arXiv subjects

M. W. Beims

Publications and source records attributed to M. W. Beims.

11 recordsLinked to original sources

arXiv2019

Decay of distance autocorrelation and Lyapunov exponents

This work presents numerical evidences that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance autocorrelation are observed for different systems, namely exponential decays for the quadratic map, logarithmic for the Hénon map and power-law for the conservative standard map. In all these cases the decay exponent is close to the positive Lyapunov exponent. For hyperbolic conservative systems, the power-law decay of the distance autocorrelation tends to be guided by the smallest Lyapunov exponent.

nlin.CD↗

arXiv2016

System-environment correlations for dephasing two-qubit states coupled to thermal baths

Based on the exact dynamics of a two-qubit system and environment, we investigate system-environment (SE) quantum and classical correlations. The coupling is chosen to represent a dephasing channel for one of the qubits and the environment is a proper thermal bath. First we discuss the general issue of dilation for qubit phase damping. Based on the usual thermal bath of harmonic oscillators, we derive criteria of separability and entanglement between an initial $X$ state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature $T_{\mathrm{crit}}$. On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to $T_{\mathrm{crit}}$ the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.

quant-ph↗

arXiv2016

Generalized discord, entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in two-qubit systems under (non-)Markovian channels: Hierarchy of quantum resources and chronology of deaths and births

Generalized quantum discord $(D_q)$, Einstein-Podolsky-Rosen steering $(S)$, entanglement $(E)$, and Bell nonlocality ($N$), are logically distinct quantifiers of quantum correlations. All these measures capture nonclassical aspects of quantum states and play some role as resources in quantum information processing. In this work, we look for the hierarchy satisfied by these quantum correlation witnesses for a class of two-qubit states. We show that $N \triangleright S\triangleright E\triangleright D_q$, meaning that nonlocality implies steering, which in turn implies entanglement, which then implies $q$-discord. For the quantum states under concern, we show that the invariance of this hierarchy under noisy quantum channels directly implies a death chronology. Additionally, we have found that sudden death of all quantum resources except discord is absent only for a subset of states of measure zero. At last, we provide an illustration of another consequence of the aforementioned hierarchy, namely, the existence of a sudden birth chronology under non-Markovian channels.

quant-ph↗

arXiv2016

Rotational directionality via symmetry-breaking in an electrostatic motor

We theoretically investigate how one can achieve a preferred rotational direction for the case of a simple electrostatic motor. The motor is composed by a rotor and two electronic reservoirs. Electronic islands on the rotor can exchange electrons with the reservoirs. An electrostatic field exerts a force on the occupied islands. The charge dynamics and the electrostatic field drive rotations of the rotor. Coupling to an environment lead to damping on the rotational degree of freedom. We use two different approaches to the charge dynamics in the electronic islands: hopping process and mean-field. The hopping process approach takes into account charge fluctuations, which can appear along Coulomb blockade effects in nanoscale systems. The mean-field approach neglects the charge fluctuations on the islands, which is typically suitable for larger systems. We show that for a system described by the mean-field equations one can in principle prepare initial conditions to obtain a desired rotational direction. In contrast, this is not possible in the stochastic description. However, for both cases one can achieve rotational directionality by changing the geometry of the rotor. By scanning the space formed by the relevant geometric parameters we find optimal geometries, while fixing the dissipation and driving parameters. Remarkably, in the hopping process approach perfect rotational directionality is possible for a large range of geometries.

cond-mat.soft↗

arXiv2015

Characterizing Weak Chaos using Time Series of Lyapunov Exponents

We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered (stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The dynamics is then investigated looking at the consecutive time spent in each regime, the transition between different regimes, and the regions in the phase-space associated to them. Applying our methodology to a chain of coupled standard maps we obtain: (i) that it allows for an improved numerical characterization of stickiness in high-dimensional Hamiltonian systems, when compared to the previous analyses based on the distribution of recurrence times; (ii) that the transition probabilities between different regimes are determined by the phase-space volume associated to the corresponding regions; (iii) the dependence of the Lyapunov exponents with the coupling strength.

nlin.CD↗

arXiv2015

Quantum-classical transition and quantum activation of ratchet currents in the parameter space

The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zero temperature quantum environment. We show that vacuum fluctuations blur the generic isoperiodic stable structures found in the classical case. Such structures tend to survive when a measure of statistical dependence between the quantum and classical currents are displayed in the parameter space. In addition, we show that quantum fluctuations can be used to overcome transport barriers in the phase space. Related quantum ratchet current activation regions are spotted in the parameter space. Results are discussed {based on quantum, semiclassical and classical calculations. While the semiclassical dynamics involves vacuum fluctuations, the classical map is driven by thermal noise.

nlin.CD↗

arXiv2014

Monogamy and backflow of mutual information in non-Markovian thermal baths

We investigate the dynamics of information among the parties of tripartite systems. We start by proving two results concerning the monogamy of mutual information. The first one states that mutual information is monogamous for generic tripartite pure states. The second shows that in general mutual information is monogamous only if the amount of genuine tripartite correlations is large enough. Then, we analyze the internal dynamics of tripartite systems whose parties do not exchange energy. In particular, we allow for one of the subsystems to play the role of a finite thermal bath. As a result, we find a typical scenario in which local information tends to be converted into delocalized information. Moreover, we show that (i) the information flow is reversible for finite thermal baths at low temperatures, (ii) monogamy of mutual information is respected throughout the dynamics, and (iii) genuine tripartite correlations are typically present. Finally, we analytically calculate a quantity capable of revealing favorable regimes for non-Markovianity in our model.

quant-ph↗

arXiv2011

Three unequal masses on a ring and soft triangular billiards

The dynamics of three soft interacting particles on a ring is shown to correspond to the motion of one particle inside a soft triangular billiard. The dynamics inside the soft billiard depends only on the {\it masses ratio} between particles and {\it softness ratio} of the particles interaction. The transition from soft to hard interaction can be appropriately explored using potentials for which the corresponding equations of motion are well defined in the hard wall limit. Numerical examples are shown for the soft Toda-like interaction and the error function.

nlin.CD↗

arXiv2011

Quantum energy decays and decoherence in discrete baths

The quantum average energy decay and the purity decay are studied for a system particle as a function of the number of constituents of a discrete bath model. The system particle is subjected to two distinct physical situations: the harmonic oscillator (HO) and the Morse potential. The environment (bath) is composed by a {\it finite} number N of uncoupled HOs, characterizing the structured bath, which in the limit $N\to\infty$ is assumed to have an ohmic, sub-ohmic or super-ohmic spectral density. For very low values of N the mean energy and purity remain constant in time but starts to decay for intermediate values (10<N<20), where two distinct time regimes are observed: two exponential decays for relatively short times and a power-law decay for larger times. In this interval of N decoherence occurs for short times and a non-Markovian dynamics is expected for larger times. When $N$ increases, energy and coherence decay very fast and a Markovian dynamics is expected to occur. Wave packet dynamics is used to determine the evolution of the particle inside the system potentials.

quant-ph↗

arXiv2010

Footprints of sticky motion in the phase space of higher dimensional nonintegrable conservative systems

"Sticky" motion in mixed phase space of conservative systems is difficult to detect and to characterize, in particular for high dimensional phase spaces. Its effect on quasi-regular motion is quantified here with four different measures, related to the distribution of the finite time Lyapunov exponents. We study systematically standard maps from the uncoupled two-dimensional case up to coupled maps of dimension $20$. We find that sticky motion in all unstable directions above a threshold $K_{d}$ of the nonlinearity parameter $K$ for the high dimensional cases $d=10,20$. Moreover, as $K$ increases we can clearly identify the transition from quasiregular to totally chaotic motion which occurs simultaneously in all unstable directions. The results show that all four statistical measures sensitively probe sticky motion in high dimensional systems.

nlin.CD↗

arXiv2009

Soft wall effects on interacting particles in billiards

The effect of physically realizable wall potentials (soft walls) on the dynamics of two interacting particles in a one-dimensional (1D) billiard is examined numerically. The 1D walls are modeled by the error function and the transition from hard to soft walls can be analyzed continuously by varying the softness parameter $σ$. For $σ\to 0$ the 1D hard wall limit is obtained and the corresponding wall force on the particles is the $δ$-function. In this limit the interacting particle dynamics agrees with previous results obtained for the 1D hard walls. We show that the two interacting particles in the 1D soft walls model is equivalent to one particle inside a soft right triangular billiard. Very small values of $σ$ substantiously change the dynamics inside the billiard and the mean finite-time Lyapunov exponent decreases significantly as the consequence of regular islands which appear due to the low-energy double collisions (simultaneous particle-particle-1D wall collisions). The rise of regular islands and sticky trajectories induced by the 1D wall softness is quantified by the number of occurrences of the most probable finite-time Lyapunov exponent. On the other hand, chaotic motion in the system appears due to the high-energy double collisions. In general we observe that the mean finite-time Lyapunov exponent decreases when $σ$ increases, but the number of occurrences of the most probable finite-time Lyapunov exponent increases, meaning that the phase-space dynamics tends to be more ergodiclike. Our results suggest that the transport efficiency of interacting particles and heat conduction in periodic structures modeled by billiards will strongly be affected by the smoothness of physically realizable walls.

nlin.CD↗