The spectral boundary of the Asymmetric Simple Exclusion Process (ASEP) -- free fermions, Bethe ansatz and random matrix theory

• URL: http://arxiv.org/abs/2402.00662v1
• Date: Thu, 1 Feb 2024 15:20:43 GMT
• Title: The spectral boundary of the Asymmetric Simple Exclusion Process (ASEP) -- free fermions, Bethe ansatz and random matrix theory
• Authors: Goran Nakerst, Toma\v{z} Prosen, Masudul Haque
• Abstract summary: In non-equilibrium statistical mechanics, the Asymmetric Simple Exclusion Process serves as a paradigmatic example. We investigate the spectral characteristics of the ASEP, focusing on the spectral boundary of its generator matrix.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In non-equilibrium statistical mechanics, the Asymmetric Simple Exclusion Process (ASEP) serves as a paradigmatic example. We investigate the spectral characteristics of the ASEP, focusing on the spectral boundary of its generator matrix. We examine finite ASEP chains of length $L$, under periodic (pbc) and open boundary conditions (obc). Notably, the spectral boundary exhibits $L$ spikes for pbc and $L+1$ spikes for obc. Treating the ASEP generator as an interacting non-Hermitian fermionic model, we extend the model to have tunable interaction. In the non-interacting case, the analytically computed many-body spectrum shows a spectral boundary with prominent spikes. For pbc, we use the coordinate Bethe ansatz to interpolate between the noninteracting case to the ASEP limit, and show that these spikes stem from clustering of Bethe roots. The robustness of the spikes in the spectral boundary is demonstrated by linking the ASEP generator to random matrices with trace correlations or, equivalently, random graphs with distinct cycle structures, both displaying similar spiked spectral boundaries.

Related papers

• Topological Order in the Spectral Riemann Surfaces of Non-Hermitian Systems [44.99833362998488]
  We show topologically ordered states in the complex-valued spectra of non-Hermitian systems. These arise when the distinctive exceptional points in the energy surfaces of such models are annihilated. We illustrate the characteristics of the topologically protected states in a non-Hermitian two-band model.
  arXiv  Detail & Related papers  (2024-10-24T10:16:47Z)
• Total and Symmetry resolved Entanglement spectra in some Fermionic CFTs from the BCFT approach [0.0]
  We study the universal total and symmetry-resolved entanglement spectra for a single interval of some $2$d Fermionic CFTs. The partition of Hilbert space is achieved by cutting out discs around the entangling boundary points and imposing boundary conditions preserving the extended symmetry under scrutiny.
  arXiv  Detail & Related papers  (2024-02-12T10:42:17Z)
• Full range spectral correlations and their spectral form factors in chaotic and integrable models [0.0]
  Correlations between the eigenenergies of a system's spectrum can be a defining feature of quantum chaos. We show how each spectral distance participates in building it -- the linear ramp cannot be formed by short-range energy correlations only. We illustrate our findings in the XXZ spin chain with disorder, which interpolates between chaotic and integrable behavior.
  arXiv  Detail & Related papers  (2023-11-15T19:00:01Z)
• Effects of detuning on $\mathcal{PT}$-symmetric, tridiagonal, tight-binding models [0.0]
  Non-Hermitian, tight-binding $mathcalPT$-symmetric models are extensively studied in the literature. Here, we investigate two forms of non-Hermitian Hamiltonians to study the $mathcalPT$-symmetry breaking thresholds and features of corresponding surfaces of exceptional points (EPs) Taken together, our results provide a detailed understanding of detuned tight-binding models with a pair of gain-loss potentials.
  arXiv  Detail & Related papers  (2023-02-26T01:36:59Z)
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices [0.0]
  We investigate the spectral topology of one-dimensional lattices where the nonreciprocal hoppings within the nearest $r_d$ neighboring sites are the same. For the purely off-diagonal model without onsite potentials, the energy spectrum of the lattice forms an inseparable loop that intertwines with itself in the complex energy plane. We propose an experimental scheme to realize the long-range nonreciprocal models by exploiting electrical circuits.
  arXiv  Detail & Related papers  (2022-02-01T09:30:44Z)
• Simulation of absorption spectra of molecular aggregates: a Hierarchy of Stochastic Pure States approach [68.8204255655161]
  hierarchy of pure states (HOPS) provides a formally exact solution based on local, trajectories. Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregares requires a formulation in terms of normalized trajectories.
  arXiv  Detail & Related papers  (2021-11-01T16:59:54Z)
• Fano interference in quantum resonances from angle-resolved elastic scattering [62.997667081978825]
  We show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules.
  arXiv  Detail & Related papers  (2021-05-12T20:41:25Z)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains [1.6295305195753724]
  We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains.
  arXiv  Detail & Related papers  (2020-05-21T07:02:04Z)
• Observation of Hermitian and Non-Hermitian Diabolic Points and Exceptional Rings in Parity-Time symmetric ZRC and RLC Dimers [62.997667081978825]
  We show how appears non-Hermitian degeneracy points in the spectrum and how they are protected against a Hermitian perturbation. This work opens a gold road for investigations on topological electrical circuits for robust transport of information at room temperature.
  arXiv  Detail & Related papers  (2020-04-17T15:51:49Z)

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.