Related papers: Quantum Noise in Quantum Optics: the Stochastic Sc…
In this article, we consider the following stochastic fractional diffusion equation \begin{equation*} \left(\partial^{\beta}+\dfrac{\nu}{2}\left(-\Delta\right)^{\alpha / 2}\right) u(t, x)= \lambda\: I_{0_+}^{\gamma}\left[u(t, x) \dot{W}(t,…
Squeezing of light's quantum noise requires temporal rearranging of photons. This again corresponds to creation of quantum correlations between individual photons. Squeezed light is a non-classical manifestation of light with great…
Regularization by noise for certain classes of fluid dynamic equations, a theme dear to Giuseppe Da Prato (see G. Da Prato and A. Debussche, Ergodicity for the 3D stochastic Navier-Stokes equations, J. Math. Pures Appl., 2003), is reviewed…
Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.
Interpreting the noise in a stochastic differential equation, in particular the It\^o versus Stratonovich dilemma, is a problem that has generated a lot of debate in the physical literature. In the last decades, a third interpretation of…
Lecture notes of the Les Houches Summer School on 'Strongly interacting quantum systems out of equilibrium'.
A comment on the paper "Truncated Schwinger-Dyson Equations and Gauge Covariance in QED3", Few-Body Syst. 41, 185 (2007) [hep-ph/0511291].
Light scattering from resonantly or nearly resonantly excited systems, known as resonance fluorescence, has been gaining importance as a versatile tool for investigating quantum states of matter and readout of quantum information, recently…
Lectures at VII Jorge Andre Swieca Summer School in Nuclear Physics; Brasil; Jan 22 - Feb 4 1995. To be published by Plenum Press (C.A.Amaral Nunes ed.)
We consider the problem of the error in soliton transmission in long-haul optical fibers caused by the spontaneous emission of noise inherent to amplification. We study two types of noises driving the stochastic focusing cubic one…
We study quantum correlations and quantum noise in the soliton collision described by a general two-soliton solution of the nonlinear Schr\"odinger equation, by using the back-propagation method. Our results include the standard case of a…
Diffusive scaling of position moments and a central limit theorem are obtained for the mean position of a quantum particle hopping on a cubic lattice and subject to a random potential consisting of a large static part and a small part that…
In this paper we develop an existence theory for the Cauchy problem to the stochastic Hunter-Saxton equatio, and prove several properties of the blow-up of its solutions. An important part of the paper is the continuation of solutions to…
In this article, we investigate an interacting particle system featuring random intensities, individual noise, and environmental noise, commonly referred to as stochastic point vortex model. The model serves as an approximation for the…
We discuss the recent paper by A. Dar\'os and L.K. Arruda (On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation, J. Diff. Equat., 266 (2019), 1946-1968). Our intention is to correct some…
This paper discusses questions concerning the foundations of quantum mechanics (entanglement, wave collapse, irreversibility) with reference to the issues raised during a Minisymposium held in Helsinki, 1.6-3.6 in 1992, where A Shimony, A…
These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects,…
Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including…
We study the focusing stochastic nonlinear Schr\"odinger equation in one spatial dimension with multiplicative noise, driven by a Wiener process white in time and colored in space, in the $L^2$-critical and supercritical cases. The mass…
Recently a model of metric fluctuations has been proposed which yields an effective Schr\"odinger equation for a quantum particle with a modified inertial mass, leading to a violation of the weak equivalence principle. The renormalization…