Related papers: Quantum Trajectories. Spectral Gap, Quasi-compactn…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
What is the quantum system? Consider the wavefunction of the electron, what we call single particle wave-function and assume that it contains N wave packets. If we pass all the wave packets through an electric field, all are deflected, as…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
We investigate the stability of quantum Markov processes with respect to perturbations of their transition maps. In the first part, we introduce a condition number that measures the sensitivity of fixed points of a quantum channel to…
A quantum dot is a sub-micron-scale conducting device containing up to several thousand electrons. Transport through a quantum dot at low temperatures is a quantum-coherent process. This review focuses on dots in which the electron's…
We investigate the time-dependent, coherent, and dissipative dynamics of bound particles in single multilevel quantum dots in the presence of sequential tunnelling transport. We focus on the nonequilibrium regime where several channels are…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
We employ the quantum jump trajectory approach to construct a systematic framework to study the thermodynamics at the trajectory level in a nonequilibrium open quantum system under discrete feedback control. Within this framework, we derive…
Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light…
We develop a comprehensive framework for characterizing fluctuations in quantum transport and nonequilibrium thermodynamics using two complementary approaches: full counting statistics and first-passage times. Focusing on open quantum…
We obtain non-Gaussian limit laws for one-dimensional random walk in a random environment assuming that the environment is a function of a stationary Markov process. This is an extension of the work of Kesten, M. Kozlov and Spitzer for…
This paper proposes a quantum algorithm for Markov chain spectral gap estimation that is quasi-optimal (i.e., optimal up to a polylogarithmic factor) in the number of vertices for all parameters, and additionally quasi-optimal in the…
We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $N$-photon state. To determine the conditional evolution of the quantum system depending on continuous in time…
The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…
We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…
Starting from a generalization of the quantum trajectory theory (based on the stochastic Schr\"odinger equation - SSE), non-Markovian models of quantum dynamics are derived. In order to describe non-Markovian effects, the approach used in…
We develop a microscopic theory for biasing the quantum trajectories of an open quantum system, which renders rare trajectories typical. To this end we consider a discrete-time quantum dynamics, where the open system collides sequentially…
We consider the question of asymptotic stability of quantum trajectories undergoing quantum non-demolition imperfect measurement, that is to say the convergence of the estimated trajectory towards the true trajectory whose parameters and…
A central feature of quantum mechanics is that a measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system…