our paper to the description of PT-symmetric systems is
underlined. Paper published: Phys.Rev.A 95, 022117 (2017
Scarring in open quantum systems
We study scarring phenomena in open quantum systems. We show numerical
evidence that individual resonance eigenstates of an open quantum system
present localization around unstable short periodic orbits in a similar way as
their closed counterparts. The structure of eigenfunctions around these
classical objects is not destroyed by the opening. This is exposed in a
paradigmatic system of quantum chaos, the cat map.Comment: 4 pages, 4 figure
Localization in open quantum systems
In an isolated single-particle quantum system a spatial disorder can induce
Anderson localization. Being a result of interference, this phenomenon is
expected to be fragile in the face of dissipation. Here we show that
dissipation can drive a disordered system into a steady state with tunable
localization properties. This can be achieved with a set of identical
dissipative operators, each one acting non-trivially only on a pair of
neighboring sites. Operators are parametrized by a uniform phase, which
controls selection of Anderson modes contributing to the state. On the
microscopic level, quantum trajectories of a system in a localized steady
regime exhibit intermittent dynamics consisting of long-time sticking events
near selected modes interrupted by jumps between them.Comment: 5 pages, 5 figure
Dynamics of open quantum systems
The coupling between the states of a system and the continuum into which it
is embedded, induces correlations that are especially large in the short time
scale. These correlations cannot be calculated by using a statistical or
perturbational approach. They are, however, involved in an approach describing
structure and reaction aspects in a unified manner. Such a model is the SMEC
(shell model embedded in the continuum). Some characteristic results obtained
from SMEC as well as some aspects of the correlations induced by the coupling
to the continuum are discussed.Comment: 16 pages, 5 figure
Pure Stationary States of Open Quantum Systems
Using Liouville space and superoperator formalism we consider pure stationary
states of open and dissipative quantum systems. We discuss stationary states of
open quantum systems, which coincide with stationary states of closed quantum
systems. Open quantum systems with pure stationary states of linear oscillator
are suggested. We consider stationary states for the Lindblad equation. We
discuss bifurcations of pure stationary states for open quantum systems which
are quantum analogs of classical dynamical bifurcations.Comment: 7p., REVTeX
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