Related papers: First Passage Times for Continuous Quantum Measure…
Biological events are often initiated when a random "searcher" finds a "target," which is called a first passage time (FPT). In some biological systems involving multiple searchers, an important timescale is the time it takes the slowest…
How long a stochastic process survives before leaving a domain depends not only on its intrinsic dynamics but also on how it is observed. Classical first-passage theory assumes continuous monitoring with absorbing boundaries…
We define the hitting (or absorbing) time for the case of continuous quantum walks by measuring the walk at random times, according to a Poisson process with measurement rate $\lambda$. From this definition we derive an explicit formula for…
In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation.…
Monitored many-body systems fall broadly into two dynamical phases, ``entangling'' or ``disentangling'', separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of…
First-passage observables (FPO) are central to understanding stochastic processes in confined domains, with applications spanning chemical reaction kinetics, foraging behavior, and molecular transport. While extensive analytical results…
We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…
We investigate the statistics of the first-passage time (FPT) to a fractal self-similar boundary of the Koch snowflake. When the starting position is fixed near the absorbing boundary, the FPT distribution exhibits an apparent power-law…
Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many…
We consider the temporal correlations of the quantum state of a qubit subject to simultaneous continuous measurement of two non-commuting qubit observables. Such qubit state correlators are defined for an ensemble of qubit trajectories,…
We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a…
A fundamental task in photonics is to characterise an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Amongst many ways to achieve this, single-photon probes can be used in a…
What is the right statistics for the measurements of arrival times of a quantum particle? Although this question is very old, it is still open. Usual experiments are performed in far-field regime and this question becomes unimportant, as a…
A fluctuation theorem is examined for the first-passage time of a biomolecular machine (e.g., a motor protein or an enzyme) in a nonequilibrium steady-state. For such machines in which the driven, observable process is coupled to a hidden…
In recent years, dynamical quantum phase transitions (DQPTs) have emerged as a useful theoretical concept to characterize nonequilibrium states of quantum matter. DQPTs are marked by singular behavior in an \textit{effective free energy}…
A quantum system S undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a stochastic master equation and its solution is called a quantum trajectory.…
Probability currents are fundamental in characterizing the kinetics of non-equilibrium processes. Notably, the steady-state current $J_{ss}$ for a source-sink system can provide the exact mean-first-passage time (MFPT) for the transition…
The two-dimensional backward Fokker-Planck equation is used to calculate the mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle driven by a rotating magnetic field. It is shown that a magnetic field that is rapidly…
We demonstrate that the probability distribution of the net number of electrons passing through a quantum system in a junction obeys a steady-state fluctuation theorem (FT) which can be tested experimentally by the full counting statistics…
First passage time (FPT) is the time a particle, subject to some stochastic process, hits or crosses a closed surface for the very first time. $\tau$-leaping methods are a class of stochastic algorithms in which, instead of simulating every…