Related papers: Analytical operator solution of master equations d…
We study the global hypoellipticity and solvability of strongly invariant operators and systems of strongly invariant operators on closed manifolds. Our approach is based on the Fourier analysis induced by an elliptic pseudo-differential…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…
Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a…
A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer…
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…
Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions…
We describe an ambisonics enhancement method that increases the signal strength in specified directions at low computational cost. The method can be used in a static setup to emphasize the signal arriving from a particular direction or set…
We propose a general method for simplifying master equations by eliminating from the description rapidly evolving states. The physical recipe we impose is the suppression of these states and a renormalization of the rates of all the…
In this paper we discuss a master equation applied to the two level system of an atom and derive an exact solution to it in an abstract manner. We also present a problem and a conjecture based on the three level system. Our results may give…
Quantum master equations are an important tool in quantum optics and quantum information theory. For systems comprising a small to medium number of atoms (or qubits), the non-truncated equations are usually solved numerically. In this…
The exact fermion master equation previously obtained in [Phys. Rev. B \textbf{78}, 235311 (2008); New J. Phys. \textbf{12}, 083013 (2010)] describes the dynamics of quantum states of a principal system of fermionic particles under the…
Given an observable and its operator product expansion (OPE), we present expressions that carefully disentangle truncated sums of the perturbative series in powers of $\alpha$ from the non-perturbative (NP) corrections. This splitting is…
On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied…
Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to…
In the field of atom optics, the basis of many experiments is a two level atom coupled to a light field. The evolution of this system is governed by a master equation. The irreversible components of this master equation describe the…
The phase-field method has become a useful tool for the simulation of classical metallurgical phase transformations as well as other phenomena related to materials science. The thermodynamic consistency that forms the basis of these…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…