353 research outputs found
Quantizing the damped harmonic oscillator
We consider the Fermi quantization of the classical damped harmonic
oscillator (dho). In past work on the subject, authors double the phase space
of the dho in order to close the system at each moment in time. For an
infinite-dimensional phase space, this method requires one to construct a
representation of the CAR algebra for each time. We show that unitary dilation
of the contraction semigroup governing the dynamics of the system is a logical
extension of the doubling procedure, and it allows one to avoid the
mathematical difficulties encountered with the previous method.Comment: 4 pages, no figure
Engineered nonlinear lattices
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term a quasilattice, which interpolates between a lattice system and a continuous system.Peer ReviewedPostprint (published version
Algebraic Model for scattering of three-s-cluster systems. II. Resonances in the three-cluster continuum of 6He and 6Be
The resonance states embedded in the three-cluster continuum of 6He and 6Be
are obtained in the Algebraic Version of the Resonating Group Method. The model
accounts for a correct treatment of the Pauli principle. It also provides the
correct three-cluster continuum boundary conditions by using a Hyperspherical
Harmonics basis. The model reproduces the observed resonances well and achieves
good agreement with other models. A better understanding for the process of
formation and decay of the resonance states in six-nucleon systems is obtained.Comment: 8 pages, 10 postscript figures, submitted to Phys. Rev.
Localization of shadow poles by complex scaling
Through numerical examples we show that the complex scaling method is suited
to explore the pole structure in multichannel scattering problems. All poles
lying on the multisheeted Riemann energy surface, including shadow poles, can
be revealed and the Riemann sheets on which they reside can be identified.Comment: 6 pages, Latex with Revtex, 3 figures (not included) available on
reques
Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices
A direct and exact method for calculating the density of states for systems
with localized potentials is presented. The method is based on explicit
inversion of the operator . The operator is written in the discrete
variable representation of the Hamiltonian, and the Toeplitz property of the
asymptotic part of the obtained {\it infinite} matrix is used. Thus, the
problem is reduced to the inversion of a {\it finite} matrix
Resonance-free Region in scattering by a strictly convex obstacle
We prove the existence of a resonance free region in scattering by a strictly
convex obstacle with the Robin boundary condition. More precisely, we show that
the scattering resonances lie below a cubic curve which is the same as in the
case of the Neumann boundary condition. This generalizes earlier results on
cubic poles free regions obtained for the Dirichlet boundary condition.Comment: 29 pages, 2 figure
A complementary metal-oxide-semiconductor compatible monocantilever 12-point probe for conductivity measurements on the nanoscale
Second order perturbation theory for embedded eigenvalues
We study second order perturbation theory for embedded eigenvalues of an
abstract class of self-adjoint operators. Using an extension of the Mourre
theory, under assumptions on the regularity of bound states with respect to a
conjugate operator, we prove upper semicontinuity of the point spectrum and
establish the Fermi Golden Rule criterion. Our results apply to massless
Pauli-Fierz Hamiltonians for arbitrary coupling.Comment: 30 pages, 2 figure
Three-body resonances in He-6, Li-6, and Be-6, and the soft dipole mode problem of neutron halo nuclei
Using the complex scaling method, the low-lying three-body resonances of
He, Li, and Be are investigated in a parameter-free microscopic
three-cluster model. In He a 2, in Li a 2 and a 1, and in
Be the 0 ground state and a 2 excited state is found. The other
experimentally known 2 state of Li cannot be localized by our present
method. We have found no indication for the existence of the predicted 1
soft dipole state in He. We argue that the sequential decay mode of He
through the resonant states of its two-body subsystem can lead to peaks in the
excitation function. This process can explain the experimental results in the
case of Li, too. We propose an experimental analysis, which can decide
between the soft dipole mode and the sequential decay mode.Comment: REVTEX, Submitted to Phys. Rev. C, 12 pages, 2 postscript figures are
available upon request. CALTECH, MAP-16
Resonance Lifetimes from Complex Densities
The ab-initio calculation of resonance lifetimes of metastable anions
challenges modern quantum-chemical methods. The exact lifetime of the
lowest-energy resonance is encoded into a complex "density" that can be
obtained via complex-coordinate scaling. We illustrate this with one-electron
examples and show how the lifetime can be extracted from the complex density in
much the same way as the ground-state energy of bound systems is extracted from
its ground-state density
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