231 research outputs found
Fluctuating observation time ensembles in the thermodynamics of trajectories
The dynamics of stochastic systems, both classical and quantum, can be
studied by analysing the statistical properties of dynamical trajectories. The
properties of ensembles of such trajectories for long, but fixed, times are
described by large-deviation (LD) rate functions. These LD functions play the
role of dynamical free-energies: they are cumulant generating functions for
time-integrated observables, and their analytic structure encodes dynamical
phase behaviour. This "thermodynamics of trajectories" approach is to
trajectories and dynamics what the equilibrium ensemble method of statistical
mechanics is to configurations and statics. Here we show that, just like in the
static case, there is a variety of alternative ensembles of trajectories, each
defined by their global constraints, with that of trajectories of fixed total
time being just one of these. We show that an ensemble of trajectories where
some time-extensive quantity is constant (and large) but where total
observation time fluctuates, is equivalent to the fixed-time ensemble, and the
LD functions that describe one ensemble can be obtained from those that
describe the other. We discuss how the equivalence between generalised
ensembles can be exploited in path sampling schemes for generating rare
dynamical trajectories.Comment: 12 pages, 5 figure
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
Thermodynamics of quantum jump trajectories in systems driven by classical fluctuations
The large-deviation method can be used to study the measurement trajectories
of open quantum systems. For optical arrangements this formalism allows to
describe the long time properties of the (non-equilibrium) photon counting
statistics in the context of a (equilibrium) thermodynamic approach defined in
terms of dynamical phases and transitions between them in the trajectory space
[J.P. Garrahan and I. Lesanovsky, Phys. Rev. Lett. 104, 160601 (2010)]. In this
paper, we study the thermodynamic approach for fluorescent systems coupled to
complex reservoirs that induce stochastic fluctuations in their dynamical
parameters. In a fast modulation limit the thermodynamics corresponds to that
of a Markovian two-level system. In a slow modulation limit, the thermodynamic
properties are equivalent to those of a finite system that in an infinite-size
limit is characterized by a first-order transition. The dynamical phases
correspond to different intensity regimes, while the size of the system is
measured by the transition rate of the bath fluctuations. As a function of a
dimensionless intensive variable, the first and second derivative of the
thermodynamic potential develop an abrupt change and a narrow peak
respectively. Their scaling properties are consistent with a double-Gaussian
probability distribution of the associated extensive variable.Comment: 12 pages, 3 figure
Solvable class of non-Markovian quantum multipartite dynamics
We study a class of multipartite open quantum dynamics for systems with an arbitrary number of qubits. The non-Markovian quantum master equation can involve arbitrary single or multipartite and time-dependent dissipative coupling mechanisms, expressed in terms of strings of Pauli operators. We formulate the general constraints that guarantee the complete positivity of this dynamics. We characterize in detail the underlying mechanisms that lead to memory effects, together with properties of the dynamics encoded in the associated system rates. We specifically derive multipartite “eternal” non-Markovian master equations that we term hyperbolic and trigonometric due to the time dependence of their rates. For these models we identify a transition between positive and periodically divergent rates. We also study non-Markovian effects through an operational (measurement-based) memory witness approach
A classical appraisal of quantum definitions of non-Markovian dynamics
We consider the issue of non-Markovianity of a quantum dynamics starting from
a comparison with the classical definition of Markovian process. We point to
the fact that two sufficient but not necessary signatures of non-Markovianity
of a classical process find their natural quantum counterpart in recently
introduced measures of quantum non-Markovianity. This behavior is analyzed in
detail for quantum dynamics which can be built taking as input a class of
classical processes.Comment: 15 pages, 6 figures; to appear in J. Phys. B, Special Issue on "Loss
of coherence and memory effects in quantum dynamics
Detection of quantum non-Markovianity close to the Born-Markov approximation
We calculate in an exact way the conditional past-future correlation for the decay dynamics of a two-level system in a bosonic bath. Different measurement processes are considered. In contrast to quantum memory measures based solely on system propagator properties, here memory effects are related to a convolution structure involving two system propagators and the environment correlation. This structure allows to detect memory effects even close to the validity of the Born-Markov approximation. An alternative operational-based definition of environment-to-system backflow of information follows from this result. We provide experimental support to our results by implementing the dynamics and measurements in a photonic experiment.Fil: Silva, Thais De Lima. Universidade Federal do Rio de Janeiro; BrasilFil: Walborn, Stephen P.. Universidade Federal do Rio de Janeiro; BrasilFil: Santos, Marcelo F.. Universidade Federal do Rio de Janeiro; BrasilFil: Aguilar, Gabriel H.. Universidade Federal do Rio de Janeiro; BrasilFil: Budini, Adrian Adolfo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad Tecnológica Nacional; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin
Quantum regression theorem for non-Markovian Lindblad equations
We find the conditions under which a quantum regression theorem can be
assumed valid for non-Markovian master equations consisting in Lindblad
superoperators with memory kernels. Our considerations are based on a
generalized Born-Markov approximation, which allows us to obtain our results
from an underlying Hamiltonian description. We demonstrate that a non-Markovian
quantum regression theorem can only be granted in a stationary regime if the
dynamics satisfies a quantum detailed balance condition. As an example we study
the correlations of a two level system embedded in a complex structured
reservoir and driven by an external coherent field.Comment: 14 pages, 5 figures. Extended version. The GBMA is deduced from
projector technique. A new appendix is adde
Functional characterization of generalized Langevin equations
We present an exact functional formalism to deal with linear Langevin
equations with arbitrary memory kernels and driven by any noise structure
characterized through its characteristic functional. No others hypothesis are
assumed over the noise, neither the fluctuation dissipation theorem. We found
that the characteristic functional of the linear process can be expressed in
terms of noise's functional and the Green function of the deterministic
(memory-like) dissipative dynamics. This object allow us to get a procedure to
calculate all the Kolmogorov hierarchy of the non-Markov process. As examples
we have characterized through the 1-time probability a noise-induced interplay
between the dissipative dynamics and the structure of different noises.
Conditions that lead to non-Gaussian statistics and distributions with long
tails are analyzed. The introduction of arbitrary fluctuations in fractional
Langevin equations have also been pointed out
Dynamical Reduction Models with General Gaussian Noises
We consider the effect of replacing in stochastic differential equations
leading to the dynamical collapse of the statevector, white noise stochastic
processes with non white ones. We prove that such a modification can be
consistently performed without altering the most interesting features of the
previous models. One of the reasons to discuss this matter derives from the
desire of being allowed to deal with physical stochastic fields, such as the
gravitational one, which cannot give rise to white noises. From our point of
view the most relevant motivation for the approach we propose here derives from
the fact that in relativistic models the occurrence of white noises is the main
responsible for the appearance of untractable divergences. Therefore, one can
hope that resorting to non white noises one can overcome such a difficulty. We
investigate stochastic equations with non white noises, we discuss their
reduction properties and their physical implications. Our analysis has a
precise interest not only for the above mentioned subject but also for the
general study of dissipative systems and decoherence.Comment: 22 pages, Late
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