Test of quantum action for the inverse square potential

Huard, D.J.E.; Kröger, H.; Melkonyan, G.; Moriarty, K.J.M.; Nadeau, Louis

doi:10.1103/physreva.68.034101

Cited by 3 publications

(4 citation statements)

References 32 publications

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“…To address the above questions, we apply the concept of the quantum action, developed in Refs. [15,16,17,18,19,20]. It expresses quantum transition amplitudes…”

Section: Introductionmentioning

confidence: 99%

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Comparison of classical chaos with quantum chaos

Caron¹,

Huard²,

Kröger³

et al. 2004

J. Phys. A: Math. Gen.

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“…To address the above questions, we apply the concept of the quantum action, developed in Refs. [15,16,17,18,19,20]. It expresses quantum transition amplitudes…”

Section: Introductionmentioning

confidence: 99%

“…There may be several such stationary points. The quantum action has been explored numerically [15,16,17,20] for confinement-type potentials (bound state spectrum), e.g. the inverse square potential and polynomial potentials.…”

Section: Introductionmentioning

confidence: 99%

Comparison of classical chaos with quantum chaos

Caron¹,

Huard²,

Kröger³

et al. 2004

J. Phys. A: Math. Gen.

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“…[1]). Because the quantum action has been constructed from the classical action by taking into account quantum fluctuations [19,20,21,22,23,24,25], hence the softening of chaos in the quantum system must be due to quantum fluctuations. We suspect that such softening effect may not solely show up in chaos.…”

Section: Cases Where Quantum Chaos Was Found To Be Weakermentioning

confidence: 99%

“…In Eqs. (24,26) we have expressed the parameters of the quantum action in terms of the parameters of the classical action. However, it remains to compute the energy E (1) .…”

mentioning

confidence: 99%

Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?

Kröger

Laprise

Melkonyan

et al.

Understanding Complex Systems

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Is quantum chaos weaker than classical chaos?

et al. 2004

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We investigate chaotic behavior in a 2-D Hamiltonian system -oscillators with anharmonic coupling. We compare the classical system with quantum system. Via the quantum action, we construct Poincaré sections and compute Lyapunov exponents for the quantum system. We find that the quantum system is globally less chaotic than the classical system. We also observe with increasing energy the distribution of Lyapunov exponts approaching a Gaussian with a strong correlation between its mean value and energy. Introduction. Quantum chaos has been experimentally observed in irregular energy spectra of nuclei, of atoms perturbed by strong electromagnetic fields [1], and in billiard systems [2,3,4]. Irregular patterns have been found in the wave functions of the quantum mechanical stadium billard [5], where scars are reminders of classical motion [6]. Recently, dynamical tunneling in atoms between regular islands has been observed. The transition is enhanced by chaos [7,8]. Spectra of fully chaotic quantum systems can statistically be described by random matrices [9], which corresponds to a level density distribution of Wigner-type, while integrable (nonchaotic) quantum system yield a Poissonian distribution. Here we ask: What happens between these two extremes? For example, an hydrogen atom exposed to a weak exterior magnetic field shows a level distribution, which is neither Poissonian nor Wignerian. Can we compare classical chaos with quantum chaos? And is the quantum system more or less chaotic than the corresponding classical system? Also we address the following problem: An understanding of how classically regular and chaotic phase space is reflected in quantum systems is an open problem. Semiclassical methods of quantisation (EKB, Gutzwiller's trace formula) are not amenable to mixed dynamical systems [10]. Here we suggest a solution using the concept of the quantum action [13,14]. It parametrizes quantum transition amplitudes in

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Test of quantum action for the inverse square potential

Cited by 3 publications

References 32 publications

Comparison of classical chaos with quantum chaos

Comparison of classical chaos with quantum chaos

Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?

Is quantum chaos weaker than classical chaos?

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