Search results for "Perturbation expansion"

showing 2 items of 2 documents

Scaling property of variational perturbation expansion for a general anharmonic oscillator with xp-potential

1995

We prove a powerful scaling property for the extremality condition in the recently developed variational perturbation theory which converts divergent perturbation expansions into exponentially fast convergent ones. The proof is given for the energy eigenvalues of an anharmonic oscillator with an arbitrary $x^p$-potential. The scaling property greatly increases the accuracy of the results.

Perturbation expansionPhysicsVariational perturbation theoryAnharmonicityGeneral Physics and AstronomyPerturbation (astronomy)ScalingEigenvalues and eigenvectorsMathematical physicsPhysics Letters A
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Quantum averaging for driven systems with resonances

2000

Abstract We discuss the effects of resonances in driven quantum systems within the context of quantum averaging techniques in the Floquet representation. We consider in particular iterative methods of KAM type and the extensions needed to take into account resonances. The approach consists in separating the coupling terms into resonant and nonresonant components at a given scale of time and intensity. The nonresonant part can be treated with perturbative techniques, which we formulate in terms of KAM-type unitary transformations that are close to the identity. These can be interpreted as averaging procedures with respect to the dynamics defined by effective uncoupled Hamiltonians. The reson…

Statistics and ProbabilityFloquet theoryIterative methodCondensed Matter PhysicsUnitary statePerturbation expansionRenormalizationsymbols.namesakeClassical mechanicsQuantum mechanicssymbolsHamiltonian (quantum mechanics)QuantumMathematicsPhysica A: Statistical Mechanics and its Applications
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