Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume 2022, Issue 5, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1742-5468/ac6256
Keywords
stochastic particle dynamics; quantum wires; stationary states
Categories
Funding
- Science and Engineering Research Board (SERB), India under SERB-TARE scheme [TAR/2018/000023]
- SERBMATRICS scheme [MTR/2019/000560]
- SERB-CRG scheme [CRG/2020/000596]
- ICTP- Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
- Indian National Science Academy
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This study presents a general theoretical framework for describing the average behavior of a quantum system under non-unitary evolution and random interruptions. The study finds that, under certain interactions, particles can localize at specific positions and it is possible to suppress the temporal decay of the particle's probability through projection measurements.
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. The formalism is very general in that it applies to any quantum system, to any form of non-unitary interaction, and to any probability distribution for the random times. 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, e.g. in modelling nano wires. Considering the case of 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, owing to spontaneous quantum fluctuations tunnels between the nearest-neighbour sites. We consider two representative forms of interactions, one that implements a stochastic reset of quantum dynamics in which the density operator is at random times reset to its initial form, and one in which projective measurements are 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 (MSD) of the particle about its initial location. This stands in stark contrast to the behavior in the absence of interactions, when the particle has an unbounded growth of the MSD in time, with no signatures of localization. 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 it does not require us to perform measurements at exactly regular intervals that are hallmarks of such scenarios.
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