Environment-dependent transport in multiple asymmetric well potentials

Physica A: Statistical Mechanics and its Applications

Strunz

2014

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.

Section: Introductionmentioning

confidence: 99%

Quantum energy and coherence exchange with discrete baths

Galiceanu

Physica A: Statistical Mechanics and its Applications

Strunz

2014

“…Further, our damping mechanism differs from the velocity dependent friction in the Gaussian thermostat, obtained the requiring energy conservation at any time, and from the more general damping mechanism proposed in the Nosé-Hoover thermostat [14]. The finite N model considered here has been used to study environment effects on the transport of particles in ratchets [15] and the role of Levy walks on the mobility in ratchet potentials [16].…”

Section: Introductionmentioning

confidence: 99%

Chaotic motion at the emergence of the time averaged energy decay

Manchein

Rosa

Physica D: Nonlinear Phenomena

2009

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

“…Equations (7) and (8) are linear in all physical quantities and can be solved analytically. After straightforward calculations we obtain the following solutions for the environment coordinates:…”

Section: Generalized Mapmentioning

confidence: 99%

“…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: 99%

Finite kicked environments and the fluctuation-dissipation relation

2014

Phys. Rev. E

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.