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Let $L$ be a positive definite self-adjoint operator on the $L^2$-space associated to a $\si$-finite measure space. Let $H$ be the dual space of the domain of $L^{1/2}$ w.r.t. $L^2(\mu)$. By using an It\^o type inequality for the $H$-norm…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
The standard treatment of neutrino oscillations usually relies on factorization which assumes neutrino production, propagation, and detection are independent processes. As a consequence, the total probability is given by the product of…
We present the new Guided Moments ($\texttt{GM}$) formalism for neutrino modeling in astrophysical scenarios like core-collapse supernovae and neutron star mergers. The truncated moments approximation ($\texttt{M1}$) and Monte-Carlo…
We construct a spectral representation of neutrino propagator in moving matter or in external magnetic field. In both cases there exists fixed four-dimensional axis of polarization, such that the corresponding spin projectors commute with…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
We present a new approach to the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field,…
We introduce a general formulation of the fluctuation-dissipation relations (FDR) holding also in far-from-equilibrium stochastic dynamics. A great advantage of this version of the FDR is that it does not require the explicit knowledge of…
We study neutrino oscillations within the framework of extended theories of gravity. Based on the covariant reformulation of Pontecorvo formalism, we evaluate the oscillation probability of neutrinos propagating in static spacetimes…
We derive general expressions at the one-loop level for the coefficients of the covariant structure of the neutrino self-energy in the presence of a constant magnetic field. The neutrino energy spectrum and index of refraction are obtained…
A numerical model based on the finite-difference time-domain method is developed to simulate fluctuations which accompany the dephasing of atomic polarization and the decay of excited state's population. This model is based on the…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
A derivation of stochastic Schrodinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
The rapid development of neutrino astronomy, which is expressed, among other things, in the emergence of new neutrino mega-projects capable of efficient registering astrophysical neutrino fluxes requires a detailed knowledge of neutrino…
Simultaneous treatment of neutrino oscillations and collisions in astrophysical environments requires the use of (quantum) kinetic equations. Despite major advances in the field of quantum kinetics, the structure of the kinetic equations…