1,223 research outputs found
Quasi-exact-solution of the Generalized Exe Jahn-Teller Hamiltonian
We consider the solution of a generalized Exe Jahn-Teller Hamiltonian in the
context of quasi-exactly solvable spectral problems. This Hamiltonian is
expressed in terms of the generators of the osp(2,2) Lie algebra. Analytical
expressions are obtained for eigenstates and eigenvalues. The solutions lead to
a number of earlier results discussed in the literature. However, our approach
renders a new understanding of ``exact isolated'' solutions
The distribution of extremal points of Gaussian scalar fields
We consider the signed density of the extremal points of (two-dimensional)
scalar fields with a Gaussian distribution. We assign a positive unit charge to
the maxima and minima of the function and a negative one to its saddles. At
first, we compute the average density for a field in half-space with Dirichlet
boundary conditions. Then we calculate the charge-charge correlation function
(without boundary). We apply the general results to random waves and random
surfaces. Furthermore, we find a generating functional for the two-point
function. Its Legendre transform is the integral over the scalar curvature of a
4-dimensional Riemannian manifold.Comment: 22 pages, 8 figures, corrected published versio
A note on wave set-up
Seaward of the breaker zone, the observations of Saville are in good qualitative agreement with the prediction that the mean surface level is increasingly depressed towards the shoreline
Topological properties of Berry's phase
By using a second quantized formulation of level crossing, which does not
assume adiabatic approximation, a convenient formula for geometric terms
including off-diagonal terms is derived. The analysis of geometric phases is
reduced to a simple diagonalization of the Hamiltonian in the present
formulation. If one diagonalizes the geometric terms in the infinitesimal
neighborhood of level crossing, the geometric phases become trivial for any
finite time interval . The topological interpretation of Berry's phase such
as the topological proof of phase-change rule thus fails in the practical
Born-Oppenheimer approximation, where a large but finite ratio of two time
scales is involved.Comment: 9 pages. A new reference was added, and the abstract and the
presentation in the body of the paper have been expanded and made more
precis
Peierls transition in the quantum spin-Peierls model
We use the density matrix renormalization group method to investigate the
role of longitudinal quantized phonons on the Peierls transition in the
spin-Peierls model. For both the XY and Heisenberg spin-Peierls model we show
that the staggered phonon order parameter scales as (and the
dimerized bond order scales as ) as (where
is the electron-phonon interaction). This result is true for both linear and
cyclic chains. Thus, we conclude that the Peierls transition occurs at
in these models. Moreover, for the XY spin-Peierls model we show
that the quantum predictions for the bond order follow the classical prediction
as a function of inverse chain size for small . We therefore conclude
that the zero phase transition is of the mean-field type
Some model experiments on continental shelf waves
This paper describes some model experiments that verify the theoretical form of continental shelf waves. Both the dispersion relationship and the positions of the orbital gyres are confirmed. The existence of a maximum frequency for each mode, with a corresponding zero group velocity, may be of significance for field observations
Steep sharp-crested gravity waves on deep water
A new type of steady steep two-dimensional irrotational symmetric periodic
gravity waves on inviscid incompressible fluid of infinite depth is revealed.
We demonstrate that these waves have sharper crests in comparison with the
Stokes waves of the same wavelength and steepness. The speed of a fluid
particle at the crest of new waves is greater than their phase speed.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
The initial development of a jet caused by fluid, body and free surface interaction. Part 5. Parasitic capillary waves on an initially horizontal surface
Switching of Geometric Phase in Degenerate Systems
The geometric and open path phases of a four-state system subject to time
varying cyclic potentials are computed from the Schr\"{o}dinger equation. Fast
oscillations are found in the non-adiabatic case. For parameter values such
that the system possesses degenerate levels, the geometric phase becomes
anomalous, undergoing a sign switch. A physical system to which the results
apply is a molecular dimer with two interacting electrons. Additionally, the
sudden switching of the geometric phase promises to be an efficient control in
two-qubit quantum computing.Comment: 15 pages, 4 figures,accepted by Physics Letters A (2000
Enhanced Electron Pairing in a Lattice of Berry Phase Molecules
We show that electron hopping in a lattice of molecules possessing a Berry
phase naturally leads to pairing. Our building block is a simple molecular site
model inspired by C, but realized in closer similarity with Na. In
the resulting model electron hopping must be accompanied by orbital operators,
whose function is to switch on and off the Berry phase as the electron number
changes. The effective hamiltonians (electron-rotor and electron-pseudospin)
obtained in this way are then shown to exhibit a strong pairing phenomenon, by
means of 1D linear chain case studies. This emerges naturally from numerical
studies of small -site rings, as well as from a BCS-like mean-field theory
formulation. The pairing may be explained as resulting from the exchange of
singlet pairs of orbital excitations, and is intimately connected with the
extra degeneracy implied by the Berry phase when the electron number is odd.
The relevance of this model to fullerides, to other molecular superconductors,
as well as to present and future experiments, is discussed.Comment: 30 pages, RevTe
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