Wigner function for a particle in an infinite lattice
We study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a one-dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definiti...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2012-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/14/10/103009 |
| _version_ | 1827874479197388800 |
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| author | M Hinarejos A Pérez M C Bañuls |
| author_facet | M Hinarejos A Pérez M C Bañuls |
| author_sort | M Hinarejos |
| collection | DOAJ |
| description | We study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a one-dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definition of the Wigner function in this case and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system, which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states and to their superpositions. |
| first_indexed | 2024-03-12T16:52:54Z |
| format | Article |
| id | doaj.art-ab02feafb30c407889959af9359e340e |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:52:54Z |
| publishDate | 2012-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-ab02feafb30c407889959af9359e340e2023-08-08T11:06:24ZengIOP PublishingNew Journal of Physics1367-26302012-01-01141010300910.1088/1367-2630/14/10/103009Wigner function for a particle in an infinite latticeM Hinarejos0A Pérez1M C Bañuls2Departament de Física Teòrica and IFIC, Universitat de València-CSIC , Dr Moliner 50, E-46100 Burjassot, SpainDepartament de Física Teòrica and IFIC, Universitat de València-CSIC , Dr Moliner 50, E-46100 Burjassot, SpainMax-Planck-Institut für Quantenoptik , Hans-Kopfermann-Strasse 1, Garching D-85748, GermanyWe study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a one-dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definition of the Wigner function in this case and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system, which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states and to their superpositions.https://doi.org/10.1088/1367-2630/14/10/103009 |
| spellingShingle | M Hinarejos A Pérez M C Bañuls Wigner function for a particle in an infinite lattice New Journal of Physics |
| title | Wigner function for a particle in an infinite lattice |
| title_full | Wigner function for a particle in an infinite lattice |
| title_fullStr | Wigner function for a particle in an infinite lattice |
| title_full_unstemmed | Wigner function for a particle in an infinite lattice |
| title_short | Wigner function for a particle in an infinite lattice |
| title_sort | wigner function for a particle in an infinite lattice |
| url | https://doi.org/10.1088/1367-2630/14/10/103009 |
| work_keys_str_mv | AT mhinarejos wignerfunctionforaparticleinaninfinitelattice AT aperez wignerfunctionforaparticleinaninfinitelattice AT mcbanuls wignerfunctionforaparticleinaninfinitelattice |