Semiclassical propagation of spin-coherent states

Novaes, Marcel

doi:10.1103/physreva.72.042102

Cited by 7 publications

(6 citation statements)

References 59 publications

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“…Indeed, it seems that semiclassical approaches containing just one contributing trajectory do not contemplate more complex behaviors, as oscillations and revivals, or even longer evolution times. Usually, such features are well described in semiclassical physics only when more trajectories are considered [37][38][39]. Then we expect that, in general, our derivation be valid just for short values of time, region where just one trajectory is able to reproduce quantum results.…”

Section: Discussionmentioning

confidence: 79%

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Entanglement dynamics via semiclassical propagators in systems of two spins

Ribeiro

Angelo

2012

Phys. Rev. A

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We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the purity of the reduced density matrix as function of time. The final formula, subsidiary to the linear entropy, shows that the short-time dynamics of entanglement depends exclusively on the stability of trajectories governed by the underlying classical Hamiltonian. Also, this semiclassical measure is shown to reproduce the general properties of its quantum counterpart and give the expected result in the large spin limit. The accuracy of the semiclassical formula is further illustrated in a problem of phase exchange for two particles of spin j.

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Section: Discussionmentioning

confidence: 79%

“…The Heisenberg equation i (d Ĥ(k) 0 /dt) = [ Ĥ(k) 0 , Ĥ0 + Ĥ] = 0 implies that there is no energy exchange between the spins. This is why Hamiltonian (37) is said to describe a phase coupling.…”

Section: B Case Study: Phase Couplingmentioning

confidence: 99%

Entanglement dynamics via semiclassical propagators in systems of two spins

Ribeiro

Angelo

2012

Phys. Rev. A

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“…It has been shown in the literature that interference phenomena can be reproduced by semiclassical approaches involving more than one trajectory (see, for instance, Ref. [34]). We expect a similar strategy to be able to improve our results for longer times.…”

Section: Then Eq (44) Becomesmentioning

confidence: 99%

Entanglement dynamics via coherent-state propagators

Ribeiro

Angelo

2010

Phys. Rev. A

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The dynamical generation of entanglement in closed bipartite systems is investigated in the semiclassical regime. We consider a model of two particles, initially prepared in a product of coherent states, evolving in time according to a generic Hamiltonian, and derive a formula for the linear entropy of the reduced density matrix using the semiclassical propagator in the coherent-state representation. The formula is explicitly written in terms of quantities that define the stability of classical trajectories of the underlying classical system. The formalism is then applied to the problem of two nonlinearly coupled harmonic oscillators and the result is shown to be in remarkable agreement with the exact quantum measure of entanglement in the short-time regime. An important byproduct of our approach is a unified semiclassical formula which contemplates both the coherent-state propagator and its complex conjugate.

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“…1, taking into account complex trajectories is incontestable to achieve excellent accuracy between quantum and semiclassical results. It is worth mentioning that, in similar semiclassical approaches, the inclusion of complex trajectories was already proven fundamental to mimic the quantum behavior [56][57][58].…”

Section: Final Remarksmentioning

confidence: 99%

Entanglement dynamics of spins using a few complex trajectories

Scherer,

Ribeiro

2021

Preprint

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In this work, we consider two spins initially prepared in a product of coherent states and study their entanglement dynamics due to a general interacting Hamiltonian. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator, assumed as an entanglement quantifier. The resulting expression depends on sets of four trajectories, originated from the underlying classical description, and having mutually connected final phase-space points. Such classical elements, which are capable to reproduce the quantum entanglement even for long values of propagation time, arise when we assume a proper analytical continuation of the classical phase space onto a complex domain. We apply this theory to a particular physical system, showing that taking into account only a few sets of complex trajectories is enough to get an excellent agreement between the semiclassical linear entropy of the reduced density operator and its quantum counterpart.

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Semiclassical propagation of spin-coherent states

Cited by 7 publications

References 59 publications

Entanglement dynamics via semiclassical propagators in systems of two spins

Entanglement dynamics via semiclassical propagators in systems of two spins

Entanglement dynamics via coherent-state propagators

Entanglement dynamics of spins using a few complex trajectories

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