Search results for "Algebraic methods"
showing 4 items of 4 documents
The algebra eigenstates method for some systems with spin-like interactions
2006
International audience; An extension of the algebra eigenstates formalism is proposed to solve the eigenvalue equation for a class of problems involving "spin interactions". The method is detailed for the harmonic oscillator, su(2) and su(1, 1) algebras. Special emphasis is given to the resolution of problems in vibronic spectroscopy involving doubly degenerate electronic states.
Algebraic time-reversal operation
1999
International audience; We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups U(5) U(4) K(4) = A(4) ^ S(4) S(4) Td. We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the time inversion symmetry. As a result we can determine the TR behavior of purely algebraic operators.
Scale-free relaxation of a wave packet in a quantum well with power-law tails
2013
We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: A quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ~ x^{-2} and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.
A short note on O*-algebras and quantum dynamics
2009
We review some recent results concerning algebraic dynamics and O*-algebras. We also give a perturbative condition which can be used, in connection with previous results, to define a time evolution via a limiting procedure.