Complex semiclassical theory for non-Hermitian quantum systems

Abstract

Non-Hermitian quantum systems exhibit fascinating characteristics such as non-Hermitian topological phenomena and skin effect, yet their studies are limited by the intrinsic difficulties associated with their eigenvalue problems, especially in larger systems and higher dimensions. In Hermitian systems, the semiclassical theory has played an active role in analyzing spectrum, eigenstate, phase, transport properties, etc. Here, we establish a complex semiclassical theory applicable to non-Hermitian quantum systems by an analytical continuation of the physical variables such as momentum, position, time, and energy in the equations of motion and quantization condition to the complex domain. Further, we propose a closed-orbit scheme and physical meaning under such complex variables. We demonstrate that such a framework straightforwardly yields complex energy spectra and quantum states, topological phases and transitions, and even the skin effect in non-Hermitian quantum systems, presenting an unprecedented perspective toward nontrivial non-Hermitian physics, even with larger systems and higher dimensions.

16 pages, 10 figures

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Topological Origin of Non-Hermitian Skin Effects
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Topological phase transition in non-Hermitian quasicrystals
• New topological invariants in non-Hermitian systems

Cited by in corpus (7)

• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Extrinsic Mechanisms of Phonon Magnetic Moment
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Quantum-to-semiclassical Husimi dynamics of non-Hermitian localization transitions
• Recurrence method in Non-Hermitian Systems
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions