Quantum-information entropies for highly excited states of single-particle systems with power-type potentials
The asymptotics of the Boltzmann-Shannon information entropy as well as the Renyi entropy for the quantum probability density of a single-particle system with a confining (i.e., bounded below) power-type potential V(x)=x^2k with k∈N and x∈R, is investigated in the position and momentum spaces within...
| Main Authors: | , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | http://hdl.handle.net/10835/4869 https://doi.org/10.1103/PhysRevA.66.062109 |
| _version_ | 1789406750885019648 |
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| author | Dehesa, J. S. Martínez-Finkelshtein, Andrei Sorokin, V. N. |
| author_facet | Dehesa, J. S. Martínez-Finkelshtein, Andrei Sorokin, V. N. |
| author_sort | Dehesa, J. S. |
| collection | DSpace |
| description | The asymptotics of the Boltzmann-Shannon information entropy as well as the Renyi entropy for the quantum probability density of a single-particle system with a confining (i.e., bounded below) power-type potential V(x)=x^2k with k∈N and x∈R, is investigated in the position and momentum spaces within the semiclassical (WKB) approximation. It is found that for highly excited states both physical entropies, as well as their sum, have a logarithmic dependence on its quantum number not only when k=1 (harmonic oscillator), but also for any fixed k. As a by-product, the extremal case k→∞ (the infinite well potential) is also rigorously analyzed. It is shown that not only the position-space entropy has the same constant value for all quantum states, which is a known result, but also that the momentum-space entropy is constant for highly excited states. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-4869 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-48692023-04-12T19:39:44Z Quantum-information entropies for highly excited states of single-particle systems with power-type potentials Dehesa, J. S. Martínez-Finkelshtein, Andrei Sorokin, V. N. The asymptotics of the Boltzmann-Shannon information entropy as well as the Renyi entropy for the quantum probability density of a single-particle system with a confining (i.e., bounded below) power-type potential V(x)=x^2k with k∈N and x∈R, is investigated in the position and momentum spaces within the semiclassical (WKB) approximation. It is found that for highly excited states both physical entropies, as well as their sum, have a logarithmic dependence on its quantum number not only when k=1 (harmonic oscillator), but also for any fixed k. As a by-product, the extremal case k→∞ (the infinite well potential) is also rigorously analyzed. It is shown that not only the position-space entropy has the same constant value for all quantum states, which is a known result, but also that the momentum-space entropy is constant for highly excited states. 2017-06-20T06:28:24Z 2017-06-20T06:28:24Z 2002 info:eu-repo/semantics/article ©2002 American Physical Society http://hdl.handle.net/10835/4869 https://doi.org/10.1103/PhysRevA.66.062109 en https://journals.aps.org/pra/abstract/10.1103/PhysRevA.66.062109 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess American Physical Society |
| spellingShingle | Dehesa, J. S. Martínez-Finkelshtein, Andrei Sorokin, V. N. Quantum-information entropies for highly excited states of single-particle systems with power-type potentials |
| title | Quantum-information entropies for highly excited states of single-particle systems with power-type potentials |
| title_full | Quantum-information entropies for highly excited states of single-particle systems with power-type potentials |
| title_fullStr | Quantum-information entropies for highly excited states of single-particle systems with power-type potentials |
| title_full_unstemmed | Quantum-information entropies for highly excited states of single-particle systems with power-type potentials |
| title_short | Quantum-information entropies for highly excited states of single-particle systems with power-type potentials |
| title_sort | quantum-information entropies for highly excited states of single-particle systems with power-type potentials |
| url | http://hdl.handle.net/10835/4869 https://doi.org/10.1103/PhysRevA.66.062109 |
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