Related papers: Stochastic path integrals can be derived like quan…
We prove the Ito-Tanaka formula and the existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we define the stochastic integrals as forward-type pathwise integrals introduced…
We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian…
A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
The book deals with a stochastic formulation of path integration in real time, by rotating the_space_ variables over exp(i pi/4). Preliminary chapters deal with quantum and classical mechanics, probability theory and stochastic calculus,…
We provide a detailed exposition of the connections between Boltzmann machines commonly utilized in machine learning problems and the ideas already well known in quantum statistical mechanics through Feynman's description of the same. We…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…
The probability current is a vital quantity in the Fokker-Planck description of stochastic processes. It characterizes non-equilibrium stationary states and appears in linear response calculations. We recover and review the probability…
In this work we introduce a phase-space description based on the positive P representation for bosonic fields interacting with a system of quantum emitters. The formalism is applicable to collective light-matter interactions and open…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, It\^o diffusive process is generalized by incorporating a multiplicative noise term…
Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them…
We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…
Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…