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The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
A microscopic model of interacting oscillators, which admits two conserved quantities, volume, and energy, is investigated. We begin with a system driven by a general nonlinear potential under high-temperature regime by taking the inverse…
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the…
Bose gas in a random external field is considered. The sigma model like effective action both for weak and strong random fields compared with the interaction between particles is derived by averaging over the random field and integration…
We present a stochastic theory for the nonequilibrium dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
We study the zero-dimensional prototype of the path integrals in quantum mechanics and quantum field theory, with the action $S(\phi)=\frac{\sigma }{2}\phi^{2}+\frac{\lambda}{4}\phi^{4}$. Using the Lefschetz thimble decomposition and the…
In stochastic quantization, ordinary 4-dimensional Euclidean quantum field theory is expressed as a functional integral over fields in 5 dimensions with a fictitious 5th time. This is advantageous, in particular for gauge theories, because…
We review the method of stochastic quantization for a scalar field theory. We first give a brief survey for the case of self-interacting scalar fields, implementing the stochastic perturbation theory up to the one-loop level. The…
A corollary to the Reeh-Schlieder theorem is proved: that the time-ordered Vacuum Expectation Values and the S-matrix of a regularized Lagrangian quantum theory can be approximated by a local operator that uses nonlinear functionals of a…
The fluctuation-dissipation theory is grounded on the Langevin condition expressing the local independence between the thermal force and the particle velocity history. Upon hydrodynamic grounds, it is reasonable to relax this condition in…
Quantum gravity effects of zeroth order in the Planck constant are investigated in the framework of the low-energy effective theory. A special emphasis is placed on establishing the correspondence between classical and quantum theories, for…
Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in…
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…
Recently two generalized nonlinear Schr\"{o}dinger equations have been proposed by Chavanis [Eur. Phys. J. Plus 132 (2017) 286] by applying Nottale's theory of scale relativity relying on a fractal space-time to describe dissipation in…
We present a new method to derive low-lying N-dimensional quantum wave functions by quadrature along a single trajectory. The N-dimensional Schroedinger equation is cast into a series of readily integrable first order ordinary differential…
The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|~ g^2 T. Such a situation is typical for the processes of electroweak baryon number…
This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like…
The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…