124,466 research outputs found
A geometric approach to integrability conditions for Riccati equations
Several instances of integrable Riccati equations are analyzed from the
geometric perspective of the theory of Lie systems. This provides us a unifying
viewpoint for previous approaches.Comment: 14 page
Integrability of Lie systems through Riccati equations
Integrability conditions for Lie systems are related to reduction or
transformation processes. We here analyse a geometric method to construct
integrability conditions for Riccati equations following these approaches. This
approach provides us with a unified geometrical viewpoint that allows us to
analyse some previous works on the topic and explain new properties. Moreover,
this new approach can be straightforwardly generalised to describe
integrability conditions for any Lie system. Finally, we show the usefulness of
our treatment in order to study the problem of the linearisability of Riccati
equations.Comment: Corrected typo
Entanglement production and decoherence-free subspace of two single-mode cavities embedded in a common environment
A system consisting of two identical single-mode cavities coupled to a common
environment is investigated within the framework of algebraic dynamics. Based
on the left and right representations of the Heisenberg-Weyl algebra, the
algebraic structure of the master equation is explored and exact analytical
solutions of this system are obtained. It is shown that for such a system, the
environment can produce entanglement in contrast to its commonly believed role
of destroying entanglement. In addition, the collective zero-mode eigen
solutions of the system are found to be free of decoherence against the
dissipation of the environment. These decoherence-free states may be useful in
quantum information and quantum computation.Comment: 10 pages, 7 figures, Revtex
A geometric approach to time evolution operators of Lie quantum systems
Lie systems in Quantum Mechanics are studied from a geometric point of view.
In particular, we develop methods to obtain time evolution operators of
time-dependent Schrodinger equations of Lie type and we show how these methods
explain certain ad hoc methods used in previous papers in order to obtain exact
solutions. Finally, several instances of time-dependent quadratic Hamiltonian
are solved.Comment: Accepted for publication in the International Journal of Theoretical
Physic
Utility of su(1,1)-Algebra in a Schematic Nuclear su(2)-Model
The su(2)-algebraic model interacting with an environment is investigated
from a viewpoint of treating the dissipative system. By using the
time-dependent variational approach with a coherent state and with the help of
the canonicity condition, the time-evolution of this quantum many-body system
is described in terms of the canonical equations of motion in the classical
mechanics. Then, it is shown that the su(1,1)-algebra plays an essential role
to deal with this model. An exact solution with appropriate initial conditions
is obtained by means of Jacobi's elliptic function. The implication to the
dissipative process is discussed.Comment: 14 pages using PTPTeX.st
A new level-dependent coarsegrid correction scheme for indefinite Helmholtz problems
In this paper we construct and analyse a level-dependent coarsegrid
correction scheme for indefinite Helmholtz problems. This adapted multigrid
method is capable of solving the Helmholtz equation on the finest grid using a
series of multigrid cycles with a grid-dependent complex shift, leading to a
stable correction scheme on all levels. It is rigourously shown that the
adaptation of the complex shift throughout the multigrid cycle maintains the
functionality of the two-grid correction scheme, as no smooth modes are
amplified in or added to the error. In addition, a sufficiently smoothing
relaxation scheme should be applied to ensure damping of the oscillatory error
components. Numerical experiments on various benchmark problems show the method
to be competitive with or even outperform the current state-of-the-art
multigrid-preconditioned Krylov methods, like e.g. CSL-preconditioned GMRES or
BiCGStab.Comment: 21 page
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