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Unitary evolution for a two-level quantum system in fractional-time scenario
D Cius1, L Menon2, M A F Dos Santos2
1Programa de Pós-Graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, 84030-900 Ponta Grossa, Paraná, Brazil.
Physical Review. E
|December 23, 2022
Summary
Researchers mapped nonunitary time-evolution operators from fractional-time Schrödinger equations to unitary ones. This was achieved using a dynamical Hilbert space and a time-dependent metric operator, enabling standard quantum mechanics interpretations.
Area of Science:
- Quantum Mechanics
- Theoretical Physics
Background:
- Fractional-time Schrödinger equation (FTSE) leads to nonunitary time-evolution operators.
- Nonunitary evolution does not preserve the norm of quantum states, complicating interpretation.
Purpose of the Study:
- To demonstrate the possibility of mapping nonunitary operators to unitary ones.
- To enable standard quantum mechanics interpretations for systems described by FTSE.
Main Methods:
- Utilized a time-dependent non-Hermitian quantum formalism.
- Introduced a dynamical Hilbert space with a time-dependent metric operator.
- Constructed a Hermitian time-dependent Dyson map.
Main Results:
- Successfully mapped nonunitary time-evolution operators to unitary ones.
- Showcased that the system evolves unitarily with respect to the time-dependent metric.
- Provided three examples of Hamiltonians and their corresponding unitary dynamics and Dyson maps.
Conclusions:
- The proposed method allows for a unitary description of quantum systems governed by FTSE.
- This approach facilitates proper interpretation of quantum mechanics for non-Hermitian systems.
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