New families of non-parity-time-symmetric complex potentials with all-real spectra
Abstract
New families of non-parity-time-symmetric complex potentials with all-real spectra are derived by the supersymmetry method and the pseudo-Hermiticity method. With the supersymmetry method, we find families of non-parity-time-symmetric complex partner potentials, which share the same spectrum as base potentials with known real spectra, such as the (complex) Wadati potentials. Different from previous supersymmetry derivations of potentials with real spectra, our derivation does not utilize discrete eigenmodes of base potentials. As a result, our partner potentials feature explicit analytical expressions, which contain free functions. With the pseudo-Hermiticity method, we derive a new class of non-parity-time-symmetric complex potentials with free functions and constants, whose eigenvalues appear as conjugate pairs. This eigenvalue symmetry forces the spectrum to be all-real for a wide range of choices of these functions and constants in the potential. Tuning these free functions and constants, phase transition can also be induced, where conjugate pairs of complex eigenvalues emerge in the spectrum.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 01, 2020
- Source ID
- 10.1063/1.5124255
Entities
People
- Bijan Bagchi
- Jianke Yang
Organizations
- Air Force Office of Scientific Research
- National Science Foundation
- Shiv Nadar Institution of Eminence Deemed to be University
- University of Vermont