Coherent and Incoherent Dynamics in a Periodically Driven Bistable System

Dittrich, Thomas; Großmann, Frank; Hänggi, Peter; Oelschlägel, B.; Utermann, R.

doi:10.1007/978-94-011-0169-1_4

Cited by 2 publications

(4 citation statements)

References 39 publications

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“…It is noteworthy that the inverse particle number 1/N can be thought of as an effective Planck constant, thus allowing for the comparison with the results obtained for single-particle models [52,53,54,55]; note in addition those cited in the mini-review [54].…”

Section: Model Study: Bose-hubbard Dimermentioning

confidence: 99%

Asymptotic Floquet states of open quantum systems: the role of interaction

et al. 2017

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When a periodically modulated many-body quantum system is weakly coupled to an environment, the combined action of these temporal modulations and dissipation steers the system towards a state characterized by a time-periodic density operator. To resolve this asymptotic non-equilibrium state at stroboscopic instants of time, we use the dissipative propagator over one period of modulations, 'Floquet map', and evaluate the stroboscopic density operator as its invariant. Particle interactions control properties of the map and thus the features of its invariant. In addition, the spectrum of the map provides insight into the system relaxation towards the asymptotic state and may help to understand whether it is possible (or not) to construct a stroboscopic time-independent Lindblad generator which mimics the action of the original time-dependent one. We illustrate the idea with a scalable many-body model, a periodically modulated Bose-Hubbard dimer. We contrast the relations between the interaction-induced bifurcations in a mean-field description with the numerically exact stroboscopic evolution and discuss the characteristics of the genuine quantum many-body state vs the characteristics of its mean-field counterpart.

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Section: Model Study: Bose-hubbard Dimermentioning

confidence: 99%

Asymptotic Floquet states of open quantum systems: the role of interaction

et al. 2017

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“…In Fig. 4, we compare the S dependencies of the tunnel splittings and the overlaps for the seven quasienergy doublets from lea ), 1¢2) to [ ¢13), 1¢14) [17,18]. Qualitatively, they are strikingly similar: There is only a weak S dependence, reflecting the influence of the growing first resonance, for S ~ l0 -3.…”

Section: Tunnel Splittings and The Onset Of Chaosmentioning

confidence: 93%

“…The breakup of the tunnel doublets in the chaotic layer is not a direct consequence of the Lyapunov exponent of the classical dynamics being positive there, but rests on the global condition that diffusive spreading connects all parts of the chaotic layer, bridging the symmetry plane. In order to allow for a numerical check, we quantify the distinction between "regular" and "chaotic" eigenstates on the basis of the overlap of the Husimi representation [36] of an eigenstate with the chaotic layer in phase space [17,18]. To illustrate these concepts, the Husimi distribution for the quasienergy state 1¢7) is superposed, in Fig.…”

Section: Tunnel Splittings and The Onset Of Chaosmentioning

confidence: 99%

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Driven tunneling: New possibilities for coherent and incoherent quantum transport

Dittrich

Hänggi

Oelschlägel

et al.

25 Years of Non-Equilibrium Statistical Mechanics

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We study the conservative as well as the dissipative quanta] dynamics in a harmonically driven, quartic double-well potential. In the deep quanta] regime, we find coherent modifications of tunneling, including its complete suppression. In the semiclassical regime of the conservative system, the dynamics is dominated by the interplay of tunneling and chaotic diffusion. A strong correlation exists between the tunnel splittings and the overlaps of the associated doublet states with the chaotic layer. With weak dissipation, remnants of coherent behaviour occur as transients, such as the tunneling between symmetry-related pairs of limit cycles. The coherent suppression of tunneling observed in the conservative case is stabilized by weak incoherence.The quanta] stationary states are broadened anisotropica]ly due to quantum noise, as compared to the corresponding classical attractors.

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Coherent and Incoherent Dynamics in a Periodically Driven Bistable System

Cited by 2 publications

References 39 publications

Asymptotic Floquet states of open quantum systems: the role of interaction

Asymptotic Floquet states of open quantum systems: the role of interaction

Driven tunneling: New possibilities for coherent and incoherent quantum transport

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