Quantum unitary evolution interspersed with repeated non-unitary interactions at random times: The method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain

• URL: http://arxiv.org/abs/2106.14181v2
• Date: Fri, 25 Mar 2022 03:21:08 GMT
• Title: Quantum unitary evolution interspersed with repeated non-unitary interactions at random times: The method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain
• Authors: Debraj Das, Sushanta Dattagupta, Shamik Gupta
• Abstract summary: We provide two explicit applications of the formalism in the context of the so-called tight-binding model relevant in various contexts in solid-state physics. We consider two forms of interactions: reset of quantum dynamics, in which the density operator is at random times reset to its initial form, and projective measurements performed on the system at random times.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical framework to obtain the average density operator of the system at any time during the dynamical evolution. The average is with respect to the classical randomness associated with the random time intervals between successive interactions, which we consider to be independent and identically-distributed random variables. We provide two explicit applications of the formalism in the context of the so-called tight-binding model relevant in various contexts in solid-state physics. In one dimension, the corresponding tight-binding chain models the motion of a charged particle between the sites of a lattice, wherein the particle is for most times localized on the sites, but which owing to spontaneous quantum fluctuations tunnels between nearest-neighbour sites. We consider two representative forms of interactions: stochastic reset of quantum dynamics, in which the density operator is at random times reset to its initial form, and projective measurements performed on the system at random times. In the former case, we demonstrate with our exact results how the particle is localized on the sites at long times, leading to a time-independent mean-squared displacement of the particle about its initial location. In the case of projective measurements at random times, we show that repeated projection to the initial state of the particle results in an effective suppression of the temporal decay in the probability of the particle to be found on the initial state. The amount of suppression is comparable to the one in conventional Zeno effect scenarios, but which however does not require performing measurements at exactly regular intervals that are hallmarks of such scenarios.

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)
• Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
  Signatures of localization have been observed in condensed matter and cold atomic systems. We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths. We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
  arXiv  Detail & Related papers  (2023-03-13T12:45:25Z)
• Stochastic resets in the context of a tight-binding chain driven by an oscillating field [0.0]
  We study in the framework of the driven tight-binding chain (TBC) the issue of quantum unitary dynamics interspersed at random times with resets. We establish the remarkable effect of localization of the TBC particle on the sites of the underlying lattice at long times.
  arXiv  Detail & Related papers  (2022-09-28T14:08:50Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Measurement induced quantum walks [0.0]
  We investigate a quantum walk on a graph with classical and quantum mechanical properties. For a quantum walk on a line we show that in our system the first detection probability decays classically like $(texttime)-3/2$.
  arXiv  Detail & Related papers  (2021-08-30T08:11:24Z)
• Symmetry-resolved dynamical purification in synthetic quantum matter [1.2189422792863447]
  We show that symmetry-resolved information spreading is inhibited due to the competition of coherent and incoherent dynamics. Our work shows that symmetry plays a key role as a magnifying glass to characterize many-body dynamics in open quantum systems.
  arXiv  Detail & Related papers  (2021-01-19T19:01:09Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• On Evolution of Coherent States as Quantum Counterpart of Classical Dynamics [0.0]
  Quantum dynamics of coherent states is studied within quantum field theory. We use two complementary methods: by organizing the evolution as a Taylor series in elapsed time and by perturbative expansion in coupling within the interaction-picture formalism.
  arXiv  Detail & Related papers  (2020-11-23T06:08:29Z)
• Feynman Propagator for a System of Interacting Scalar Particles in the Fokker Theory [62.997667081978825]
  The functional integral on the generalized phase space is defined as the initial one in quantum theory. The measure of integration in the generalized configuration space of world particle lines is determined. A modification of the propagator is proposed, in which the role of independent time parameters is taken by the time coordinates of the particles in Minkowski space.
  arXiv  Detail & Related papers  (2020-02-10T09:09:45Z)
• Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath [0.0]
  This work addresses quantum adiabatic decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system-environment interaction Hamiltonian that represents a partition of non-interacting subsystems.
  arXiv  Detail & Related papers  (2019-12-30T16:39:38Z)

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.