Hilbert space geometry change by a nonadiabatic electromagnetic field

• URL: http://arxiv.org/abs/2609.06800v1
• Date: Sun, 06 Sep 2026 19:38:23 GMT
• Title: Hilbert space geometry change by a nonadiabatic electromagnetic field
• Abstract summary: A change in the geometry of the Hilbert space of a quantum system interacting with a nonadiabatic electromagnetic field is found.<n>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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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