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Hilbert space geometry change by a nonadiabatic electromagnetic field

  • Ivan Georgiev Koprinkov
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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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Cite

BibTeXRIS
BibTeX
@misc{koprinkov2026hilbert,
  title = {{Hilbert space geometry change by a nonadiabatic electromagnetic field}},
  author = {Ivan Georgiev Koprinkov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06800},
  eprint = {2609.06800},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06800},
}
RIS
TY  - UNPB
TI  - Hilbert space geometry change by a nonadiabatic electromagnetic field
AU  - Ivan Georgiev Koprinkov
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06800
UR  - https://arxiv.org/abs/2609.06800
AB  - 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.
ER  -