1,235 research outputs found
Chern-Simons Reduction and non-Abelian Fluid Mechanics
We propose a non-Abelian generalization of the Clebsch parameterization for a
vector in three dimensions. The construction is based on a group-theoretical
reduction of the Chern-Simons form on a symmetric space. The formalism is then
used to give a canonical (symplectic) discussion of non-Abelian fluid
mechanics, analogous to the way the Abelian Clebsch parameterization allows a
canonical description of conventional fluid mechanics.Comment: 12 pages, REVTeX; revised for publication in Phys Rev D; email to
[email protected]
Reversed anisotropies and thermal contraction of FCC (110) surfaces
The observed anisotropies of surface vibrations for unreconstructed FCC metal
(110) surfaces are often reversed from the "common sense" expectation. The
source of these reversals is investigated by performing ab initio density
functional theory calculations to obtain the surface force constant tensors for
Ag(110), Cu(110) and Al(110). The most striking result is a large enhancement
in the coupling between the first and third layers of the relaxed surface,
which strongly reduces the amplitude of out-of-plane vibrations of atoms in the
first layer. This also provides a simple explanation for the thermal
contraction of interlayer distances. Both the anisotropies and the thermal
contraction arise primarily as a result of the bond topology, with all three
(110) surfaces showing similar behavior.Comment: 13 pages, in revtex format, plus 1 postscript figur
Siegert pseudostates: completeness and time evolution
Within the theory of Siegert pseudostates, it is possible to accurately
calculate bound states and resonances. The energy continuum is replaced by a
discrete set of states. Many questions of interest in scattering theory can be
addressed within the framework of this formalism, thereby avoiding the need to
treat the energy continuum. For practical calculations it is important to know
whether a certain subset of Siegert pseudostates comprises a basis. This is a
nontrivial issue, because of the unusual orthogonality and overcompleteness
properties of Siegert pseudostates. Using analytical and numerical arguments,
it is shown that the subset of bound states and outgoing Siegert pseudostates
forms a basis. Time evolution in the context of Siegert pseudostates is also
investigated. From the Mittag-Leffler expansion of the outgoing-wave Green's
function, the time-dependent expansion of a wave packet in terms of Siegert
pseudostates is derived. In this expression, all Siegert pseudostates--bound,
antibound, outgoing, and incoming--are employed. Each of these evolves in time
in a nonexponential fashion. Numerical tests underline the accuracy of the
method
Spontaneous Interlayer Charge Transfer near the Magnetic Quantum Limit
Experiments reveal that a confined electron system with two equally-populated
layers at zero magnetic field can spontaneously break this symmetry through an
interlayer charge transfer near the magnetic quantum limit. New fractional
quantum Hall states at unusual total filling factors such as \nu = 11/15 (= 1/3
+ 2/5) stabilize as signatures that the system deforms itself, at substantial
electrostatic energy cost, in order to gain crucial correlation energy by
"locking in" separate incompressible liquid phases at unequal fillings in the
two layers (e.g., layered 1/3 and 2/5 states in the case of \nu = 11/15).Comment: 4 pages, 4 figures (1 color) included in text. Related papers at
http://www.ee.princeton.edu/~hari/papers.htm
Sticky Spheres, Entropy barriers and Non-equilibrium phase transitions
A sticky spheres model to describe slow dynamics of a non-equilibrium system
is proposed. The dynamical slowing down is due to the presence of entropy
barriers. We present an exact mean field analysis of the model and demonstrate
that there is a non-equilibrium phase transition from an exponential cluster
size distribution to a powerlaw.Comment: 10pages text and 2 figure
A natural Finsler--Laplace operator
We give a new definition of a Laplace operator for Finsler metric as an
average with regard to an angle measure of the second directional derivatives.
This definition uses a dynamical approach due to Foulon that does not require
the use of connections nor local coordinates. We show using 1-parameter
families of Katok--Ziller metrics that this Finsler--Laplace operator admits
explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio
Relaxation and reconstruction on (111) surfaces of Au, Pt, and Cu
We have theoretically studied the stability and reconstruction of (111)
surfaces of Au, Pt, and Cu. We have calculated the surface energy, surface
stress, interatomic force constants, and other relevant quantities by ab initio
electronic structure calculations using the density functional theory (DFT), in
a slab geometry with periodic boundary conditions. We have estimated the
stability towards a quasi-one-dimensional reconstruction by using the
calculated quantities as parameters in a one-dimensional Frenkel-Kontorova
model. On all surfaces we have found an intrinsic tensile stress. This stress
is large enough on Au and Pt surfaces to lead to a reconstruction in which a
denser surface layer is formed, in agreement with experiment. The
experimentally observed differences between the dense reconstruction pattern on
Au(111) and a sparse structure of stripes on Pt(111) are attributed to the
details of the interaction potential between the first layer of atoms and the
substrate.Comment: 8 pages, 3 figures, submitted to Physical Review
Measures on Banach Manifolds and Supersymmetric Quantum Field Theory
We show how to construct measures on Banach manifolds associated to
supersymmetric quantum field theories. These measures are mathematically
well-defined objects inspired by the formal path integrals appearing in the
physics literature on quantum field theory. We give three concrete examples of
our construction. The first example is a family of measures on a
space of functions on the two-torus, parametrized by a polynomial (the
Wess-Zumino-Landau-Ginzburg model). The second is a family \mu_\cG^{s,t} of
measures on a space \cG of maps from to a Lie group (the
Wess-Zumino-Novikov-Witten model). Finally we study a family
of measures on the product of a space of connection s on the trivial principal
bundle with structure group on a three-dimensional manifold with a
space of \fg-valued three-forms on
We show that these measures are positive, and that the measures
\mu_\cG^{s,t} are Borel probability measures. As an application we show that
formulas arising from expectations in the measures \mu_\cG^{s,1} reproduce
formulas discovered by Frenkel and Zhu in the theory of vertex operator
algebras. We conjecture that a similar computation for the measures
where is a homology three-sphere, will yield the
Casson invariant of Comment: Minor correction
Temperature dependent surface relaxations of Ag(111)
The temperature dependent surface relaxation of Ag(111) is calculated by
density-functional theory. At a given temperature, the equilibrium geometry is
determined by minimizing the Helmholtz free energy within the quasiharmonic
approximation. To this end, phonon dispersions all over the Brillouin zone are
determined from density-functional perturbation theory. We find that the
top-layer relaxation of Ag(111) changes from an inward contraction (-0.8 %) to
an outward expansion (+6.3%) as the temperature increases from T=0 K to 1150 K,
in agreement with experimental findings. Also the calculated surface phonon
dispersion curves at room temperature are in good agreement with helium
scattering measurements. The mechanism driving this surface expansion is
analyzed.Comment: 6 pages, 7 figures, submitted to Phys. Rev. B (May 1998). Other
related publications can be found at
http://www.rz-berlin.mpg.de/th/paper.htm
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