Consider a generalized Oseen evolution operator in 3D exterior domains, that is generated by a non-autonomous linearized system arising from time-dependent rigid motions. This was found by Hansel and Rhandi, and then ...
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Consider a generalized Oseen evolution operator in 3D exterior domains, that is generated by a non-autonomous linearized system arising from time-dependent rigid motions. This was found by Hansel and Rhandi, and then the theory was developed by the second author, however, desired regularity properties such as estimate of the temporal derivative as well as the H & ouml;lder estimate have remained open. The present paper provides us with those properties together with weighted estimates of the evolution operator. The results are then applied to the Navier-Stokes initial value problem, so that a new theorem on existence of a unique strong Lq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>q$$\end{document}-solution locally in time is proved.
The Lie-algebra technique is employed to construct symmetric expansions for the evolution operator of a molecular system with the Hamiltonian H-0 + V. An efficient representation for the evolution operator exp(-i/(h) ...
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The Lie-algebra technique is employed to construct symmetric expansions for the evolution operator of a molecular system with the Hamiltonian H-0 + V. An efficient representation for the evolution operator exp(-i/(h) over bar(H-0 + V)t) = exp(-i/6 (h) over bar Vt)exp(-i/2 (h) over bar H(0)t)exp(-2i/3 (h) over bar Vt-it(3)/72 (h) over bar(3)[[H-0,V],V])exp(-i/2 (h) over bar H(0)t)exp(-i/6 (h) over bar Vt), presented as an example is accurate up to the fifth order in time. (C) 1999 Elsevier Science B.V. All rights reserved.
In this paper the order of convergence of the evolution operator method used to solve a nonlinear autonomous system in ODE's [2] is investigated. The order is found, to be 2N+1 where N comes from the [N+1,N] Pade&...
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In this paper the order of convergence of the evolution operator method used to solve a nonlinear autonomous system in ODE's [2] is investigated. The order is found, to be 2N+1 where N comes from the [N+1,N] Pade' approximation used in the method. The order is independent of the choice of the weight function.
A unitary factorization of the evolution operator at order four is derived from the Magnus expansion with a time-dependent potential. Its efficiency is tested on various mesh treatments of a forced harmonic oscillator...
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A unitary factorization of the evolution operator at order four is derived from the Magnus expansion with a time-dependent potential. Its efficiency is tested on various mesh treatments of a forced harmonic oscillator. With respect to second order, accuracies are improved by more than an order of magnitude. (C) 2003 Elsevier B.V. All rights reserved.
This paper deals with the evolution operator of evolution algebras. The main goal is to obtain novel results of this operator, both in the case in which it is a derivation and when it is a homomorphism of algebras. Th...
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This paper deals with the evolution operator of evolution algebras. The main goal is to obtain novel results of this operator, both in the case in which it is a derivation and when it is a homomorphism of algebras. These new results constitute a criterion for classifying evolution algebras satisfying one of these conditions. An algorithm to obtain all these degenerate evolution algebras starting from those of smaller dimensions is also constructed.
Using the evolution operator method, we construct coherent states of a nonrelativistic free particle with a variable mass M(t) and a nonrelativistic particle with a variable mass M(t) in a homogeneous alternating fiel...
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Using the evolution operator method, we construct coherent states of a nonrelativistic free particle with a variable mass M(t) and a nonrelativistic particle with a variable mass M(t) in a homogeneous alternating field. Under certain physical conditions, they can be regarded as semiclassical states of particles. We discuss the properties (in particular, the completeness relation, the minimization of the uncertainty relations, and the time evolution of the corresponding probability density) of the found coherent states in detail. We also construct exact wave functions of the oscillator type and of the plane-wave type for the considered systems and compute the quantum Wigner distribution functions for the wave functions of coherent and oscillator states. We establish the unitary equivalence of the problems of a free particle and a particle in a homogeneous alternating field.
For the spatial stochastic susceptible-infected-susceptible model, we consider the perturbative series expansion of the gap between the dominant and subdominant eigenvalues of the evolution operator. We compute explic...
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For the spatial stochastic susceptible-infected-susceptible model, we consider the perturbative series expansion of the gap between the dominant and subdominant eigenvalues of the evolution operator. We compute explicitly the first terms of the series expansion of the gap with difference equations for the calculation of states.
In this letter the explicit form of the evolution operator of the Tavis-Cummings model with three and four atoms is given. This is an important progress in quantum optics or mathematical physics.
In this letter the explicit form of the evolution operator of the Tavis-Cummings model with three and four atoms is given. This is an important progress in quantum optics or mathematical physics.
We reassess in this letter the issue of a paradox in quantum mechanics discussed in the literature. We indicate how this paradox can be solved, or at least avoided, through a simple application of the time evolution t...
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We reassess in this letter the issue of a paradox in quantum mechanics discussed in the literature. We indicate how this paradox can be solved, or at least avoided, through a simple application of the time evolution theorem.
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