Emergent non-Hermitian physics in generalized Lotka-Volterra model

• URL: http://arxiv.org/abs/2207.04473v2
• Date: Wed, 6 Sep 2023 02:37:19 GMT
• Title: Emergent non-Hermitian physics in generalized Lotka-Volterra model
• Authors: Tengzhou Zhang and Zi Cai
• Abstract summary: We study the non-Hermitian physics emerging from a predator-prey ecological model described by a generalized Lotka-Volterra equation. In the phase space, this nonlinear equation exhibits both chaotic and localized dynamics, which are separated by a critical point.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we study the non-Hermitian physics emerging from a predator-prey ecological model described by a generalized Lotka-Volterra equation. In the phase space, this nonlinear equation exhibits both chaotic and localized dynamics, which are separated by a critical point. These distinct dynamics originate from the interplay between the periodicity and non-Hermiticity of the effective Hamiltonian in the linearized equation of motion. Moreover, the dynamics at the critical point, such as algebraic divergence, can be understood as an exceptional point in the context of non-Hermitian physics.

Related papers

• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{PT}$ symmetry [49.1574468325115]
  We analyze models governed by the replicator equation of evolutionary game theory and related Lotka-Volterra systems of population dynamics. We study the emergence of exceptional points in two cases: (a) when the governing symmetry properties are tied to global properties of the models, and (b) when these symmetries emerge locally around stationary states.
  arXiv  Detail & Related papers  (2024-11-19T02:15:59Z)
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Non-Hermitian glide-time symmetry [17.423012765773063]
  We study a one-dimensional non-Hermitian system with glide-time reversal (GT) symmetry. We discover that the GT symmetry leads to unique physical properties and enables rich dynamic phenomena in non-Hermitian systems. Remarkably, we reveal the dynamic NHSEs that exhibit diverse behaviors across distinct dynamic phases.
  arXiv  Detail & Related papers  (2024-09-20T10:16:42Z)
• Dynamical topology of chiral and nonreciprocal state transfers in a non-Hermitian quantum system [11.467872077398688]
  We study topological chiral and nonreciprocal dynamics by encircling the exceptional points (EPs) of non-Hermitian Hamiltonians in a trapped ion system. These dynamics are topologically robust against external perturbations even in the presence dissipation-induced nonadiabatic processes. Our results mark a significant step towards exploring topological properties of open quantum systems.
  arXiv  Detail & Related papers  (2024-06-05T07:51:58Z)
• Quantum dynamics in the self-consistent quadratic approximation [0.0]
  A self-consistent quadratic theory is presented to account for nonlinear contributions in quantum dynamics. The dynamics is proven trace-preserving, with the Hamiltonian acting as a constant of motion for initial Gaussian states.
  arXiv  Detail & Related papers  (2024-03-17T20:13:41Z)
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays [41.94295877935867]
  In the noninteracting case, quantized Thouless pumps can only occur when a topological singularity is encircled adiabatically. In the presence of interactions, such topological transport can even persist for exotic paths in which the system gets arbitrarily close to the noninteracting singularity.
  arXiv  Detail & Related papers  (2024-02-14T16:58:21Z)
• Simultaneous Transport Evolution for Minimax Equilibria on Measures [48.82838283786807]
  Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures. By adding entropic regularization, our main result establishes global convergence towards the global equilibrium.
  arXiv  Detail & Related papers  (2022-02-14T02:23:16Z)
• Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning [30.238425143378414]
  We investigate the physics-constrained learning of implicit dynamical embeddings, leveraging neural ordinary differential equation (NODE) representations. A key objective is to constrain their boundedness, which promotes the generalization of the learned dynamics to arbitrary initial condition.
  arXiv  Detail & Related papers  (2022-02-11T16:40:46Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• 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)
• Non-unitary dynamics of Sachdev-Ye-Kitaev chain [20.29920872216941]
  We construct a series of one-dimensional non-unitary dynamics based on the Sachdev-Ye-Kitaev model. We analyze the entanglement dynamics using the path integral formalism in the large $N$ limit.
  arXiv  Detail & Related papers  (2020-08-27T07:15:58Z)
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems [0.0]
  Berry phases strongly affect the properties of crystalline materials. In non-Hermitian systems, generalizations of the Berry connection have been analyzed. We show that non-Hermiticity is manifested in anomalous weight rate and velocity terms.
  arXiv  Detail & Related papers  (2020-04-28T18:00:12Z)
• Emergent conformal symmetry in non-unitary random dynamics of free fermions [5.063902536614336]
  We present random quantum circuit models for non-unitary quantum dynamics of free fermions in one spatial dimension. Numerical simulations reveal that the dynamics tends towards steady states with logarithmic violations of the entanglement area law and power law correlation functions.
  arXiv  Detail & Related papers  (2020-04-20T19:09:08Z)

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.