oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
On some dynamical and geometrical properties of the Maxwell-Bloch equations with a quadratic control  [PDF]
Tudor Binzar,Cristian Lazureanu
Physics , 2014,
Abstract: In this paper, we analyze the stability of the real-valued Maxwell-Bloch equations with a control that depends on state variables quadratically. We also investigate the topological properties of the energy-Casimir map, as well as the existence of periodic orbits and explicitly construct the heteroclinic orbits.
On the Generalized Maxwell-Bloch Equations
Pavle Saksida
Symmetry, Integrability and Geometry : Methods and Applications , 2006,
Abstract: A new Hamiltonian structure of the Maxwell-Bloch equations is described. In this setting the Maxwell-Bloch equations appear as a member of a family of generalized Maxwell-Bloch systems. The family is parameterized by compact semi-simple Lie groups, the original Maxwell-Bloch system being the member corresponding to SU(2). The Hamiltonian structure is then used in the construction of a new family of symmetries and the associated conserved quantities of the Maxwell-Bloch equations.
On the Generalized Maxwell-Bloch Equations  [PDF]
Pavle Saksida
Physics , 2006, DOI: 10.3842/SIGMA.2006.038
Abstract: A new Hamiltonian structure of the Maxwell-Bloch equations is described. In this setting the Maxwell-Bloch equations appear as a member of a family of generalized Maxwell-Bloch systems. The family is parameterized by compact semi-simple Lie groups, the original Maxwell-Bloch system being the member corresponding to SU(2). The Hamiltonian structure is then used in the construction of a new family of symmetries and the associated conserved quantities of the Maxwell-Bloch equations.
Poisson geometry of the Maxwell-Bloch top system and stability problem  [PDF]
Mihai Ivan
Mathematics , 2014,
Abstract: Dynamics of Maxwell-Bloch top system, that includes Maxwell-Bloch and Lorenz-Hamilton equations as particular cases, is studied in the framework Poisson geometry. Constants of motion as well as the relation of solution to that of pendulum are presented. Equilibrium states are determined and their complete stability analysis are performed. Results are applied to an optimal control problem on the Lie group G4.
Symmetries of the Maxwell-Bloch equations with the rotating wave approximation  [PDF]
Ioan Casu
Mathematics , 2014, DOI: 10.1134/S1560354714050037
Abstract: In this paper a symplectic realization for the Maxwell-Bloch equations with the rotating wave approximation is given, which also leads to a Lagrangian formulation. We show how Lie point symmetries generate a third constant of motion for the considered dynamical system.
Geometrical Properties of Feynman Path Integrals  [PDF]
Timur F. Kamalov
Physics , 2008,
Abstract: This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields background. We are finding to the imagined Feynman Path a classical model of test particles as geodesic trajectory in the curved space of Projected Hilbert space on Bloch's sphere.
Q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice  [PDF]
Andrei Rybin,Jussi Timonen,Gennadii Varzugin,Robin K. Bullough
Physics , 2000, DOI: 10.1088/0305-4470/34/1/312
Abstract: We report for the first time exact solutions of a completely integrable nonlinear lattice system for which the dynamical variables satisfy a q-deformed Lie algebra - the Lie-Poisson algebra su_q(2). The system considered is a q-deformed lattice for which in continuum limit the equations of motion become the envelope Maxwell-Bloch (or SIT) equations describing the resonant interaction of light with a nonlinear dielectric. Thus the N-soliton solutions we here report are the natural q-deformations, necessary for a lattice, of the well-known multi-soliton and breather solutions of self-induced transparency (SIT). The method we use to find these solutions is a generalization of the Darboux-Backlund dressing method. The extension of these results to quantum solitons is sketched.
A geometrical angle on Feynman integrals  [PDF]
A. I. Davydychev,R. Delbourgo
Mathematics , 1997, DOI: 10.1063/1.532513
Abstract: A direct link between a one-loop N-point Feynman diagram and a geometrical representation based on the N-dimensional simplex is established by relating the Feynman parametric representations to the integrals over contents of (N-1)-dimensional simplices in non-Euclidean geometry of constant curvature. In particular, the four-point function in four dimensions is proportional to the volume of a three-dimensional spherical (or hyperbolic) tetrahedron which can be calculated by splitting into birectangular ones. It is also shown that the known formula of reduction of the N-point function in (N-1) dimensions corresponds to splitting the related N-dimensional simplex into N rectangular ones.
Diffraction of Bloch Wave Packets for Maxwell's Equations  [PDF]
Grégoire Allaire,Mariapia Palombaro,Jeffrey Rauch
Mathematics , 2012, DOI: 10.1142/S0219199713500405
Abstract: We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct accurate approximate solutions of three scale WKB type. The leading profile is both transported at the group velocity and dispersed by a Schr\"odinger equation given by the quadratic approximation of the Bloch dispersion relation. A weak ray average hypothesis guarantees stability. Compared to earlier work on scalar wave equations, the generator is no longer elliptic. Coercivity holds only on the complement of an infinite dimensional kernel. The system structure requires many innovations.
Weighted Bloch spaces and quadratic integrals  [PDF]
Evgueni Doubtsov
Mathematics , 2013,
Abstract: Let $\mathcal{B}^{\omega}(B_d)$ denote the $\omega$-weighted Bloch space in the unit ball $B_d$ of $\mathbb{C}^d$, $d\ge 1$. We show that the quadratic integral $$ \int_x^1 \frac{\omega^2(t)}{t}\, dt,\quad 0
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.