Hilbert space geometry change by a nonadiabatic electromagnetic field

Abstract:A change in the geometry of the Hilbert space of a quantum system interacting with a nonadiabatic electromagnetic field is found. To identify its physical origin, the evolution of orthogonality to non-orthogonality of the states of the quantum system has been investigated based on the matrix elements of the quantum states in three main physical cases: a quantum system in zero external field (closed quantum system), a quantum system in slowly changing (adiabatic) field, and a quantum system in rapidly changing (nonadiabatic) field. The quantum states are orthogonal in the first two cases and change to non-orthogonal in a nonadiabatic field, following continuously the parameters of the field. A time-dependent Fubini-Study metric of the Hilbert space can be determined based on the matrix elements of the quantum states in the nonadiabatic case. Such a dynamical metric of the Hilbert space in quantum mechanics resembles the dynamical metric of spacetime in general relativity.

arXiv:2609.06800 [quant-ph]

(or arXiv:2609.06800v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.06800 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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