Tight-binding model subject to conditional resets at random times

Abstract

We investigate the dynamics of a quantum system subjected to a time-dependent and conditional resetting protocol. Namely, we ask: what happens when the unitary evolution of the system is repeatedly interrupted at random time instants with an instantaneous reset to a specified set of reset configurations taking place with a probability that depends on the current configuration of the system at the instant of reset? Analyzing the protocol in the framework of the so-called tight-binding model describing the hopping of a quantum particle to nearest-neighbour sites in a one-dimensional open lattice, we obtain analytical results for the probability of finding the particle on the different sites of the lattice. We explore a variety of dynamical scenarios, including the one in which the resetting time intervals are sampled from an exponential as well as from a power-law distribution, and a set-up that includes a Floquet-type Hamiltonian involving an external periodic forcing. Under exponential resetting, and in both presence and absence of the external forcing, the system relaxes to a stationary state characterized by localization of the particle around the reset sites. The choice of the reset sites plays a defining role in dictating the relative probability of finding the particle at the reset sites as well as in determining the overall spatial profile of the site-occupation probability. Indeed, a simple choice can be engineered that makes the spatial profile highly asymmetric even when the bare dynamics does not involve the effect of any bias. Furthermore, analyzing the case of power-law resetting serves to demonstrate that the attainment of the stationary state in this quantum problem is not always evident and depends crucially on whether the distribution of reset time intervals has a finite or an infinite mean.

23 pages, 8 figures; v2: close to published version, 25 pages, 8 figures

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Cited by in corpus (8)

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• Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it
• Resonances of recurrence time of monitored quantum walks
• Manipulating phases in many-body interacting systems with subsystem resetting
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting
• Entanglement of bosonic systems under monitored evolution
• Fractionally Quantized Recurrence Detection Times in Monitored Quantum Many-Body Systems