Representations of commutation relations in Dissipative Quantum Mechanics

2021/01/26 by Makarov, K. A., Tsekanovskii, E.
#47N50 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 81Q10 #Secondary: 35P20 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2101.10923

Abstract

We prove the uniqueness theorem for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions that are close to unitaries. We also discuss related mathematical problems of continuous monitoring of quantum systems and provide rigorous foundations for the exponential decay phenomenon of a resonant state in quantum mechanics.

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