Optimal transport in a ratchet coupled to a modulated environment: The role of Levy walks

Rosa, Jane; Beims, Marcus W.

doi:10.1016/j.physa.2007.08.014

Cited by 17 publications

(10 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us consider the problem composed by a particle under the influence of an asymmetric potential (the system) interacting with N independent harmonic oscillators (the environment). The dimensionless equations of motion are (see [16] for more details)…”

Section: The Modelmentioning

confidence: 99%

Chaotic motion at the emergence of the time averaged energy decay

Manchein

Rosa

Beims

2009

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the $N$ environment oscillators and becomes chaotic in the interval $13\le N\le15$, where the system time averaged energy starts to decay. To characterize the nonlinear motion we estimate the Lyapunov exponent (LE), determine the power spectrum and the Kaplan-Yorke dimension. For much larger values of $N$ the energy of the system particle is completely transferred to the environment and the corresponding LEs decrease. Numerical evidences show the connection between the variations of the {\it amplitude} of the particles energy time oscillation with the time averaged energy decay and trapped trajectories.Comment: 18 pages and 10 figure

show abstract

Section: The Modelmentioning

confidence: 99%

Chaotic motion at the emergence of the time averaged energy decay

Manchein

Rosa

Beims

2009

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…Some experiments in which the non-Markovian behavior arises due to the discreteness of the bath can be mentioned: high-Q microwave cavities, quantum optics in materials with a photonic band gap, output coupling from a Bose-Einstein condensate to create an atom laser [28][29][30][31][32] or the decoherence phenomenon [33][34][35][36]. From the classical point of view, in the context of finite baths with uncoupled HO, there are some works which analyze the effect of discrete (structured) baths on the system energy decay [9,25,26] and on ratchet transport [37,38]. The main result found is that finite baths may induce a non-Markovian dynamics on the system particle.…”

Section: Introductionmentioning

confidence: 99%

Quantum energy and coherence exchange with discrete baths

Galiceanu

Beims

Strunz

2014

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

h i g h l i g h t s• Quantum coherence of systems coupled to finite baths composed of N harmonic oscillators is investigated. • A stochastic Schrödinger equation is solved numerically. • The energy and purity exchange between system and bath are described in details as a function of the numbers of bath harmonic oscillators.• The non-Markovian dynamics due to finite baths is analyzed. a b s t r a c tCoherence and quantum average energy exchange are studied for a system particle as a function of the number N of constituents of a discrete bath model. The time evolution of the energy and coherence, determined via the system purity (proportional to the linear entropy of the quantum statistical ensemble), are obtained solving numerically the Schrödinger equation. A new simplified stochastic Schrödinger equation is derived which takes into account the discreteness of the bath. The environment (bath) is composed of a finite number N of uncoupled harmonic oscillators (HOs), characterizing a structured bath, for which a non-Markovian behavior is expected. Two distinct physical situations are assumed for the system particle: the HO and the Morse potential. In the limit N → ∞ the bath is assumed to have an ohmic, sub-ohmic or super-ohmic spectral density. In the case of the HO, for very low values of N ( 10) the mean energy and purity oscillate between HO and bath indefinitely in time, while for intermediate and larger values (N ∼ 10 → 500) they start to decay with two distinct time regimes: exponential for relatively short times and powerlaw for larger times. In the case of the Morse potential we only observe an exponential decay for large values of N while for small N's, due to the anharmonicity of the potential, no recurrences of the mean energy and coherences are observed. Wave packet dynamics is used to determine the evolution of the particle inside the system potentials. For both systems the time behavior of a non-Markovianity measure is analyzed as a function of N and is shown to be directly related to the time behavior of the purity.

show abstract

“…The first attempt to theoretically describe a finite environment composed of HOs was realized by [11]. In general the behavior of the main system due to the finite bath may change drastically [7,[12][13][14][15][16]. Moreover, when kicked HOs are used for the bath, the usual fluctuation-dissipation relation is not valid anymore, memory effects are present and the dissipation process can be very complex [17].…”

Section: Introductionmentioning

confidence: 99%

Dissipative dynamics in a finite chaotic environment: Relationship between damping rate and Lyapunov exponent

2015

View full text Add to dashboard Cite

We consider the energy flow between a classical one-dimensional harmonic oscillator and a set of N two-dimensional chaotic oscillators, which represents the finite environment. Using linear response theory we obtain an analytical effective equation for the system harmonic oscillator, which includes a frequency dependent dissipation, a shift, and memory effects. The damping rate is expressed in terms of the environment mean Lyapunov exponent. A good agreement is shown by comparing theoretical and numerical results, even for environments with mixed (regular and chaotic) motion. Resonance between system and environment frequencies is shown to be more efficient to generate dissipation than larger mean Lyapunov exponents or a larger number of bath chaotic oscillators.

show abstract

Optimal transport in a ratchet coupled to a modulated environment: The role of Levy walks

Cited by 17 publications

References 33 publications

Chaotic motion at the emergence of the time averaged energy decay

Chaotic motion at the emergence of the time averaged energy decay

Quantum energy and coherence exchange with discrete baths

Dissipative dynamics in a finite chaotic environment: Relationship between damping rate and Lyapunov exponent

Contact Info

Product

Resources

About