2018/05/13 by M. A. Simón Martínez, Álvaro Buendía, Martínez, M. A. Simón +4
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.48550/arxiv.1805.04968
openalex publication_date 2018/05/13 · arxiv created 2018/05/18 · arxiv updated 2018/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss Hamiltonian symmetries and invariants for quantum systems driven by non-Hermitian Hamiltonians. For time-independent Hermitian Hamiltonians, a unitary or antiunitary transformation AHA^† that leaves the Hamiltonian H unchanged represents a symmetry of the Hamiltonian, which implies the commutativity [H,A]=0, and a conservation law, namely the invariance of expectation values of A. For non-Hermitian Hamiltonians, H^† comes into play as a distinct operator that complements H in generalized unitarity relations. The above description of symmetries has to be extended to include also A-pseudohermiticity relations of the form AH=H^† A. A superoperator formulation of Hamiltonian symmetries is provided and exemplified for Hamiltonians of a particle moving in one-dimension considering the set of A operators forming Klein's 4-group: parity, time-reversal, parity&time-reversal, and unity. The link between symmetry and conservation laws is discussed and shown to be more subtle for non-Hermitian than for Hermitian Hamiltonians.