Quantum recurrences: Probe to study quantum chaos

Saif, Farhan

doi:10.1103/physreve.62.6308

Cited by 18 publications

(17 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(183), and the Gaussian expansion coefficients in Eqn. (153) for the a n , we can evaluate the time-dependent Wigner function for the infinite well. As examples, we show in Figs.…”

Section: Phase-space Picture Of Fractional Revivals Using the Wigner mentioning

confidence: 99%

See 1 more Smart Citation

Quantum wave packet revivals

2004

View full text Add to dashboard Cite

The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially localized quantum states which have a short-term, quasi-classical time evolution, which then can spread significantly over several orbits, only to reform later in the form of a quantum revival in which the spreading reverses itself, the wave packet relocalizes, and the semi-classical periodicity is once again evident. Relocalization of the initial wave packet into a number of smaller copies of the initial packet ('minipackets' or 'clones') is also possible, giving rise to fractional revivals. Systems exhibiting such behavior are a fundamental realization of time-dependent interference phenomena for bound states with quantized energies in quantum mechanics and are therefore of wide interest in the physics and chemistry communities.We review the theoretical machinery of quantum wave packet construction leading to the existence of revivals and fractional revivals, in systems with one (or more) quantum number(s), as well as discussing how information on the classical period and revival time is encoded in the energy eigenvalue spectrum. We discuss a number of one-dimensional model systems which exhibit revival behavior, including the infinite well, the quantum bouncer, and others, as well as several two-dimensional integrable quantum billiard systems. Finally, we briefly review the experimental evidence for wave packet revivals in atomic, molecular, and other systems, and related revival phenomena in condensed matter and optical systems.

show abstract

“…(183), and the Gaussian expansion coefficients in Eqn. (153) for the a n , we can evaluate the time-dependent Wigner function for the infinite well. As examples, we show in Figs.…”

Section: Phase-space Picture Of Fractional Revivals Using the Wigner mentioning

confidence: 99%

“…(The effect on the bouncer of the application of a periodic external driving force, especially on the structure of revivals, has also been discussed (152), (153).) The Schrödinger equation for this system can be written as…”

Section: Energy Eigenfunctions and Eigenvaluesmentioning

confidence: 99%

Quantum wave packet revivals

2004

View full text Add to dashboard Cite

show abstract

“…Quantum recurrences in periodically driven quantum chaotic systems [15,16,17,18] and in general higher dimensional systems are proved to be generic [19,20]. The phenomena is vital to extend the horizons of nanotechnology and to develop newer experimental techniques to study surface structures with atomic size resolution [21].…”

Section: Introductionmentioning

confidence: 99%

Quantum recurrences in driven power-law potentials

2006

Self Cite

View full text Add to dashboard Cite

The recurrence phenomena of an initially well localized wave packet are studied in periodically driven power-law potentials. For our general study we divide the potentials in two kinds, namely tightly binding and loosely binding potentials. In the presence of an external periodically modulating force, these potentials may exhibit classical and quantum chaos. The dynamics of a quantum wave packet in the modulated potentials displays recurrences at various time scales. We develop general analytical relations for these times and discuss their parametric dependence.

show abstract

“…We explain these recurrences of a quantum particle in a quantumchaotic system, which manifests complex dynamics in its classical counterpart. Due to their dependence on modulation effects, these dynamical recurrences are different from those * ayubok@gmail.com † farhan@qau.edu.pk taking place in an undriven system and may be considered as a probe to study quantum chaos [24]. Dynamical recurrences in a bounded driven system originate from the simultaneous excitation of discrete quasienergy states [25,26].…”

Section: Introductionmentioning

confidence: 99%

Delicate and robust dynamical recurrences of matter waves in driven optical crystals

Ayub

Saif

2012

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

We study dynamical recurrences of a Bose-Einstein condensate in an optical crystal subject to a periodic external driving force. The recurrence behavior of the condensate is analyzed as a function of time close to nonlinear resonances occurring in the classical counterpart. Our mathematical formalism for the recurrence time scales is presented as delicate recurrences, which take place, for instance, when the lattice is perturbed weakly and robust recurrences, which may manifest themselves for a sufficiently strong external driving force. The analysis not only is valid for a dilute condensate, but also is applicable for the strongly interacting homogeneous condensate provided; the external modulation causes no significant change in the density profile of the condensate. We explain the parametric dependence of the dynamical recurrence times, which can easily be realized in laboratory experiments. In addition, we find good agreement between the obtained analytical results and the numerical calculations.

show abstract

Quantum recurrences: Probe to study quantum chaos

Cited by 18 publications

References 24 publications

Quantum wave packet revivals

Quantum wave packet revivals

Quantum recurrences in driven power-law potentials

Delicate and robust dynamical recurrences of matter waves in driven optical crystals

Contact Info

Product

Resources

About