1,525 research outputs found
Entanglement in the classical limit: quantum correlations from classical probabilities
We investigate entanglement for a composite closed system endowed with a
scaling property allowing to keep the dynamics invariant while the effective
Planck constant hbar_eff of the system is varied. Entanglement increases as
hbar_eff goes to 0. Moreover for sufficiently low hbar_eff the evolution of the
quantum correlations, encapsulated for example in the quantum discord, can be
obtained from the mutual information of the corresponding \emph{classical}
system. We show this behavior is due to the local suppression of path
interferences in the interaction that generates the entanglement. This behavior
should be generic for quantum systems in the classical limit.Comment: 10 pages 3 figure
Quantum Chaos and Random Matrix Theory - Some New Results
New insight into the correspondence between Quantum Chaos and Random Matrix
Theory is gained by developing a semiclassical theory for the autocorrelation
function of spectral determinants. We study in particular the unitary operators
which are the quantum versions of area preserving maps. The relevant Random
Matrix ensembles are the Circular ensembles. The resulting semiclassical
expressions depend on the symmetry of the system with respect to time reversal,
and on a classical parameter where U is the classical 1-step
evolution operator. For system without time reversal symmetry, we are able to
reproduce the exact Random Matrix predictions in the limit . For
systems with time reversal symmetry we can reproduce only some of the features
of Random Matrix Theory. For both classes we obtain the leading corrections in
. The semiclassical theory for integrable systems is also developed,
resulting in expressions which reproduce the theory for the Poissonian ensemble
to leading order in the semiclassical limit.Comment: LaTeX, 16 pages, to appear in a special issue of Physica D with the
proceedings of the workshop on "Physics and Dynamics Between Chaos, Order,
and Noise", Berlin, 199
Is efficiency of classical simulations of quantum dynamics related to integrability?
Efficiency of time-evolution of quantum observables, and thermal states of
quenched hamiltonians, is studied using time-dependent density matrix
renormalization group method in a family of generic quantum spin chains which
undergo a transition from integrable to non-integrable - quantum chaotic case
as control parameters are varied. Quantum states (observables) are represented
in terms of matrix-product-operators with rank D_\epsilon(t), such that
evolution of a long chain is accurate within fidelity error \epsilon up to time
t. We find that rank generally increases exponentially, D_\epsilon(t) \propto
\exp(const t), unless the system is integrable in which case we find polynomial
increase.Comment: 4 pages; v2. added paragraph discussing pure state
Phase Transitions in Generalised Spin-Boson (Dicke) Models
We consider a class of generalised single mode Dicke Hamiltonians with
arbitrary boson coupling in the pseudo-spin - plane. We find exact
solutions in the thermodynamic, large-spin limit as a function of the coupling
angle, which allows us to continuously move between the simple dephasing and
the original Dicke Hamiltonians. Only in the latter case (orthogonal static and
fluctuating couplings), does the parity-symmetry induced quantum phase
transition occur.Comment: 6 pages, 5 figue
Dissipative Quantum Ising model in a cold atomic spin-boson mixture
Using cold bosonic atoms with two (hyperfine) ground states, we introduce a
spin-boson mixture which allows to implement the quantum Ising model in a
tunable dissipative environment. The first specie lies in a deep optical
lattice with tightly confining wells and forms a spin array; spin-up/down
corresponds to occupation by one/no atom at each site. The second specie forms
a superfluid reservoir. Different species are coupled coherently via laser
transitions and collisions. Whereas the laser coupling mimics a transverse
field for the spins, the coupling to the reservoir sound modes induces a
ferromagnetic (Ising) coupling as well as dissipation. This gives rise to an
order-disorder quantum phase transition where the effect of dissipation can be
studied in a controllable manner.Comment: 4 pages, 2 figures, 1 table; Title modified and cosmetic change
Non-Markovian non-stationary completely positive open quantum system dynamics
By modeling the interaction of a system with an environment through a renewal
approach, we demonstrate that completely positive non-Markovian dynamics may
develop some unexplored non-standard statistical properties. The renewal
approach is defined by a set of disruptive events, consisting in the action of
a completely positive superoperator over the system density matrix. The random
time intervals between events are described by an arbitrary waiting-time
distribution. We show that, in contrast to the Markovian case, if one performs
a system-preparation (measurement) at an arbitrary time, the subsequent
evolution of the density matrix evolution is modified. The non-stationary
character refers to the absence of an asymptotic master equation even when the
preparation is performed at arbitrary long times. In spite of this property, we
demonstrate that operator expectation values and operators correlations have
the same dynamical structure, establishing the validity of a non-stationary
quantum regression hypothesis. The non-stationary property of the dynamic is
also analyzed through the response of the system to an external weak
perturbation.Comment: 13 pages, 3 figure
Lindblad rate equations
In this paper we derive an extra class of non-Markovian master equations
where the system state is written as a sum of auxiliary matrixes whose
evolution involve Lindblad contributions with local coupling between all of
them, resembling the structure of a classical rate equation. The system
dynamics may develops strong non-local effects such as the dependence of the
stationary properties with the system initialization. These equations are
derived from alternative microscopic interactions, such as complex environments
described in a generalized Born-Markov approximation and tripartite
system-environment interactions, where extra unobserved degrees of freedom
mediates the entanglement between the system and a Markovian reservoir.
Conditions that guarantees the completely positive condition of the solution
map are found. Quantum stochastic processes that recover the system dynamics in
average are formulated. We exemplify our results by analyzing the dynamical
action of non-trivial structured dephasing and depolarizing reservoirs over a
single qubit.Comment: 12 pages, 2 figure
Statistics of conductance oscillations of a quantum dot in the Coulomb-blockade regime
The fluctuations and the distribution of the conductance peak spacings of a
quantum dot in the Coulomb-blockade regime are studied and compared with the
predictions of random matrix theory (RMT). The experimental data were obtained
in transport measurements performed on a semiconductor quantum dot fabricated
in a GaAs-AlGaAs heterostructure. It is found that the fluctuations in the peak
spacings are considerably larger than the mean level spacing in the quantum
dot. The distribution of the spacings appears Gaussian both for zero and for
non-zero magnetic field and deviates strongly from the RMT-predictions.Comment: 7 pages, 4 figure
- …