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 $\hbar_{\rm eff}$ 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