Non-Hermitian description of the dynamics of inter-chain pair tunnelling
arXiv:1705.09493 · doi:10.1103/PhysRevA.95.052122
Abstract
We study inter-chain pair tunnelling dynamics based on an exact two-particle solution for a two-leg ladder. We show that the Hermitian Hamiltonian shares a common two-particle eigenstate with a corresponding non-Hermitian Hubbard Hamiltonian in which the non-Hermiticity arises from an on-site interaction of imaginary strength. Our results provides that the dynamic processes of two-particle collision and across-legs tunnelling are well described by the effective non-Hermitian Hubbard Hamiltonian based on the eigenstate equivalence. We also find that any common eigenstate is always associated with the emergence of spectral singularity in the non-Hermitian Hubbard model. This result is valid for both Bose and Fermi systems and provides a clear physical implication of the non-Hermitian Hubbard model.
10 pages, 4 figures
References in corpus (13)
- Theory of single-photon transport in a single-mode waveguide coupled to a cavity containing a two-level atom
- Faster than Hermitian Quantum Mechanics
- No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
- Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
- A non-Hermitian symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
- Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
- PT-Symmetric Wave Chaos
- Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
- Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
- Delta-Function Potential with a Complex Coupling
- Scattering theory with localized non-Hermiticities
- Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree
- Gauging non-Hermitian Hamiltonians