1,508 research outputs found
Second quantized formulation of geometric phases
The level crossing problem and associated geometric terms are neatly
formulated by the second quantized formulation. This formulation exhibits a
hidden local gauge symmetry related to the arbitrariness of the phase choice of
the complete orthonormal basis set. By using this second quantized formulation,
which does not assume adiabatic approximation, a convenient exact formula for
the geometric terms including off-diagonal geometric terms is derived. The
analysis of geometric phases is then reduced to a simple diagonalization of the
Hamiltonian, and it is analyzed both in the operator and path integral
formulations. If one diagonalizes the geometric terms in the infinitesimal
neighborhood of level crossing, the geometric phases become trivial (and thus
no monopole singularity) for arbitrarily large but finite time interval .
The integrability of Schr\"{o}dinger equation and the appearance of the
seemingly non-integrable phases are thus consistent. The topological proof of
the Longuet-Higgins' phase-change rule, for example, fails in the practical
Born-Oppenheimer approximation where a large but finite ratio of two time
scales is involved and is identified with the period of the slower system.
The difference and similarity between the geometric phases associated with
level crossing and the exact topological object such as the Aharonov-Bohm phase
become clear in the present formulation. A crucial difference between the
quantum anomaly and the geometric phases is also noted.Comment: 22 pages, 3 figures. The analysis in the manuscript has been made
more precise by including a brief account of the hidden local gauge symmetry
and by adding several new equations. This revised version is to be published
in Phys. Rev.
Mechanisms for the circular polarization of astrophysical OH masers in star-forming regions and the inferred magnetic fields
Results of further calculations to explore the cause for the circular polarization of astrophysical OH masers in regions of star formation are presented. Calculations are given for both the nonlinear, Zeeman overlap mechanishm, and the Cook mechanism. The previous result that magnetic field strengths of a few milligauss or greater are required, still survives
Identification of Very Red Counterparts of SiO Maser and OH/IR Objects in the GLIMPSE Survey
Using the 3.6/4.5/5.8/8.0 micron images with 1.2 arcsec pixel resolution from
the Spitzer/GLIMPSE survey, we investigated 23 masing and 18 very red objects
that were not identified in the 2MASS survey. Counterparts for all selected
objects were found in the GLIMPSE images. Color indices in these IR bands
suggest the presence of a high-extinction layer of more than a few tenths of a
solar mass in front of the central star. Furthermore, radio observations in the
SiO and H2O maser lines found characteristic maser-line spectra of the embedded
objects, e.g., the SiO J=1-0 line intensity in the v=2 state stronger than that
of the v=1 state, or very widespread H2O maser emission spectra. This indicates
that these objects are actually enshrouded by very thick circumstellar matter,
some of which cannot be ascribed to the AGB wind of the central star.
Individually interesting objects are discussed, including two newly found water
fountains and an SiO source with nebulosity.Comment: High resolution figures available at
ftp://ftp.nro.nao.ac.jp/nroreport/no653.pdf.gz. ApJ No. 655 no.1 issue in
pres
XXZ Bethe states as highest weight vectors of the loop algebra at roots of unity
We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at
roots of unity is a highest weight vector of the loop algebra, for some
restricted sectors with respect to eigenvalues of the total spin operator
, and evaluate explicitly the highest weight in terms of the Bethe roots.
We also discuss whether a given regular Bethe state in the sectors generates an
irreducible representation or not. In fact, we present such a regular Bethe
state in the inhomogeneous case that generates a reducible Weyl module. Here,
we call a solution of the Bethe ansatz equations which is given by a set of
distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero
Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio
Level statistics of XXZ spin chains with a random magnetic field
The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied
under random magnetic field. We show explicitly how the level statistics
depends on the lattice size L, the anisotropy parameter , and the mean
amplitude of the random magnetic field h. In the energy spectrum, quantum
integrability competes with nonintegrability derived from the randomness, where
the XXZ interaction is modified by the parameter . When ,
the level-spacing distribution mostly shows Wigner-like behavior, while when
=0, Poisson-like behavior appears although the system is nonintegrable
due to randomness. Poisson-like behavior also appears for in the
large h limit. Furthermore, the level-spacing distribution depends on the
lattice size L, particularly when the random field is weak.Comment: 4 pages, 3 figures, to be published in Phys. Rev.
Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs
We present formulas for the Clebsch-Gordan coefficients and the Racah
coefficients for the root of unity representations (-dimensional
representations with ) of . We discuss colored vertex
models and colored IRF (Interaction Round a Face) models from the color
representations of . We construct invariants of trivalent colored
oriented framed graphs from color representations of .Comment: 39 pages, January 199
Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupled XXZ spin chains
The level-spacing distributions of XXZ spin chains with next-nearest-neighbor
couplings are studied under periodic boundary conditions. We confirm that
integrable XXZ spin chains mostly have the Poisson distribution as expected. On
the contrary, the level-spacing distributions of next-nearest-neighbor coupled
XXZ chains are given by non-Wigner distributions. It is against the
expectations, since the models are nonintegrable.Comment: 4 pages, 4 figures, to be published in Physical Review
Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations
We present a necessary and sufficient condition for a finite-dimensional
highest weight representation of the loop algebra to be irreducible. In
particular, for a highest weight representation with degenerate parameters of
the highest weight, we can explicitly determine whether it is irreducible or
not. We also present an algorithm for constructing finite-dimensional highest
weight representations with a given highest weight. We give a conjecture that
all the highest weight representations with the same highest weight can be
constructed by the algorithm. For some examples we show the conjecture
explicitly. The result should be useful in analyzing the spectra of integrable
lattice models related to roots of unity representations of quantum groups, in
particular, the spectral degeneracy of the XXZ spin chain at roots of unity
associated with the loop algebra.Comment: 32 pages with no figure; with corrections on the published versio
Topological entropy of a stiff ring polymer and its connection to DNA knots
We discuss the entropy of a circular polymer under a topological constraint.
We call it the {\it topological entropy} of the polymer, in short. A ring
polymer does not change its topology (knot type) under any thermal
fluctuations. Through numerical simulations using some knot invariants, we show
that the topological entropy of a stiff ring polymer with a fixed knot is
described by a scaling formula as a function of the thickness and length of the
circular chain. The result is consistent with the viewpoint that for stiff
polymers such as DNAs, the length and diameter of the chains should play a
central role in their statistical and dynamical properties. Furthermore, we
show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure
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