Related papers: A functional calculus for the magnetization dynami…
Given a smooth manifold $M$ (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the G\r{a}rding inequality…
Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations…
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…
We propose a numerical technique for calculating effective actions of electromagnetic backgrounds based on the worldline formalism. As a conceptually simple example, we consider scalar electrodynamics in three dimensions to one-loop order.…
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
The description of interacting many-electron systems in external magnetic fields is considered in the framework of the optimized effective potential method extended to current-spin-density functional theory. As a case study, a…
Using the worldline formalism we compute an effective action for fermions under a temporally modulated electric field and a spatially modulated magnetic field. It is known that the former leads to an enhanced Schwinger Mechanism, while we…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
In this article, a few problems related to multiscale modelling of magnetic materials at finite temperatures and possible ways of solving these problems are discussed. The discussion is mainly centred around two established multiscale…
An efficient method to compute magnetic exchange interactions in systems with strong correlations is introduced. It is based on a magnetic force theorem which evaluates linear response due to rotations of magnetic moments and uses a novel…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
We develop the general formalism for the study of neutrino propagation in presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival probabilities and higher…
Numerical integration of a stochastic Landau-Lifshitz-Gilbert equation is used to study dynamic processes in single-domain nanoscale magnets at nonzero temperatures. Special attention is given to including thermal fluctuations as a Langevin…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Markovian master equations underlie many areas of modern physics and, despite their apparent simplicity, they encode a rich and complex dynamics which is still under active research. We identify a class of continuous variable Markovian…
In this article, we put forward a new approach to electrodynamics of materials. Based on the identification of induced electromagnetic fields as the microscopic counterparts of polarization and magnetization, we systematically employ the…
Spin torques, that is, effects of conduction electrons on magnetization dynamics, are calculated microscopically in the first order in spatial gradient and time derivative of magnetization. Special attention is paid to the so-called…