5,124 research outputs found
OTOC, complexity and entropy in bi-partite systems
There is a remarkable interest in the study of Out-of-time ordered
correlators (OTOCs) that goes from many body theory and high energy physics to
quantum chaos. In this latter case there is a special focus on the comparison
with the traditional measures of quantum complexity such as the spectral
statistics, for example. The exponential growth has been verified for many
paradigmatic maps and systems. But less is known for multi-partite cases. On
the other hand the recently introduced Wigner separability entropy (WSE) and
its classical counterpart (CSE) provide with a complexity measure that treats
equally quantum and classical distributions in phase space. We have compared
the behavior of these measures in a system consisting of two coupled and
perturbed cat maps with different dynamics: double hyperbolic (HH), double
elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and
the WSE have essentially the same behavior, providing with a complete
characterization in generic bi-partite systems and at the same time revealing
them as very good measures of quantum complexity for phase space distributions.
Moreover, we establish a relation between both quantities by means of a
recently proven theorem linking the second Renyi entropy and OTOCs.Comment: 6 pages, 5 figure
Classical to quantum correspondence in dissipative directed transport
We compare the quantum and classical properties of the (Quantum) Isoperiodic
Stable Structures -- (Q)ISSs -- which organize the parameter space of a
paradigmatic dissipative ratchet model, i.e. the dissipative modified kicked
rotator. We study the spectral behavior of the corresponding classical
Perron-Frobenius operators with thermal noise and the quantum superoperators
without it for small values. We find a remarkable similarity
between the classical and quantum spectra. This finding significantly extends
previous results -- obtained for the mean currents and asymptotic distributions
only -- and on the other hand unveils a classical to quantum correspondence
mechanism where the classical noise is qualitatively different from the quantum
one. This is crucial not only for simple attractors but also for chaotic ones,
where just analyzing the asymptotic distribution reveals insufficient.
Moreover, we provide with a detailed characterization of relevant eigenvectors
by means of the corresponding Weyl-Wigner distributions, in order to better
identify similarities and differences. Finally, this model being generic, it
allows us to conjecture that this classical to quantum correspondence mechanism
is a universal feature of dissipative systems.Comment: 7 pages, 6 figure
Semiclassical Coherent States propagator
In this work, we derived a semiclassical approximation for the matrix
elements of a quantum propagator in coherent states (CS) basis that avoids
complex trajectories, it only involves real ones. For that propose, we used
the, symplectically invariant, semiclassical Weyl propagator obtained by
performing a stationary phase approximation (SPA) for the path integral in the
Weyl representation. After what, for the transformation to CS representation
SPA is avoided, instead a quadratic expansion of the complex exponent is used.
This procedure also allows to express the semiclassical CS propagator uniquely
in terms of the classical evolution of the initial point, without the need of
any root search typical of Van Vleck Gutzwiller based propagators. For the case
of chaotic Hamiltonian systems, the explicit time dependence of the CS
propagator has been obtained. The comparison with a
\textquotedbl{}realistic\textquotedbl{} chaotic system that derives from a
quadratic Hamiltonian, the cat map, reveals that the expression here derived is
exact up to quadratic Hamiltonian systems.Comment: 13 pages, 2 figure. Accepted for publication in PR
Order reductions of Lorentz-Dirac-like equations
We discuss the phenomenon of preacceleration in the light of a method of
successive approximations used to construct the physical order reduction of a
large class of singular equations. A simple but illustrative physical example
is analyzed to get more insight into the convergence properties of the method.Comment: 6 pages, LaTeX, IOP macros, no figure
Observation of a tricritical wedge filling transition in the 3D Ising model
In this Letter we present evidences of the occurrence of a tricritical
filling transition for an Ising model in a linear wedge. We perform Monte Carlo
simulations in a double wedge where antisymmetric fields act at the top and
bottom wedges, decorated with specific field acting only along the wegde axes.
A finite-size scaling analysis of these simulations shows a novel critical
phenomenon, which is distinct from the critical filling. We adapt to
tricritical filling the phenomenological theory which successfully was applied
to the finite-size analysis of the critical filling in this geometry, observing
good agreement between the simulations and the theoretical predictions for
tricritical filling.Comment: 5 pages, 3 figure
Quadratic cavity soliton optical frequency combs
We theoretically investigate the formation of frequency combs in a dispersive second-harmonic generation cavity system, and predict the existence of quadratic cavity solitons in the absence of a temporal walk-off
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