Arbitrary relaxation rate under non-Hermitian matrix iterations

• URL: http://arxiv.org/abs/2312.14617v1
• Date: Fri, 22 Dec 2023 11:18:35 GMT
• Title: Arbitrary relaxation rate under non-Hermitian matrix iterations
• Authors: Ja\v{s} Bensa
• Abstract summary: We study the exponential relaxation of observables propagated with a non-Hermitian transfer matrix. We show that the decay rate can be an arbitrary value between the second largest eigenvalue and the largest value in the pseudospectrum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study the exponential relaxation of observables, propagated with a non-Hermitian transfer matrix, an example being out-of-time-ordered correlations (OTOC) in brickwall (BW) random quantum circuits. Until a time that scales as the system size, the exponential decay of observables is not usually determined by the second largest eigenvalue of the transfer matrix, as one can naively expect, but it is in general slower -- this slower decay rate was dubbed "phantom eigenvalue". Generally, this slower decay is given by the largest value in the pseudospecturm of the transfer matrix, however we show that the decay rate can be an arbitrary value between the second largest eigenvalue and the largest value in the pseudospectrum. This arbitrary decay can be observed for example in the propagation of OTOC in periodic boundary conditions BW circuits. To explore this phenomenon, we study a 1D biased random walk coupled to two reservoirs at the edges, and prove that this simple system also exhibits phantom eigenvalues.

Related papers

• 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)
• Two-step phantom relaxation of out-of-time-ordered correlations in random circuits [0.0]
  We study out-of-time-ordered correlation functions in various random quantum circuits. We show that the average dynamics is governed by a Markovian propagator.
  arXiv  Detail & Related papers  (2021-12-14T10:35:12Z)
• Effect of Emitters on Quantum State Transfer in Coupled Cavity Arrays [48.06402199083057]
  We study the effects of atoms in cavities which can absorb and emit photons as they propagate down the array. Our model is equivalent to previously examined spin chains in the one-excitation sector and in the absence of emitters.
  arXiv  Detail & Related papers  (2021-12-10T18:52:07Z)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)
• Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom [0.0]
  We study random quantum circuits and their rate of producing bipartite entanglement. The problem is mapped to a Markovian process and proved that there are large spectral equivalence classes. We numerically demonstrate that the phenomenon occurs also in random circuits with non-optimal generic gates.
  arXiv  Detail & Related papers  (2021-01-14T13:11:29Z)
• Multi-time correlations in the positive-P, Q, and doubled phase-space representations [0.0]
  It is shown that expressions for time-ordered normal-ordered quantum observables in the positive-P distribution replace Heisenberg operators with the bare time-dependent variables. The theory of multi-time observables in phase-space representations is extended, allowing non-perturbative treatment of many cases.
  arXiv  Detail & Related papers  (2020-11-19T21:17:31Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
  We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
  arXiv  Detail & Related papers  (2020-03-09T21:27:02Z)
• Maximum velocity quantum circuits [0.0]
  We consider the long-time limit of out-of-time-order correlators (OTOCs) in two classes of quantum lattice models. We show analytic results for the long-time value of the OTOC on and inside the light cone.
  arXiv  Detail & Related papers  (2020-03-02T19:00:06Z)
• Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime [32.65347128465841]
  Deep neural networks can achieve remarkable performances while interpolating the training data perfectly. Rather than the U-curve of the bias-variance trade-off, their test error often follows a "double descent" We develop a quantitative theory for this phenomenon in the so-called lazy learning regime of neural networks.
  arXiv  Detail & Related papers  (2020-03-02T17:39:31Z)

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.