Related papers: Trace formulas for stochastic evolution operators:…
The spectrum of the evolution Operator associated with a nonlinear stochastic flow with additive noise is evaluated by diagonalization in a polynomial basis. The method works for arbitrary noise strength. In the weak noise limit we…
A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of…
Periodic orbit theory is an effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory is cast in the…
We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and Gaussian noise. Using an integral representation of the evolution operator we investigate the high order corrections to the…
Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic…
We review studies of an evolution operator L for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of L yields a physically measurable property of the dynamical system,…
We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for…
We derive a Gutzwiller-type trace formula for quantum chaotic systems that accounts for both particle spin precession and discrete geometrical symmetries. This formula generalises previous results that were obtained either for systems with…
A fully regulated definition of Feynman's path integral is presented here. The proposed re-formulation of the path integral coincides with the familiar formulation whenever the path integral is well-defined. In particular, it is consistent…
Stochastic hybrid systems involve the coupling between discrete and continuous stochastic processes. They are finding increasing applications in cell biology, ranging from modeling promoter noise in gene networks to analyzing the effects of…
We report on the use of a stochastic trace estimator algorithm, based on mutually unbiased bases, for evaluating the trace of a matrix differential operator appearing in the context of lattice simulations for the discretized superstring…
We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately…
Combining fractional calculus and the Rough Path Theory we study the existence and uniqueness of mild solutions to evolutions equations driven by a H\"older continuous function with H\"older exponent in $(1/3,1/2)$. Our stochastic integral…
The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still…
In this article we are concerned with the study of the existence and uniqueness of pathwise mild solutions to evolutions equations driven by a H\"older continuous function with H\"older exponent in $(1/3,1/2)$. Our stochastic integral is a…
Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path…
Stochastic unravelings allow to efficiently simulate open system dynamics, yet their application has traditionally been restricted to master equations that preserve both Hermiticity and trace. In this work, we introduce a general framework…
Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These…
In this paper we study the longtime dynamics of mild solutions to retarded stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a preparation for this purpose we have to show the existence and uniqueness of a cocycle…
We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to…