Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states

Abstract

Time-independent scattering methods are widely employed to analyze transport in non-Hermitian systems. Their application, however, rests on a critical yet often overlooked assumption: that an incident wave is a pure superposition of scattering states. In practice, any physically realistic, spatially localized wave packet will generally have a nonzero overlap with the system's bound states, thereby violating this premise. While this violation is inconsequential in Hermitian systems, it can invalidate the conventional scattering picture in their non-Hermitian counterparts. The underlying cause is the emergence of time-growing bound states, which manifest as poles of the scattering matrix ($S$ matrix) in the first quadrant of the complex wave-number plane. Any initial overlap with these states becomes exponentially amplified, eventually dominating the long-time dynamics. Consequently, the actual evolution of a wave packet diverges dramatically from the conventional scattering picture, rendering the transmission and reflection coefficients derived from time-independent scattering methods unphysical. Using tight-binding models with non-Hermiticity introduced via imaginary on-site potentials or asymmetric hopping, we demonstrate that parameter regimes supporting such growing states are common. We therefore conclude that an analysis of $S$-matrix poles is an indispensable step to confirm the physical relevance of time-independent scattering calculations in non-Hermitian systems.

14 pages, 6 figures

References in corpus (32)

• Making Sense of Non-Hermitian Hamiltonians
• Non-Hermitian Physics
• The physics of exceptional points
• Coherent Perfect Absorbers: Time-reversed Lasers
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Nonunitary Scaling Theory of Non-Hermitian Localization
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Topological quantum state control through exceptional-point proximity
• Scattering theory with localized non-Hermiticities
• Transport and spectral features in non-Hermitian open systems
• Speeding up entanglement generation by proximity to higher-order exceptional points
• Light Localization induced by Random Imaginary Permittivities
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Asymmetric transmission through a flux-controlled non-Hermitian scattering center
• Time-reversal symmetric resolution of unity without background integrals in open quantum systems
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Wave emission and absorption at spectral singularities
• Imaginary couplings in non-Hermitian coupled-mode theory: Effects on exceptional points of optical resonators
• Pseudo-Hermiticity protects the energy-difference conservation in the scattering
• Asymmetric scattering by non-hermitian potentials
• Coupling-induced nonunitary and unitary scattering in anti-PT-symmetric non-Hermitian systems
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system
• Electron and Spin Transport in the Presence of Complex Absorbing Potential