Unitary evolution for a two-level quantum system in fractional-time scenario
arXiv:2208.13858 · doi:10.1103/PhysRevE.106.054126
Abstract
The time-evolution operator obtained from the fractional-time Schrödinger equation (FTSE) is said to be non-unitary since it does not preserve the norm of the vector state in time. As done in the time-dependent non-Hermitian quantum formalism, for a traceless non-Hermitian two-level quantum system, we demonstrate that it is possible to map the non-unitary time-evolution operator in a unitary one. It is done by considering a dynamical Hilbert space with a time-dependent metric operator, constructed from a Hermitian time-dependent Dyson map, in respect to which the system evolves in a unitary way, and the standard quantum mechanics interpretation can be made properly. To elucidate our approach, we consider three examples of Hamiltonian operators and their corresponding unitary dynamics obtained from the solutions of FTSE, and the respective Dyson maps.
arXiv comment11 pages, 6 figures
References in corpus (23)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- Fractional Quantum Mechanics and Levy Path Integrals
- Fractional Quantum Mechanics
- Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
- Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
- Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
- Fractional Schrödinger equation in optics
- Time fractional Schrodinger equation
- symmetry in a fractional Schrödinger equation
- Time-dependent version of cryptohermitian quantum theory
- Unitary quantum evolution for time-dependent quasi-Hermitian systems with non-observable Hamiltonians
- Time Dependent -Symmetric Quantum Mechanics
- On fractional time quantum dynamics
- Time Fractional Quantum Mechanics
- On the invariant method for the time-dependent non-Hermitian Hamiltonians
- Mending the broken PT-regime via an explicit time-dependent Dyson map
- Comment on "Fractional quantum mechanics" and "Fractional Schroedinger equation"
- Spontaneous emission from a two-level atom in anisotropic one-band photonic crystals: a fractional calculus approach
- Eternal life of entropy in non-Hermitian quantum systems
- Enhancement of photon creation through the pseudo-Hermitian dynamical Casimir effect
- Quantum dynamics and relaxation in comb turbulent diffusion