Related papers: Lindblad Evolution and Stochasticity: the Case of …
The Bloch equation that set the foundation for open quantum systems, was conceived by pure physical reasoning. Since then, the Lindblad (GKLS) form of a quantum master equation, its most general mathematical representation, became an…
Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified…
Every open-system dynamics can be associated to infinitely many stochastic pictures, called unravelings, which have proved to be extremely useful in several contexts, both from the conceptual and the practical point of view. Here, focusing…
The stochastic--quantum correspondence reinterprets quantum dynamics as arising from an underlying stochastic process on a configuration space. We generalize the correspondence by lifting an arbitrary stochastic kernel $\Gamma$ in finite…
We propose a simple model for the phenomenon of Eulerian spontaneous stochasticity in turbulence. This model is solved rigorously, proving that infinitesimal small-scale noise in otherwise a deterministic multi-scale system yields a…
We consider the dynamics of a 1D system evolving according to a deterministic drift and randomly forced by two types of jumps processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously…
A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which goes beyond the common secular…
Control of quantum dissipative systems can be challenging because control variables are typically part of the system Hamiltonian, which can only generate motion along unitary orbits of the system. To transit between orbits, one must harness…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
A generalization of the stochastic wave function method to quantum master equations which are not in Lindblad form is developed. The proposed stochastic unravelling is based on a description of the reduced system in a doubled Hilbert space…
Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of…
We investigate the dissipative dynamics yielded by the Lindblad equation within the coexistence region around a first order phase transition. In particular, we consider an exactly-solvable fullyconnected quantum Ising model with n-spin…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
Open quantum systems can be described by unraveling Lindblad master equations into ensembles of quantum trajectories. Here we investigate how the complexity of such trajectories is affected by conservation laws and other dynamical…
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
We propose a complete treatment of a local in time dynamics of open quantum systems. In this approach Markovian evolution turns out to be a special case of a general non-Markovian one. We provide a general representation of the local…
Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework…
This article presents a concrete mathematical framework for the generation of entangled quantum states from classical stochastic processes. We demonstrate that any density operator $\rho_{AB}$ of a composite system can be derived from the…