Unitarity of the time-evolution and observability of non-Hermitian Hamiltonians for time-dependent Dyson maps
| Autor: | M. A. de Ponte, F. S. Luiz, M. H. Y. Moussa |
|---|---|
| Přispěvatelé: | Universidade de São Paulo (USP), Universidade Estadual Paulista (Unesp) |
| Rok vydání: | 2016 |
| Předmět: |
Quantum Physics
Unitarity time-dependent dyson map Time evolution FOS: Physical sciences Condensed Matter Physics 01 natural sciences Hermitian matrix Atomic and Molecular Physics and Optics 010305 fluids & plasmas symbols.namesake SISTEMAS HAMILTONIANOS 0103 physical sciences Pseudo-Hermiticity symbols Observability time-dependent metric operator 010306 general physics Hamiltonian (quantum mechanics) Quantum Physics (quant-ph) Mathematical Physics Harmonic oscillator Mathematics Mathematical physics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP Web of Science Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP |
| DOI: | 10.48550/arxiv.1611.08286 |
| Popis: | Here we present an strategy for the derivation of a time-dependent Dyson map which ensures simultaneously the unitarity of the time evolution and the observability of a quasi-Hermitian Hamiltonian. The time-dependent Dyson map is derived through a constructed Schr\"{o}dinger-like equation governed by the non-Hermitian Hamiltonian itself; despite its time-dependence our scheme ensures the time-independence of the metric operator, a necessary condition for the observability of the quasi-Hermitian Hamiltonian. As an illustrative example we consider a driven Harmonic oscillator described by a time-dependent non-Hermitian Hamiltonian. After computing the Dyson map and demonstrating the time-independence of the associated metric operator, we successfully derive an eigenvalue equation for this time-dependent Hamiltonian which enable us to analyze the $\mathcal{PT}$-symmetry breaking process. Comment: 10 pages |
| Databáze: | OpenAIRE |
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