743 research outputs found
Optimal Topological Test for Degeneracies of Real Hamiltonians
We consider adiabatic transport of eigenstates of real Hamiltonians around
loops in parameter space. It is demonstrated that loops that map to nontrivial
loops in the space of eigenbases must encircle degeneracies. Examples from
Jahn-Teller theory are presented to illustrate the test. We show furthermore
that the proposed test is optimal.Comment: Minor corrections, accepted in Phys. Rev. Let
Scaling of Berry's Phase Close to the Dicke Quantum Phase Transition
We discuss the thermodynamic and finite size scaling properties of the
geometric phase in the adiabatic Dicke model, describing the super-radiant
phase transition for an qubit register coupled to a slow oscillator mode.
We show that, in the thermodynamic limit, a non zero Berry phase is obtained
only if a path in parameter space is followed that encircles the critical
point. Furthermore, we investigate the precursors of this critical behavior for
a system with finite size and obtain the leading order in the 1/N expansion of
the Berry phase and its critical exponent
Signed zeros of Gaussian vector fields-density, correlation functions and curvature
We calculate correlation functions of the (signed) density of zeros of
Gaussian distributed vector fields. We are able to express correlation
functions of arbitrary order through the curvature tensor of a certain abstract
Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and
two-point functions. The zeros of a two-dimensional Gaussian vector field model
the distribution of topological defects in the high-temperature phase of
two-dimensional systems with orientational degrees of freedom, such as
superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear
in J. Phys.
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
Dynamical Jahn-Teller Effect and Berry Phase in Positively Charged Fullerene I. Basic Considerations
We study the Jahn-Teller effect of positive fullerene ions C
and C. The aim is to discover if this case, in analogy with the
negative ion, possesses a Berry phase or not, and what are the consequences on
dynamical Jahn-Teller quantization. Working in the linear and spherical
approximation, we find no Berry phase in C, and
presence/absence of Berry phase for coupling of one hole to an
/ vibration. We study in particular the special equal-coupling case
(), which is reduced to the motion of a particle on a 5-dimensional
sphere. In the icosahedral molecule, the final outcome assesses the
presence/absence of a Berry phase of for the hole coupled to
/ vibrations. Some qualitative consequences on ground-state symmetry,
low-lying excitations, and electron emission from C are spelled out.Comment: 31 pages (RevTeX), 3 Postscript figures (uuencoded
A Laboratory Study of Nonlinear Surface Waves on Water
This paper describes an experimental investigation in which a large number of water waves were focused at one point in space and time to produce a large transient wave group. Measurements of the water surface elevation and the underlying kinematics are compared with both a linear wave theory and a second-order solution based on the sum of the wave-wave interactions identified by Longuet-Higgins & Stewart (1960). The data shows that the focusing of wave components produces a highly nonlinear wave group in which the nonlinearity increases with the wave amplitude and reduces with increasing bandwidth. When compared with the first- and second-order solutions, the wave-wave interactions produce a steeper wave envelope in which the central wave crest is higher and narrower, while the adjacent wave troughs are broader and less deep. The water particle kinematics are also strongly nonlinear. The accumulated experimental data suggest that the formation of a focused wave group involves a significant transfer of energy into both the higher and lower har¬monics. This is consistent with an increase in the local energy density, and the development of large velocity gradients near the water surface. Furthermore, the nonlinear wave-wave interactions are shown to be fully reversible. However, when compared to a linear solution there is a permanent change in the relative phase of the free waves. This explains the downstream shifting of the focus point (Longuet-Higgins 1974), and appears to be similar to the phase changes which result from the nonlinear interaction of solitons travelling at different velocities (Yuen & Lake 1982)
Electron--Vibron Interactions and Berry Phases in Charged Buckminsterfullerene: Part I
A simple model for electron-vibron interactions on charged
buckminsterfullerene C, , is solved both at weak and
strong couplings. We consider a single vibrational multiplet interacting
with electrons. At strong coupling the semiclassical dynamical
Jahn-Teller theory is valid. The Jahn-Teller distortions are unimodal for
=1,2,4,5 electrons, and bimodal for 3 electrons. The distortions are
quantized as rigid body pseudo--rotators which are subject to geometrical Berry
phases. These impose ground state degeneracies and dramatically change zero
point energies. Exact diagonalization shows that the semiclassical level
degeneracies and ordering survive well into the weak coupling regime. At weak
coupling, we discover an enhancement factor of for the pair binding
energies over their classical values. This has potentially important
implications for superconductivity in fullerides, and demonstrates the
shortcoming of Migdal--Eliashberg theory for molecular crystals.Comment: 29 pages (+7 figures, 3 available upon request), LATEX,
report-number: BM515
Statistics of Gravitational Microlensing Magnification. I. Two-Dimensional Lens Distribution
(Abridged) In this paper we refine the theory of microlensing for a planar
distribution of point masses. We derive the macroimage magnification
distribution P(A) at high magnification (A-1 >> tau^2) for a low optical depth
(tau << 1) lens distribution by modeling the illumination pattern as a
superposition of the patterns due to individual ``point mass plus weak shear''
lenses. We show that a point mass plus weak shear lens produces an astroid-
shaped caustic and that the magnification cross-section obeys a simple scaling
property. By convolving this cross-section with the shear distribution, we
obtain a caustic-induced feature in P(A) which also exhibits a simple scaling
property. This feature results in a 20% enhancement in P(A) at A approx 2/tau.
In the low magnification (A-1 << 1) limit, the macroimage consists of a bright
primary image and a large number of faint secondary images formed close to each
of the point masses. Taking into account the correlations between the primary
and secondary images, we derive P(A) for low A. The low-A distribution has a
peak of amplitude ~ 1/tau^2 at A-1 ~ tau^2 and matches smoothly to the high-A
distribution. We combine the high- and low-A results and obtain a practical
semi-analytic expression for P(A). This semi-analytic distribution is in
qualitative agreement with previous numerical results, but the latter show
stronger caustic-induced features at moderate A for tau as small as 0.1. We
resolve this discrepancy by re-examining the criterion for low optical depth. A
simple argument shows that the fraction of caustics of individual lenses that
merge with those of their neighbors is approx 1-exp(-8 tau). For tau=0.1, the
fraction is surprisingly high: approx 55%. For the purpose of computing P(A) in
the manner we did, low optical depth corresponds to tau << 1/8.Comment: 35 pages, including 6 figures; uses AASTeX v4.0 macros; submitted to
Ap
Geometric phases and hidden local gauge symmetry
The analysis of geometric phases associated with level crossing is reduced to
the familiar diagonalization of the Hamiltonian in the second quantized
formulation. A hidden local gauge symmetry, which is associated with the
arbitrariness of the phase choice of a complete orthonormal basis set, becomes
explicit in this formulation (in particular, in the adiabatic approximation)
and specifies physical observables. The choice of a basis set which specifies
the coordinate in the functional space is arbitrary in the second quantization,
and a sub-class of coordinate transformations, which keeps the form of the
action invariant, is recognized as the gauge symmetry. We discuss the
implications of this hidden local gauge symmetry in detail by analyzing
geometric phases for cyclic and noncyclic evolutions. It is shown that the
hidden local symmetry provides a basic concept alternative to the notion of
holonomy to analyze geometric phases and that the analysis based on the hidden
local gauge symmetry leads to results consistent with the general prescription
of Pancharatnam. We however note an important difference between the geometric
phases for cyclic and noncyclic evolutions. We also explain a basic difference
between our hidden local gauge symmetry and a gauge symmetry (or equivalence
class) used by Aharonov and Anandan in their definition of generalized
geometric phases.Comment: 25 pages, 1 figure. Some typos have been corrected. To be published
in Phys. Rev.
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