Related papers: Derivation of Maxwell-Bloch-type equations by proj…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
Using standard coordinates, the Maxwell equations in the Reissner-Nordstr\"om geometry are written in terms of a couple of scalar fields satisfying Klein-Gordon like equations. The density of states is derived in the semi-classical…
With the aim of derive a quasi-monomiality formulation in the context of discrete hypercomplex variables, one will amalgamate through a Clifford-algebraic structure of signature $(0,n)$ the umbral calculus framework with Lie-algebraic…
We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace…
One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold. Such manifolds are usually found using local…
We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a $k$-dimensional differentiable manifold $M \subseteq \mathbb{R}^m$. We assume that…
Stochastic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell's equations as used in the magnetotelluric method. The stochastic form of the exact solution of Maxwell's equations is evaluated using…
We extend quantum state tomography with minimal cumulative disturbance, first investigated in [arXiv:2406.18370], to arbitrary finite-dimensional pure states. A learner sequentially receives fresh copies of an unknown pure state, chooses a…
Following the ideas N. N. Bogoliubov used to derive the classical and quantum nonlinear kinetic equations, we give an alternative derivation of the Redfield quantum linear master equation, which is widely used in the theory of open quantum…
We explore quantum corrections of electrically charged black holes subject to vacuum polarization effects of fermion fields in QED. Solving this problem exactly is challenging so we restrict to perturbative corrections that one can obtain…
The magnetotelluric approximation of the Maxwell's equations is used to model the propagation of low frequency electro-magnetic waves in the Earth's subsurface, with the purpose of reconstructing the presence of mineral or oil deposits. We…
Complete and physically adequate analytical and semi-analytical solutions have been obtained using a practical dimensionless form of kinetic equation assuming azimuthal symmetry and Maxwellian distributions of target plasma species.…
We compute quasinormal mode frequencies for static limits of physical black holes - semi-classical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity.…
The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB…
Pointing out the incompleteness of conventional macroscopic Maxwell equations (M-eqs.), we propose a new form derived from the long wavelength approximation (LWA) of microscopic nonlocal response. From the general Hamilonian of matter and…
This paper aims to develop a Newton-type method to solve a class of nonconvex composite programs. In particular, the nonsmooth part is possibly nonconvex. To tackle the nonconvexity, we develop a notion of strong prox-regularity which is…
The combination of Maxwell and X-ray Bloch equations forms an appropriate framework to describe ultrafast time-resolved X-ray experiments on attosecond time scale in crystalline solids. However, broadband experiments such as X-ray…
Maxwell-Amp\`{e}re-Nernst-Planck (MANP) equations were recently proposed to model the dynamics of charged particles. In this study, we enhance a numerical algorithm of this system with deep learning tools. The proposed hybrid algorithm…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
Dynamics of a state of interest coupled to a non-Markovian environment is studied for the first time by concatenating the non-Markovian quantum state diffusion (QSD) equation and the Feshbach projection operator partitioning technique. An…