Can Wigner distribution functions with collisions satisfy complete positivity and energy conservation?
Villani, Matteo (Universitat Autònoma de Barcelona. Departament d'Enginyeria Electrònica)
Oriols, Xavier (Universitat Autònoma de Barcelona. Departament d'Enginyeria Electrònica)

Data:	2021
Resum:	To avoid the computational burden of many-body quantum simulation, the interaction of an electron with a photon (phonon) is typically accounted for by disregarding the explicit simulation of the photon (phonon) degree of freedom and just modeling its effect on the electron dynamics. For quantum models developed from the (reduced) density matrix or its Wigner-Weyl transformation, the modeling of collisions may violate complete positivity (precluding the typical probabilistic interpretation). In this paper, we show that such quantum transport models can also strongly violate the energy conservation in the electron-photon (electron-phonon) interactions. After comparing collisions models to exact results for an electron interacting with a photon, we conclude that there is no fundamental restriction that prevents a collision model developed within the (reduced) density matrix or Wigner formalisms to satisfy simultaneously complete positivity and energy conservation. However, at the practical level, the development of such satisfactory collision model seems very complicated. Collision models with an explicit knowledge of the microscopic state ascribed to each electron seems recommendable (Bohmian conditional wavefunction), since they allow to model collisions of each electron individually in a controlled way satisfying both complete positivity and energy conservation.
Ajuts:	European Commission 765426 Agencia Estatal de Investigación RTI2018-097876-B-C21 Agència de Gestió d'Ajuts Universitaris i de Recerca 001-P-001644
Nota:	Altres ajuts: acords transformatius de la UAB
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Matter-light interaction ; Wigner Function ; Complete positivity ; Energy conservation ; Bohmian conditional wavefunction
Publicat a:	Journal of Computational Electronics, Vol. 20, Issue 6 (December 2021) , p. 2232-2244, ISSN 1572-8137

DOI: 10.1007/s10825-021-01798-1

13 p, 3.9 MB

El registre apareix a les col·leccions:
Articles > Articles de recerca
Articles > Articles publicats