Quantum revivals and carpets in some exactly solvable systems

Abstract

We consider the revival properties of quantum systems with an eigenspectrum E_{n} proportional to n^{2}, and compare them with the simplest member of this class - the infinite square well. In addition to having perfect revivals at integer multiples of the revival time t_{R}, these systems all enjoy perfect fractional revivals at quarterly intervals of t_{R}. A closer examination of the quantum evolution is performed for the Poeschel-Teller and Rosen-Morse potentials, and comparison is made with the infinite square well using quantum carpets.

5 pages, 5 figures (1 new), minor additions, to appear in J. Phys. A

References in corpus (3)

• Asymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space
• Superrevivals in the quantum dynamics of a particle confined in a finite square well potential
• Clones and other interferance effects in the evolution of angular momentum coherent states

Cited by in corpus (10)

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• Coherent states of P{ö}schl-Teller potential and their revival dynamics
• Coherent state of a nonlinear oscillator and its revival dynamics
• Fractal Noise in Quantum Ballistic and Diffusive Lattice Systems
• Fermionic quantum carpets: From canals and ridges to solitonlike structures
• Single- to many-body crossover of a quantum carpet
• Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties
• Perfect Quantum State Revivals: Designing Arbitrary Potentials with Specified Energy Levels