Fractional wave-function revivals in the infinite square well

Aronstein, David L.; Stroud, C. R.

doi:10.1103/physreva.55.4526

Cited by 138 publications

(154 citation statements)

References 42 publications

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“…Such a relocalization of the wave packet is what is referred to as revival [4,5]. Fractional revival occurs when a number of smaller packets seen as little clones of the original one form at certain sites and show local periodicities [4,6]. Its realization in a spin chain would also allow to transport information with high efficiency via one of the clones.…”

Section: Introductionmentioning

confidence: 99%

Quantum spin chains with fractional revival

2016

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Abstract. A systematic study of fractional revival at two sites in XX quantum spin chains is presented and analytic models with this phenomenon are exhibited. The generic models have two essential parameters and a revival time that does not depend on the length of the chain. They are obtained by combining two basic ways of realizing fractional revival in a spin chain each bringing one parameter. The first proceeds through isospectral deformations of spin chains with perfect state transfer. The second arises from the recurrence coefficients of the para-Krawtchouk polynomials with a bi-lattice orthogonality grid. It corresponds to an analytic model previously identified that can possess perfect state transfer in addition to fractional revival.

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Section: Introductionmentioning

confidence: 99%

Quantum spin chains with fractional revival

2016

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“…At time t = T rev , the wave packet is rebuilt either identical or only resemblant to the original one, depending on the importance of the neglected terms higher than quadratic. In some very specific cases, the fractional wave packets are clones of the initial one as studied in the most recent paper [2] and the revival is exact. This scenario has been validated in the most spectacular manner by several authors for a wave packet in a circular orbit of the hydrogen atom [3], see also [4] and by Boris et al [5] for an elliptic orbit.…”

Section: Introductionmentioning

confidence: 99%

“…Until the work of [1] it was not realized that they could evolve according to an universal scenario. For a diatomic molecule or for a symmetric rotor, the spectrum of which are quadratic in quantum number like for the systems discussed in [2,24], the universal scenario is exact and repeats with period T rev . The main question is whether the fractional wave packets are clones or just resemblant to the initial ones.…”

Section: Introductionmentioning

confidence: 99%

“…The recurrences studied in ref. [1][2][3][4][5][6][7][8][9][10][11][12] are all devoted to wave packets and can be mathematically explained in terms of special Gauss'sums. It is necessary to point out that such sums were earlier extensively used in the physical litterature by Berry and Golberg [13], and Berry [14] who studied the full time evolution of the propagator of a nuclear spin with an hamiltonian of the form l 2 z /2J.…”

Section: Introductionmentioning

confidence: 99%

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Clones and other interference effects in the evolution of angular-momentum coherent states

Rozmej

Arvieu²

1998

Phys. Rev. A

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The aim of this article is to present the interference effects which occur during the time evolution of simple angular wave packets (WP) which can be associated to a diatomic rigid molecule (heteronuclear) or to a quantum rigid body with axial symmetry like a molecule or a nucleus. The time evolution is understood entirely within the frame of fractional revivals discovered by Averbukh and Perelman since the energy spectrum is exactly quadratic. Our objectives are to study how these interference effects differ when there is a change of the initial WP. For this purpose we introduce a two parameter set of angular momentum coherent states. From one hand this set emerge quite naturally from the three dimensional coherent states of the harmonic oscillator, from another hand this set is shown to be buit from intelligent spin states. By varying one parameter (η) a scenario of interferences occur on the sphere at fractional times of the revival time that strongly depends on η. For η = ±1 the WP, which coincides with a WP found by Mostowski, is a superposition of Bloch or Radcliffe's states and clone exactly in time according to a scenario found for the infinite square well in one dimension and also for the two dimensional rotor. In the context of intelligent spin states it is natural to study also the evolution by changing η. For η = 0 the WP is called linear and produces in time a set of rings with axial symmetry over the sphere. The WP for other values of η are called elliptic and sets of fractional waves are generated which make a transition between two symm etries. We call 'mutants' these fractional waves. For specific times a clone is produced that stands among the mutants. Therefore the change in η produces novel change in the quantum spread on the sphere. We have also constructed simple coherent states for a symmetric rotor which are applicable to molecules and nuclei. Their time evolution also shows a cloning mechanism for the rational ratio of moments of inertia. For irrational values of this ratio, the scenario of partial revivals completed by Bluhm, Kostelecky and Tudose is valid.

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“…(20) must also satisfy the general theorem in Eqn. (14). To lowest nontrivial order in t (O(t 2 )), the modulus of A(t) in this case for short times is…”

Section: Free-particle Gaussian Wave Packetsmentioning

confidence: 99%

Analytic Results for Gaussian Wave Packets in Four Model Systems: II. Autocorrelation Functions

Robinett

Bassett

2004

Found Phys Lett

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The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, ψ(x, t), with its initial value, ψ(x, 0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrödinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called 'inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.

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Fractional wave-function revivals in the infinite square well

Cited by 138 publications

References 42 publications

Quantum spin chains with fractional revival

Quantum spin chains with fractional revival

Clones and other interference effects in the evolution of angular-momentum coherent states

Analytic Results for Gaussian Wave Packets in Four Model Systems: II. Autocorrelation Functions

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