Mathematical Models for Unstable Quantum Systems and Gamow States

Entropy

Sebastián Fortín¹  Manuel Gadella²  Juan Pablo Jorge³  Marcelo Losada⁴ 

[1] CONICET, Universidad de Buenos Aires, Buenos Aires C1053 CABA, Argentina;Departamento de Física Teórica, Atómica y Optica, Universidad de Valladolid, Paseo Belén 7, 47011 Valladolid, Spain;Facultad de Filosofía y Letras, Universidad de Buenos Aires, Puan 480, Buenos Aires C1053 CABA, Argentina;Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Av. Medina Allende s/n,Córdoba 5000, Argentina;

关键词: unstable quantum systems;    Gamow vectors;    rigged Hilbert space;    Gamow functionals;    coherent Gamow states;    intrinsic irreversibility and Loschmidt echo;   

DOI  :  10.3390/e24060804

来源: DOAJ

【 摘 要 】

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo.

【 授权许可】

Unknown