Related papers: Quantum Stochastic Generators
We present an analysis based on word combinatorics of splitting integrators for Ito or Stratonovich systems of stochastic differential equations. In particular we present a technique to write down systematically the expansion of the local…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
Here it is shown that the unitary dynamics of a quantum object may be obtained as the conditional expectation of a counting process of object-clock interactions. Such a stochastic process arises from the quantization of the clock, and this…
The Boltzmann equation is one of the most famous equations and has vast applications in modern science. In the current study, we take the randomness of binary collisions into consideration and generalize the classical Boltzmann equation…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
We introduce local expectation gradients which is a general purpose stochastic variational inference algorithm for constructing stochastic gradients through sampling from the variational distribution. This algorithm divides the problem of…
A covariant nature of the Langevin equation in Ito calculus is clarified in applying stochastic quantization method to U(N) and SU(N) lattice gauge theories. The stochastic process is expressed in a manifestly general coordinate covariant…
This article sets up a formalism to describe stochastic thermodynamics for driven out-of-equilibrium open quantum systems. A stochastic Schr\"odinger equation allows to construct quantum trajectories describing the dynamics of the system…
We consider the fluctuations of a time-integrated particle current around an atypical value in a generic stochastic Markov process involving classical particles with two-site interaction and hardcore repulsion on a finite one-dimensional…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
In this work, we provide a specifc trigonometric stochastic numerical method for linear oscillators with high constant frequencies, driven by a nonlinear time-varying force and a random force. We present some theoretical considerations and…
We derive a general set of fluctuation relations for a nonequilibrium open quantum system described by a Lindblad master equation. In the special case of conservative Hamiltonian dynamics, these identities allow us to retrieve quantum…
We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton-Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
We use the It\^o stochastic calculus to give a simple derivation of the Lindblad form for the generator of a completely positive density matrix evolution, by specialization from the corresponding global form for a completely positive map.…
The longstanding question of how stochastic behaviour arises from deterministic Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable of describing this transition. In this review, we introduce the…
We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\log\rho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum…
A natural non-Markovian extension of the theory of white noise quantum trajectories is presented. In order to introduce memory effects in the formalism an Ornstein-Uhlenbeck coloured noise is considered as the output driving process. Under…
We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of…