Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUnified approach to reset processes and application to coupling between process and reset
47
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a unified approach to those observables of stochastic processes under reset that take the form of averages of functionals depending on the most recent renewal period. We derive solutions for the observables, and determine the conditions for existence and equality of their stationary values with and without reset. For intermittent reset times, we derive exact asymptotic expressions for observables that vary asymptotically as a power of time. We illustrate the general approach with general and particular results for the power spectral density, and moments of subdiffusive processes. We focus on coupling of the process and reset via a diffusion-decay process with microscopic dependence between transport and decay. In contrast to the uncoupled case, we find that restarting the particle upon decay does not produce a probability current equal to the decay rate, but instead drastically alters the time dependence of the decay rate and the resulting current.
rate research
Read More
We study the spectral properties of classical and quantum Markovian processes that are reset at random times to a specific configuration or state with a reset rate that is independent of the current state of the system. We demonstrate that this simple reset dynamics causes a uniform shift in the eigenvalues of the Markov generator, excluding the zero mode corresponding to the stationary state, which has the effect of accelerating or even inducing relaxation to a stationary state. Based on this result, we provide expressions for the stationary state and probability current of the reset process in terms of weighted sums over dynamical modes of the reset-free process. We also discuss the effect of resets on processes that display metastability. We illustrate our results with two classical stochastic processes, the totally asymmetric random walk and the one-dimensional Brownian motion, as well as two quantum models: a particle coherently hopping on a chain and the dissipative transverse field Ising model, known to exhibit metastability.
In this work we consider a stochastic movement process with random resets to the origin followed by a random residence time there before the walker restarts its motion. First, we study the transport properties of the walker, we derive an expression for the mean square displacement of the overall process and study its dependence with the statistical properties of the resets, the residence and the movement. From this general formula, we see that the inclusion of the residence after the resets is able to induce super-diffusive to sub-diffusive (or diffusive) regimes and it can also make a sub-diffusive walker reach a constant MSD or even collapse. Second, we study how the reset-and-residence mechanism affects the first arrival time of different search processes to a given position, showing that the long time behavior of the reset and residence time distributions determine the existence of the mean first arrival time.
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.
Quantum dots exhibit reproducible conductance fluctuations at low temperatures due to electron quantum interference. The sensitivity of these fluctuations to the underlying disorder potential has only recently been fully realized. We exploit this sensitivity to obtain a novel tool for better understanding the role that background impurities play in the electrical properties of high-mobility AlGaAs/GaAs heterostructures and nanoscale devices. In particular, we report the remarkable ability to first alter the disorder potential in an undoped AlGaAs/GaAs heterostructure by optical illumination and then reset it back to its initial configuration by room temperature thermal cycling in the dark. We attribute this behavior to a mixture of C background impurities acting as shallow acceptors and deep trapping by Si impurities. This alter and reset capability, not possible in modulation-doped heterostructures, offers an exciting route to studying how scattering from even small densities of charged impurities influences the properties of nanoscale semiconductor devices.
We consider how the energy cost of bit reset scales with the time duration of the protocol. Bit reset necessarily takes place in finite time, where there is an extra penalty on top of the quasistatic work cost derived by Landauer. This extra energy is dissipated as heat in the computer, inducing a fundamental limit on the speed of irreversible computers. We formulate a hardware-independent expression for this limit. We derive a closed-form lower bound on the work penalty as a function of the time taken for the protocol and bit reset error. It holds for discrete as well as continuous systems, assuming only that the master equation respects detailed balance.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
