Chaoticlike Behavior in a Quantum System without Classical Counterpart

Ashkenazy, Yosef; Horwitz, L. P.; Levitan, Jacob; Lewkowicz, M.; Rothschild, Y.

doi:10.1103/physrevlett.75.1070

Cited by 27 publications

(39 citation statements)

References 11 publications

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“…It is interesting that the Wigner type distribution is found for energies just above the barrier height while the most complex behavior of the wave function is observed for much lower energies [1]. We therefore conjecture that the usual energy level statistics criteria correspond to a signature of chaotic behavior in energy regions for which the classical behavior of the system is similar to its quantum behavior.…”

mentioning

confidence: 91%

“…For example, the double-picket structure of the low-lying spectrum is only approximate. Our results [1] in the study of the wave function with support in the neighborhood of ∼ 1 10 of the barrier height showed very complex behavior. Lewenkopf [7] has found that significant deviations occur for a δ -function barrier.…”

mentioning

confidence: 98%

“…In fact, the wave function of a particle may be thought of as representing an ensemble of points in phase space while its spread as function of time is a measure of the divergence of those points. We have recently considered the time development of a wave packet initially located at the left hand side of a square barrier embedded in an infinite well [1]. We found, in addition to the highly complex behavior of the wave packet, that the spread validity of the Ehrenfest approximation fails much more rapidly than for a wave packet in free space.…”

mentioning

confidence: 99%

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Chaotic signatures in the spectrum of a quantum double well

Berkovits

Ashkenazy

Horwitz

et al. 1997

Physica A: Statistical Mechanics and its Applications

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The spectrum of a double well constructed of a square barrier embedded in an infinite well is analyzed. Level statistics for levels slightly above the barrier show signs of Wigner statistics usually associated with quantum chaos. The correspondence with Wigner statistics improves when an ensemble of systems with slightly different barrier heights is taken, possibly reflecting an adiabatic time-dependent modulation of the barrier.

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confidence: 91%

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confidence: 98%

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confidence: 99%

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Chaotic signatures in the spectrum of a quantum double well

Berkovits

Ashkenazy

Horwitz

et al. 1997

Physica A: Statistical Mechanics and its Applications

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“…Green function for arbitrary number of point interactions inside an infinite well A system so simple as a short-range potential placed inside an 1D infinite well can sometimes present unusual dynamics [32]. In fact, it has been shown that such system can exhibit chaotic-like behavior.…”

Section: B Green Function For Arbitrary Number Of Point Interactionsmentioning

confidence: 99%

Green functions for generalized point interactions in one dimension: A scattering approach

2002

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Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities which may hide important physical aspects of the problem. In this work we present a new method to calculate the exact Green functions for general point interactions in 1D. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients, R and T , to construct G. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of N general point interactions; on a line; on a half-line; under periodic boundary conditions; and confined in a box.

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“…autonomous equations using de Broglie-Bohm's trajectory interpretation, chaos in one-dimensional quantum systems has long been considered impossible [2,3]. We will prove in this paper that chaos phenomenon does exist in one-dimensional quantum systems, if the domain of quantum motions is extended to complex space.…”

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confidence: 94%