Energy dissipation via coupling with a finite chaotic environment

Marchiori, Marcelo Amorim; Aguiar, Marcus A. M. de

doi:10.1103/physreve.83.061112

Cited by 14 publications

(39 citation statements)

References 37 publications

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“…Choosing γ i = γ and k i = k, we obtain λ = 1 − Nγ 2 /k 2 and it is reasonable to scale γ 2 with N so that an effective coupling exists, which is γ eff = γ / √ N . This agrees with results obtained using linear response theory [12].…”

Section: Contraction Rate (λ)supporting

confidence: 93%

“…(11) and (12) and the fact that X n = X n +1 − P n +1 . In this way we obtain the final map for the system only as follows:…”

Section: Generalized Mapmentioning

confidence: 96%

“…The essential distinctions to the usual continuous model is that our environment is composed of a finite number N of uncoupled kicked HOs, and the coupling between system and environment is switched on and off instantaneously (kicks) at regular times. While the effects of finite but nonkicked environments have already been studied in classical problems [8][9][10][11][12][13], kicked couplings and environments have been used to describe quantum decoherence due to the nonlinear dynamics of the environment [14,15]. Our approach is different from the dynamical systems of Langevin type presented by [16], which analyzed the dynamics of a kicked damped particle, where the kicks coming from the environment are deterministic and generated by specific nonlinear chaotic maps.…”

Section: Introductionmentioning

confidence: 98%

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Finite kicked environments and the fluctuation-dissipation relation

Beims

2014

Phys. Rev. E

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In this work we derive a generalized map for a system coupled to a kicked environment composed of a finite number N of uncoupled harmonic oscillators. Dissipation is introduced via the interaction between system and environment which is switched on and off simultaneously (kicks) at regular time intervals. It is shown that kicked environments naturally generate a non-Markovian rotated dynamics, describe more complicated system-environment couplings which involve position and momentum, and satisfy an unusual fluctuation-dissipation relation. As an example, the motion of a kicked Brownian particle is discussed.

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Section: Contraction Rate (λ)supporting

confidence: 93%

“…(11) and (12) and the fact that X n = X n +1 − P n +1 . In this way we obtain the final map for the system only as follows:…”

Section: Generalized Mapmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 98%

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Finite kicked environments and the fluctuation-dissipation relation

Beims

2014

Phys. Rev. E

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“…To render the comparison easier the coupling strength of each oscillator from the bath equals g λ = 0.008/ √ N. This effective coupling is needed so that the effect of the environment over the HO converges as N becomes large [47].…”

Section: Harmonic Potential Coupled To N Oscillatorsmentioning

confidence: 99%

Quantum energy and coherence exchange with discrete baths

Galiceanu

Beims

Strunz

2014

Physica A: Statistical Mechanics and its Applications

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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.

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“…This occurs because the systems are small and they may depend on the density of states of the involved systems and initial conditions (ICs) [25][26][27]. The Boltzmann-like distribution only occurs when the number of chaotic degrees of freedom in the bath is increased (but still finite), such that even for a single realization it is possible to see irreversible processes [28].…”

Section: Introductionmentioning

confidence: 99%

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

2015

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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.

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Energy dissipation via coupling with a finite chaotic environment

Cited by 14 publications

References 37 publications

Finite kicked environments and the fluctuation-dissipation relation

Finite kicked environments and the fluctuation-dissipation relation

Quantum energy and coherence exchange with discrete baths

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

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