Non-Bloch edge dynamics of non-Hermitian lattices

• URL: http://arxiv.org/abs/2503.13671v1
• Date: Mon, 17 Mar 2025 19:22:35 GMT
• Title: Non-Bloch edge dynamics of non-Hermitian lattices
• Authors: Wen-Tan Xue, Fei Song, Yu-Min Hu, Zhong Wang,
• Abstract summary: We investigate the time evolution of waves around the edge of non-Hermitian lattices.<n>The non-Hermitian skin effect tends to localize the wave to the edge.<n>Our work provides a coherent theory for characterizing the real-time edge dynamics of non-Hermitian lattices.
• Score: 2.2852725150656603
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The non-Hermitian skin effect, i.e., the localization of nominally bulk modes, not only drastically reshapes the spectral properties of non-Hermitian systems, but also dramatically modifies the real-time dynamics therein. Here we investigate the time evolution of waves (or quantum-mechanical particles) initialized around the edge of non-Hermitian lattices. The non-Hermitian skin effect tends to localize the wave to the edge, meaning that the real-time dynamics differs from the Bloch-theory picture. We focus on the long-time decay or growth rate of wave function, which is quantified by the Lyapunov exponents. These exponents can be obtained from the saddle points in the complex momentum space. We propose an efficient yet unambiguous criterion for identifying the dominant saddle point that determines the Lyapunov exponents. Our criterion can be precisely formulated in terms of a mathematical concept known as the Lefschetz thimble. Counterintuitively, the seemingly natural criterion based on the imaginary part of the energy fails. Our work provides a coherent theory for characterizing the real-time edge dynamics of non-Hermitian lattices. Our predictions are testable in various non-Hermitian physical platforms.

Related papers

• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Kinked linear response from non-Hermitian cold-atom pumping [3.5932002706017556]
  We find that non-Hermiticity gives rise to abrupt and prominent kinks in the semi-classical wave packet trajectories of quantum gases. This physically stems from a hitherto underappreciated intrinsic non-locality from non-Hermitian pumping. Our results showcase unique non-monotonic behavior from non-Hermitian pumping beyond the non-Hermitian skin effect.
  arXiv  Detail & Related papers  (2023-06-22T18:00:13Z)
• Observation of non-Hermitian edge burst in quantum dynamics [4.836111090297333]
  We experimentally observe a boundary-induced dynamical phenomenon known as the non-Hermitian edge burst. In contrast to the eigenstate localization, the edge burst represents a generic non-Hermitian dynamical phenomenon that occurs in real time.
  arXiv  Detail & Related papers  (2023-03-22T18:00:02Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model [44.58985907089892]
  How the property of quantum many-body system especially the phase transition will be affected by the non-hermiticity remains unclear. We show that there is a continuous phase transition induced by the non-hermiticity in QCP. We observe that the order parameter and susceptibility display infinitely even for finite size system, since non-hermiticity endows universality many-body system with different singular behaviour from classical phase transition.
  arXiv  Detail & Related papers  (2022-09-22T01:11:28Z)
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model [12.632098351321218]
  We investigate the role of non-Hermiticity in the Chern insulating Haldane model on a dice lattice. We introduce non-Hermiticity into this model in two ways -- through balanced non-Hermitian gain and loss, and by non-reciprocal hopping in one direction. Our results place the dice-Haldane model as an exciting platform to explore non-Hermitian physics.
  arXiv  Detail & Related papers  (2022-07-29T11:13:09Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Probing non-Hermitian phase transitions in curved space via quench dynamics [0.0]
  Non-Hermitian Hamiltonians are relevant to describe the features of a broad class of physical phenomena. We study the interplay of geometry and non-Hermitian dynamics by unveiling the existence of curvature-dependent non-Hermitian phase transitions.
  arXiv  Detail & Related papers  (2020-12-14T19:47:59Z)
• Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions [0.41998444721319217]
  We study the dynamics of an initial end state in nonreciprocal Su-Schrieffer-Heeger models under open boundary conditions. We find that it is dynamically more robust than its Hermitian counterpart, because the non-Hermitian skin effect can suppress the part leaking to the bulk sites.
  arXiv  Detail & Related papers  (2020-08-28T06:07:30Z)
• Analog cosmological reheating in an ultracold Bose gas [58.720142291102135]
  We quantum-simulate the reheating-like dynamics of a generic cosmological single-field model in an ultracold Bose gas. Expanding spacetime as well as the background oscillating inflaton field are mimicked in the non-relativistic limit. The proposed experiment has the potential of exploring the evolution up to late times even beyond the weak coupling regime.
  arXiv  Detail & Related papers  (2020-08-05T18:00:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.