Distribution of Kinks in an Ising Ferromagnet After Annealing and the Generalized Kibble-Zurek Mechanism

• URL: http://arxiv.org/abs/2105.09138v1
• Date: Wed, 19 May 2021 13:58:33 GMT
• Title: Distribution of Kinks in an Ising Ferromagnet After Annealing and the Generalized Kibble-Zurek Mechanism
• Authors: Jack J. Mayo, Zhijie Fan, Gia-Wei Chern, Adolfo del Campo
• Abstract summary: We consider a one-dimensional Isingmagnet induced by a temperature quench in finite time. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics. We consider linear, nonlinear, and exponential cooling schedules, among which the latter provides the most efficient shortcuts to cooling in a given time.
• Score: 0.8258451067861933
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically found under Glauber dynamics, and the distribution of the number of kinks in the final state is shown to be consistent with a Poissonian distribution. The mean kink number, the variance, and the third centered moment take the same value and obey a universal power-law scaling with the quench time in which the temperature is varied. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics for moderate cooling times away from the asymptotic limit, when the kink-number distribution takes a binomial form. We analyze the relation of these results to physics beyond the Kibble-Zurek mechanism for critical dynamics, using the kink number distribution to assess adiabaticity and its breakdown. We consider linear, nonlinear, and exponential cooling schedules, among which the latter provides the most efficient shortcuts to cooling in a given quench time. The non-thermal behavior of the final state is established by considering the trace norm distance to a canonical Gibbs state.

Related papers

• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
  We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
  arXiv  Detail & Related papers  (2023-06-16T16:41:16Z)
• Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics [9.011881058913184]
  We build a practical numerical system based on the pure-death dynamics. We show that the kernelized dynamics converge on finite time intervals, to pure gradient-death dynamics shrinks to zero. Finally we prove the long-time results on the convergence of the states of the kernelized dynamics towards the Gibbs measure.
  arXiv  Detail & Related papers  (2022-11-01T13:30:26Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• Thermalization of the Quantum Planar Rotor with external potential [0.0]
  We study decoherence, diffusion, friction, and how they thermalize a planar rotor in the presence of an external potential. We analytically and numerically verify the existence of a steady state that, in the high-temperature regime, closely approximates a Gibbs state.
  arXiv  Detail & Related papers  (2022-07-11T12:15:50Z)
• Quantum chaos and thermalization in the two-mode Dicke model [77.34726150561087]
  We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model. The two-mode Dicke model exhibits normal to superradiant quantum phase transition. We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size.
  arXiv  Detail & Related papers  (2022-07-08T11:16:29Z)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Decoherent Quench Dynamics across Quantum Phase Transitions [0.0]
  We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity.
  arXiv  Detail & Related papers  (2021-03-14T23:43:55Z)
• 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)
• Universal Statistics of Vortices in a Newborn Holographic Superconductor: Beyond the Kibble-Zurek Mechanism [52.77024349608834]
  We investigate universal signatures beyond the celebrated Kibble-Zurek mechanism (KZM) We characterize the distribution of vortices generated in a thermal quench leading to the formation of a holographic superconductor.
  arXiv  Detail & Related papers  (2021-01-06T18:06:40Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

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.