--- title: "Translations and reflections on the torus: Identities for discrete Wigner functions and transforms • CBPF Index" description: "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." canonical_url: "https://index.cbpf.br/es/publicacoes/6ad2a767639f62b11adbcfd7" locale: es meta: "og:description": "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~VHJhbnNsYXRpb25zIGFuZCByZWZsZWN0aW9ucyBvbiB0aGUgdG9ydXM6IElkZW50aXRpZXMgZm9yIGRpc2NyZXRlIFdpZ25lciBmdW5jdGlvbnMgYW5kIHRyYW5zZm9ybXM%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_~TWFyY29zIFNhcmFjZW5vOyBBLiBNLiBPem9yaW8gZGUgQWxtZWlkYQ%2Cdetalhe_~MTUvMDgvMjAxOA%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmNmZDci%2Cs_CSBBnV3js0fG42iE.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Translations and reflections on the torus: Identities for discrete Wigner functions and transforms • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~VHJhbnNsYXRpb25zIGFuZCByZWZsZWN0aW9ucyBvbiB0aGUgdG9ydXM6IElkZW50aXRpZXMgZm9yIGRpc2NyZXRlIFdpZ25lciBmdW5jdGlvbnMgYW5kIHRyYW5zZm9ybXM%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_~TWFyY29zIFNhcmFjZW5vOyBBLiBNLiBPem9yaW8gZGUgQWxtZWlkYQ%2Cdetalhe_~MTUvMDgvMjAxOA%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmNmZDci%2Cs_CSBBnV3js0fG42iE.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Nota de Física****Publicado** # **Translations and reflections on the torus: Identities for discrete Wigner functions and transforms** **Marcos Saraceno; A. M. Ozorio de Almeida** 15/08/2018 [**Descargar PDF **0,4 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbcfd7/pdf) [**Contactar al responsable**](mailto:apub@cbpf.br?subject=Translations%20and%20reflections%20on%20the%20torus%3A%20Identities%20for%20discrete%20Wigner%20functions%20and%20transforms) ## **Datos de la publicación**
Autores
Marcos Saraceno; A. M. Ozorio de Almeida
Tipo
Nota de Física
Estado
Publicado
Fecha de publicación
15/08/2018
Descripción
A finite Hilbert space can be associated to a periodic phase space, that is, a torus. A finite subgroup of operators corresponding to reflections and translations on the torus form respectively the basis for the discrete Weyl representation, including the Wigner function, and for its Fourier conjugate, the chord representation. They are invariant under Clifford transformations and obey analogous product rules to the continuous representations, so allowing for the calculation of expectations and correlations for observables. We here import new identities from the continuum for products of pure state Wigner and chord functions, involving, for instance the inverse phase space participation ratio and correlations of a state with its translate. New identities are derived involving transition Wigner or chord functions of transition operators |ψ1ψ2|. Extension of the reflection and translation operators to a doubled torus phase space leads to the representation of superoperators and so to the construction of the propagator of Wigner functions from the Weyl representation of the evolution operator.
Año
2018
Número
CBPF-NF-007/18
Vínculo con tesis
No
Vínculo con beca
No
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