Related papers: Normalized Gaussian Path Integrals
I review the generating function for quantum-statistical mechanics, known as the Feynman-Vernon influence functional, the decoherence functional, or the Schwinger-Keldysh path integral. I describe a probability-conserving $i\varepsilon$…
The transition between distinct phases of matter is characterized by the nature of fluctuations near the critical point. We demonstrate that noise spectroscopy can not only diagnose the presence of a phase transition, but can also determine…
Systems composed of interacting self-propelled particles (SPPs) display different forms of order-disorder phase transitions relevant to collective motion. In this paper we propose a generalization of the Vicsek model characterized by an…
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
We show that a basic quantum white noise process formally reproduces quantum stochastic calculus when the appropriate normal / chronological orderings are prescribed. By normal ordering techniques for integral equations and a generalization…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as…
Fr\"ohlich model equations describing phonon condensation in open systems of biological relevance are here reinvestigated in a semi-classical non-equilibrium statistical context (with "semi-classical" it is meant that the evolution of the…
Studying phase transitions in interacting quantum field theories generally requires the numerical study of the dynamical system on an N-dimensional lattice, which is, in most cases, computationally quite the challenging task even with…
The semiclassical Euclidean path integral method is applied to compute the low temperature quantum decay rate for a particle placed in the metastable minimum of a cubic potential in a {\it finite} time theory. The classical path, which…
We present a computational alternative to probabilistic simulations for non-smooth stochastic dynamical systems that are prevalent in engineering mechanics. As examples, we target (1) stochastic elasto-plastic problems, which involve…
We present the systematic formalism to derive the path-integral formulation for the hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and…
We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on…
This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and…
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…
We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional…