Search results for "Continuous spectrum"
showing 10 items of 15 documents
Floquet spectrum for two-level systems in quasiperiodic time-dependent fields
1992
We study the time evolution ofN-level quantum systems under quasiperiodic time-dependent perturbations. The problem is formulated in terms of the spectral properties of a quasienergy operator defined in an enlarged Hilbert space, or equivalently of a generalized Floquet operator. We discuss criteria for the appearance of pure point as well as continuous spectrum, corresponding respectively to stable quasiperiodic dynamics and to unstable chaotic behavior. We discuss two types of mechanisms that lead to instability. The first one is due to near resonances, while the second one is of topological nature and can be present for arbitrary ratios between the frequencies of the perturbation. We tre…
The closed form of the second-order energy shift for the discrete spectrum of atomic hydrogen
2004
The closed form of the second-order energy shift for the discrete spectrum of atomic hydrogen is obtained, which allows us to evaluate the level shift in both cases, when the intermediate states are in continuum and in the discrete spectrum, except the resonances. The values of the second-order shift of the energy of the ground state calculated by us are in good agreement with those obtained by us and other authors using the nonperturbative Floquet method in average up to a radiation intensity of 1015 W cm−2.
Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential
2020
Abstract We consider a two phase eigenvalue problem driven by the ( p , q ) -Laplacian plus an indefinite and unbounded potential, and Robin boundary condition. Using a modification of the Nehari manifold method, we show that there exists a nontrivial open interval I ⊆ R such that every λ ∈ I is an eigenvalue with positive eigenfunctions. When we impose additional regularity conditions on the potential function and the boundary coefficient, we show that we have smooth eigenfunctions.
A swept-current magnetic lens plus Si(Li) electron spectrometer with simultaneous momentum and energy selection
1975
Abstract A combined swept-current magnetic lens plus Si(Li) electron spectrometer with simultaneous momentum and energy selection is presented. The spectrometer is intended for in-beam measurements of conversion electron lines up to several MeV in energy and for nanosecond lifetime determinations, as well as for off-beam studies of continuous beta-ray spectra and conversion lines from short-lived activities. The sweeping of the lens current is automatized and the energy selection, synchronously with the momentum, is performed using a simple digital window arrangement. The performance of the spectrometer is demonstrated in conversion electron and continuous spectrum measurements. Different v…
Ober Ein Rayleigh-Ritz-Verfahren zur Bestimmung Kritischer Werte
1980
This paper is concerned with the existence of critical points for a functional f defined on the level set of a second functional g. Existence of nontrivial solutions for the nonlinear eigenvalue-problem f′(u) = λg′(u) and convergence for a nonlinear analogue to the Rayleigh-Ritz-Method is proven. The results are applied to a nonlinear ordinary eigenvalue problem where it is shown that the lowest point in the continuous spectrum of the associated linearized operator is a bifurcation point of infinite multiplicity.
Generalization of the atomic random-phase-approximation method for diatomic molecules:N2photoionization cross-section calculations
2000
Partial and total photoionization cross sections of ${\mathrm{N}}_{2}$ molecule are calculated using the generalization of the random-phase approximation (RPA) which earlier has been successfully applied to the description of the atomic photoionization processes. According to this method, at first the Hartree-Fock (HF) ground-state wave functions are calculated in prolate spheroidal coordinates using the fixed-nuclei approximation. With their help the zero order basis set of single particle Hartree-Fock wave functions containing both discrete excited states and continuous spectrum is calculated in the field of a frozen core of a singly charged ion. The calculations are performed for all fou…
A Look at Some Remarkable Mathematical Techniques
1996
The nonlinear equations that we have encountered in the previous chapters can be solved by using mathematical techniques such as the powerful inverse scattering transform (IST) (Gardner et al. 1967) and the remarkable Hirota method (Hirota 1971). Specifically, in addition to the one-soliton solutions, explicit multisoliton solutions representing the interaction of any number of solitons can be constructed. Moreover, in several cases a precise prediction, closely related to experiments, can be made by the IST of the nonlinear response of the physical system, that is, of the number of solitons that can emerge from a finite initial disturbance (Zakharov, 1980. Ablowitz and Segur 1981; Calogero…
Corrections for positon annihilation in flight in nuclear spectrometry
1973
Abstract Theories of positon single- and two-quanta annihilation in flight, the Fermi beta-decay theory, and theories of positon energy loss are used in calculations of total probabilities of annihilation in flight of positons in continuous spectra. The results are given in a nomogram useful in correcting for positon annihilation in flight in various nuclear-spectrometry experiments. Confirmation of the theoretical basis employed was obtained by comparing total absolute probabilities for annihilation in flight of 62 Cu positons in Perspex, copper, cadmium and lead, using a new differential method. The agreement with the theory was found to be excellent. A method for obtaining “correct” posi…
Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy
2012
In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting plate. Using an appropriate Bogoliubov-type transformation we can diagonalize exactly the Hamiltonian of our system in the continuum limit and obtain non-perturbative expressions for its ground-state energy. From the expressions found, the atom-wall Casimir-Polder interaction energy can be obtained, and well-know lowest-order results are recovered as a limiting case. Use and advantage of this method for dealing with other systems where perturbation theory …
Density-potential mappings in quantum dynamics
2012
In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether the density of a time-dependent quantum system determines its external potential was reformulated as a fixed point problem. This idea was used to generalize the existence and uniqueness theorems underlying time-dependent density functional theory. In this work we extend this proof to allow for more general norms and provide a numerical implementation of the fixed-point iteration scheme. We focus on the one-dimensional case as it allows for a more in-depth analysis using singular Sturm-Liouville theory and at the same time provides an easy visualization of the numerical applications in space and time. We give an ex…