Classical-quantum correspondence for multilevel systems

Gilmore, Robert; Bowden, Charles M.; Narducci, L. M.

doi:10.1103/physreva.12.1019

Cited by 146 publications

(77 citation statements)

References 16 publications

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“…These classical trajectories lie on the unit sphere, and their shape is determined by the parameter α in Eq. (4) [40]. Typical trajectories are depicted in Fig.…”

Section: Semiclassical Dynamicsmentioning

confidence: 99%

“…These states are eigenstates of the spin operatorŜ θ =Ŝ x sin θ +Ŝ z cos θ, with eigenvalueŜ θ = N/2. For large total particle number N , the semiclassical approximation yields a good description [38,40,41], and the spin operators in Eq. (2) can be re- placed by the components of a classical vector…”

Section: Semiclassical Dynamicsmentioning

confidence: 99%

“…4). Here the fixed point at Ω x = −1 becomes unstable, and bifurcates into two new, stable fixed points at [38,40]…”

Section: Semiclassical Dynamicsmentioning

confidence: 99%

“…In Sec. II, we outline the semi-classical dynamics of Hamiltonian (2) [39][40][41]. We analyze the entropy oscillations and the entropy production for short times, and compare the exact dynamics to a semi-classical approximation in Sec.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement and entropy production in coupled single-mode Bose-Einstein condensates

et al. 2017

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We investigate the time evolution of the entanglement entropy of coupled single-mode BoseEinstein condensates in a double well potential at T = 0 temperature, by combining numerical results with analytical approximations. We find that the coherent oscillations of the condensates result in entropy oscillations on the top of a linear entropy generation at short time scales. Due to dephasing, the entropy eventually saturates to a stationary value, in spite of the lack of equilibration. We show that this long time limit of the entropy reflects the semiclassical dynamics of the system, revealing the self-trapping phase transition of the condensates at large interaction strength by a sudden entropy jump. We compare the stationary limit of the entropy to the prediction of a classical microcanonical ensemble, and find surprisingly good agreement in spite of the non-equilibrium state of the system. Our predictions should be experimentally observable on a Bose-Einstein condensate in a double well potential or on a two-component condensate with inter-state coupling.

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“…These classical trajectories lie on the unit sphere, and their shape is determined by the parameter α in Eq. (4) [40]. Typical trajectories are depicted in Fig.…”

Section: Semiclassical Dynamicsmentioning

confidence: 99%

Section: Semiclassical Dynamicsmentioning

confidence: 99%

“…4). Here the fixed point at Ω x = −1 becomes unstable, and bifurcates into two new, stable fixed points at [38,40]…”

Section: Semiclassical Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Entanglement and entropy production in coupled single-mode Bose-Einstein condensates

et al. 2017

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“…A detailed derivation of the SU(M) coherent states can be found in Refs. [17][18][19]. We will just summarize a few facts about them.…”

Section: Classical Dynamics In the Su(m) Coherent States Picturementioning

confidence: 99%

Localization of Bose-Einstein condensates in optical lattices

Franzosi¹,

Giampaolo²,

Illuminati³

et al. 2011

Open Physics

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Abstract:The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, addressing the study of the discrete nonlinear Schrödinger dynamics, have predicted the spontaneous generation of (classical) breathers in coupled condensates. In the present contribute, we shall focus on localized solutions (quantum breathers) of the full Bose-Hubbard model. We will show that solutions exponentially localized in space and periodic in time exist also in absence of randomness. Thus, this kind of states, reproduce a novel quantum localization phenomenon due to the interplay between bounded energy spectrum and non-linearity.

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