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.

PhysicsDegenerate energy levelsGeneral Physics and Astronomycoherent statesElectronic statesAlgebraFormalism (philosophy of mathematics)algebraic methods[ PHYS.PHYS.PHYS-AO-PH ] Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph]vibronic spectroscopyCoherent statesVibronic spectroscopyalgebra eigenstatesHarmonic oscillatorEigenvalues and eigenvectorsGroup theory
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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.

Pure mathematicsFunction field of an algebraic variety[ PHYS.QPHY ] Physics [physics]/Quantum Physics [quant-ph]010304 chemical physics03.65.Fd Algebraic methods - 31.15.Hz Group theoryAlgebraic extensionDimension of an algebraic variety010402 general chemistry01 natural sciencesAtomic and Molecular Physics and Optics0104 chemical sciencesAlgebraic cycle[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]Algebraic methodsQuantum mechanics0103 physical sciencesAlgebraic surfaceReal algebraic geometryAlgebraic functionGroup theoryDifferential algebraic geometryMathematicsThe European Physical Journal D
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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.

PhysicsQuantum PhysicsStatistical Mechanics (cond-mat.stat-mech)Thermodynamic equilibriumWave packetFOS: Physical sciencesGeneral Physics and AstronomyObservableQuantum mechanicPower lawSettore FIS/07 - Fisica Applicata(Beni Culturali Ambientali Biol.e Medicin)03.65.Ge Solutions of wave equations: bound states 02.60.Cb Numerical simulationtunnelingpower law distributionRelaxation (physics)Statistical physicssolution of equations 03.65.Xp Tunneling traversal time quantum Zeno dynamics 02.10.Ud Linear algebra03.65.Fd Algebraic methodsQuantum Physics (quant-ph)QuantumCondensed Matter - Statistical MechanicsEigenvalues and eigenvectorsQuantum well
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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.

O*-algebras Algebraic methods Algebraic topologySettore MAT/07 - Fisica Matematica
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