Quantum phase transition in an effective three-mode model of interacting bosons.

In this work we study an effective three-mode model describing interacting bosons. These bosons can be considered as exciton-polaritons in a semiconductor microcavity at the magic angle. This model exhibits quantum phase transition (QPT) when the parameters of the corresponding Hamiltonian are continuously varied. The properties of the Hamiltonian spectrum (e.g., the distance between two adjacent energy levels) and the phase space structure of the thermodynamic limit of the model are used to indicate QPT. The relation between spectral properties of the Hamiltonian and the corresponding classical frame of the thermodynamic limit of the model is established as indicative of QPT. The average number of bosons in a specific mode and the entanglement properties of the ground state as functions of the parameters are used to characterize the order of the transition and also to construct a phase diagram. Finally, we verify our results for experimental data obtained for a setting of exciton-polaritons in a semiconductor microcavity.

Semiclassical corrections to the large- N limit of Dicke's model.

We use a semiclassical expansion as an alternative derivation of the well-known, rigorous result obtained by Hepp and Lieb for the classical limit of the spin-boson model. We also explicitly derive correction terms to the classical limit previously obtained in the context of Heisenberg equations of motion. We analyze the size and shape of the N (number of atoms) vs t (time) domain whithin which the corrections so obtained are useful.

Entanglement and classical instabilities: fingerprints of electron-hole-to-exciton phase transition in a simple model.

We propose a schematic model to study the formation of excitons in bilayer electron systems. The phase transition is signalized both in the quantum and classical versions of the model. In the present contribution we show that not only the quantum ground state but also higher energy states, up to the energy of the corresponding classical separatrix orbit, "sense" the transition. We also show two types of one-to-one correspondences in this system: On the one hand, between the changes in the degree of entanglement for these low-lying quantum states and the changes in the density of energy levels; on the other hand, between the variation in the expected number of excitons for a given quantum state and the behavior of the corresponding classical orbit.

Quantum-classical transition of the open quartic oscillator: The role of the environment.

We investigate the classical and quantum dynamics of the open quartic oscillator model. Typically quantum behavior such as collapses and revivals (also squeezing) are induced by the nonlinearity of the model. We show that purely diffusive environments, as expected, attenuate such phenomena. We obtain analytical results in both regimes classical and quantum and discuss the effect of a diffusive reservoir in the two cases. We show that "separation times" as usually defined in the literature are strongly observable (and initial condition) dependent, rendering a solid definition of a unique classical limit rather difficult. In particular, the separation time for the variance can be smaller than that for the expectation value of the position of the centroid of the wave packet. We find a hierarchy of time scales which depends on the observable and the reservoir.

Quantum time scales and the classical limit: analytic results for some simple systems.

We set up a semiclassical approximation which helps us clarify by means of several simple examples the rich variety of time scale in the quantum domain. The underlying structure of quantum and classical mechanics is so completly different that it is naive to expect to reach a classical regime by counting powers of the quantum scale variant Planck's over 2pi. We show although it is possible to define a time scale for nonclassical phenomena, but it is impossible to characterize quantum dynamics through a unique time scale, such as Ehrenfest's time. We use simple systems to critically discuss and illustrate these features of the quantum-classical limit.

Rapid decoherence in integrable systems: a border effect.

We show that rapid decoherence, usually associated with chaotic dynamics, is not necessarily a hallmark of nonintegrability: border effects in integrable systems may produce similarly drastic decoherence rates. These can be found when the subsystem under observation possesses an energy limitation as, e.g., in the N-atom Jaynes-Cummings model. We show for this model that special initial coherent wave packets exhibit entropy production rates strikingly similar to the chaotic case. Also, a (de)localization phenomenon is found to be a function of the proximity to the phase-space border.

On the interplay between symmetry breaking, integrability, and chaos in the semiclassical limit of the Heisenberg system.

In this work we present a detailed numerical analysis of the interplay between symmetry breaking, integrability, and chaos in the two- and three-spin Heisenberg models. The results suggest that a very simple and powerful tool to convey such information are the plots of the energy level spacings Delta(n) versus the energy level index n, together with the correlation plots Delta(n+1)xDelta(n). When integrability is broken, these plots are shown to identify very sharply an energy below which one has chaotic behavior. The particularly strong point in favor of such analysis is that it can be useful in partially chaotic regimes. (c) 1995 American Institute of Physics.