dorsal/arxiv
View SchemaQuantum wave packet revivals
| Authors | R. W. Robinett |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401031 |
| URL | https://arxiv.org/abs/quant-ph/0401031 |
| DOI | 10.1016/j.physrep.2003.11.002 |
Abstract
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.
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"abstract": "The numerical prediction, theoretical analysis, and experimental verification\nof the phenomenon of wave packet revivals in quantum systems has flourished\nover the last decade and a half. Quantum revivals are characterized by\ninitially localized quantum states which have a short-term, quasi-classical\ntime evolution, which then can spread significantly over several orbits, only\nto reform later in the form of a quantum revival in which the spreading\nreverses itself, the wave packet relocalizes, and the semi-classical\nperiodicity is once again evident. Relocalization of the initial wave packet\ninto a number of smaller copies of the initial packet (`minipackets\u0027 or\n`clones\u0027) is also possible, giving rise to fractional revivals. Systems\nexhibiting such behavior are a fundamental realization of time-dependent\ninterference phenomena for bound states with quantized energies in quantum\nmechanics and are therefore of wide interest in the physics and chemistry\ncommunities.\n We review the theoretical machinery of quantum wave packet construction\nleading to the existence of revivals and fractional revivals, in systems with\none (or more) quantum number(s), as well as discussing how information on the\nclassical period and revival time is encoded in the energy eigenvalue spectrum.\nWe discuss a number of one-dimensional model systems which exhibit revival\nbehavior, including the infinite well, the quantum bouncer, and others, as well\nas several two-dimensional integrable quantum billiard systems. Finally, we\nbriefly review the experimental evidence for wave packet revivals in atomic,\nmolecular, and other systems, and related revival phenomena in condensed matter\nand optical systems.",
"arxiv_id": "quant-ph/0401031",
"authors": [
"R. W. Robinett"
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"doi": "10.1016/j.physrep.2003.11.002",
"title": "Quantum wave packet revivals",
"url": "https://arxiv.org/abs/quant-ph/0401031"
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