29,094 research outputs found
Markovian embedding of non-Markovian quantum collisional models
A wide class of non-Markovian completely positive master equations can be
formulated on the basis of quantum collisional models. In this phenomenological
approach the dynamics of an open quantum system is modeled through an ensemble
of stochastic realizations that consist in the application at random times of a
(collisional) completely positive transformation over the system state. In this
paper, we demonstrate that these kinds of models can be embedded in bipartite
Markovian Lindblad dynamics consisting of the system of interest and an
auxiliary one. In contrast with phenomenological formulations, here the
stochastic ensemble dynamics an the inter-event time interval statistics are
obtained from a quantum measurement theory after assuming that the auxiliary
system is continuously monitored in time. Models where the system
inter-collisional dynamics is non-Markovian [B. Vacchini, Phys. Rev. A 87,
030101(R) (2013)] are also obtained from the present approach. The formalism is
exemplified through bipartite dynamics that leads to non-Markovian system
effects such as an environment-to-system back flow of information.Comment: 12 pages, 2 figure
Post-Markovian quantum master equations from classical environment fluctuations
In this paper we demonstrate that two commonly used phenomenological
post-Markovian quantum master equations can be derived without using any
perturbative approximation. A system coupled to an environment characterized by
self-classical configurational fluctuations, the latter obeying a Markovian
dynamics, defines the underlying physical model. Both Shabani-Lidar equation
[A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101(R) (2005)] and its
associated approximated integro-differential kernel master equation are
obtained by tracing out two different bipartite Markovian Lindblad dynamics
where the environment fluctuations are taken into account by an ancilla system.
Furthermore, conditions under which the non-Markovian system dynamics can be
unravelled in terms of an ensemble of measurement trajectories are found. In
addition, a non-Markovian quantum jump approach is formulated. Contrary to
recent analysis [L. Mazzola, E. M. Laine, H. P. Breuer, S. Maniscalco, and J.
Piilo, Phys. Rev. A 81, 062120 (2010)], we also demonstrate that these master
equations, even with exponential memory functions, may lead to non-Markovian
effects such as an environment-to-system backflow of information if the
Hamiltonian system does not commutate with the dissipative dynamics.Comment: 13 pages, 4 figure
Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
The quantum jump approach allows to characterize the stochastic dynamics
associated to an open quantum system submitted to a continuous measurement
action. In this paper we show that this formalism can consistently be extended
to non-Markovian system dynamics. The results rely in studying a measurement
process performed on a bipartite arrangement characterized by a Markovian
Lindblad evolution. Both a renewal and non-renewal extensions are found. The
general structure of non-local master equations that admit an unravelling in
terms of the corresponding non-Markovian trajectories are also found. Studying
a two-level system dynamics, it is demonstrated that non-Markovian effects such
as an environment-to-system flow of information may be present in the ensemble
dynamics.Comment: 13 pages, 3 figure
Extended q-Gaussian and q-exponential distributions from Gamma random variables
The family of q-Gaussian and q-exponential probability densities fit the
statistical behavior of diverse complex self-similar non-equilibrium systems.
These distributions, independently of the underlying dynamics, can rigorously
be obtained by maximizing Tsallis "non-extensive" entropy under appropriate
constraints, as well as from superstatistical models. In this paper we provide
an alternative and complementary scheme for deriving these objects. We show
that q-Gaussian and q-exponential random variables can always be expressed as
function of two statistically independent Gamma random variables with the same
scale parameter. Their shape index determine the complexity q-parameter. This
result also allows to define an extended family of asymmetric q-Gaussian and
modified -exponential densities, which reduce to the previous ones when the
shape parameters are the same. Furthermore, we demonstrate that simple change
of variables always allow to relate any of these distributions with a Beta
stochastic variable. The extended distributions are applied in the statistical
description of different complex dynamics such as log-return signals in
financial markets and motion of point defects in fluid flows.Comment: 11 pages, 6 figure
Central limit theorem for a class of globally correlated random variables
The standard central limit theorem with a Gaussian attractor for the sum of
independent random variables may lose its validity in presence of strong
correlations between the added random contributions. Here, we study this
problem for similar interchangeable globally correlated random variables. Under
these conditions, a hierarchical set of equations is derived for the
conditional transition probabilities. This result allows us to define different
classes of memory mechanisms that depend on a symmetric way on all involved
variables. Depending on the correlation mechanisms and single statistics, the
corresponding sums are characterized by distinct statistical probability
densities. For a class of urn models it is also possible to characterize their
domain of attraction which, as in the standard case, is parametrized by the
probability density of each random variable. Symmetric and asymmetric
-Gaussian attractors are a particular case of these models.Comment: 11 pages, 7 figures, Appendixes 5 page
Weak ergodicity breaking induced by global memory effects
We study the phenomenon of weak ergodicity breaking for a class of globally
correlated random walk dynamics defined over a finite set of states. The
persistence in a given state or the transition to another one depends on the
whole previous temporal history of the system. A set of waiting time
distributions, associated to each state, set the random times between
consecutive steps. Their mean value is finite for all states. The probability
density of time-averaged observables is obtained for different memory
mechanisms. This statistical object explicitly shows departures between time
and ensemble averages. While the mean residence time in each state may result
divergent, we demonstrate that this condition is in general not necessary for
breaking ergodicity. Hence, global memory effects are an alternative mechanism
able to induce this property. Analytical and numerical calculations support
these results.Comment: 11 pages, 3 figure
- …