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Quasi-Hermitian Formulation of Quantum Mechanics Using Two Conjugate Schrodinger Equations
- 1.0574840 - ÚJF 2024 RIV CH eng J - Článek v odborném periodiku
Znojil, Miloslav
Quasi-Hermitian Formulation of Quantum Mechanics Using Two Conjugate Schrodinger Equations.
AXIOMS. Roč. 12, č. 7 (2023), č. článku 644. E-ISSN 2075-1680
Institucionální podpora: RVO:61389005
Klíčová slova: quantum theory of unitary systems * non-Hermitian interaction representation * non-stationary physical inner products * dyadic representation of pure states * schematic quantum model of Big Bang
Obor OECD: Pure mathematics
Impakt faktor: 2, rok: 2022
Způsob publikování: Open access
https://doi.org/10.3390/axioms12070644
To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R(t)) representing another observable. In the language of physics, the information carried by R(t) not equal R+(t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Theta(t). From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrodiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Theta(t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the 'kinematical input' operator R(t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a(t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R(t) mimicking the birth of the Universe ('Big Bang') at t = 0.
Trvalý link: https://hdl.handle.net/11104/0344775
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