3,643 research outputs found
Constructing quantum vertex algebras
This is a sequel to \cite{li-qva}. In this paper, we focus on the
construction of quantum vertex algebras over \C, whose notion was formulated
in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator
algebra (over \C[[h]]) as one of the main motivations. As one of the main
steps in constructing quantum vertex algebras, we prove that every
countable-dimensional nonlocal (namely noncommutative) vertex algebra over
\C, which either is irreducible or has a basis of PBW type, is nondegenerate
in the sense of Etingof and Kazhdan. Using this result, we establish the
nondegeneracy of better known vertex operator algebras and some nonlocal vertex
algebras. We then construct a family of quantum vertex algebras closely related
to Zamolodchikov-Faddeev algebras.Comment: 37 page
Devil's staircase of incompressible electron states in a nanotube
It is shown that a periodic potential applied to a nanotube can lock
electrons into incompressible states. Depending on whether electrons are weakly
or tightly bound to the potential, excitation gaps open up either due to the
Bragg diffraction enhanced by the Tomonaga - Luttinger correlations, or via
pinning of the Wigner crystal. Incompressible states can be detected in a
Thouless pump setup, in which a slowly moving periodic potential induces
quantized current, with a possibility to pump on average a fraction of an
electron per cycle as a result of interactions.Comment: 4 pages, 1 figure, published versio
The Dirac Sea
We give an alternate definition of the free Dirac field featuring an explicit
construction of the Dirac sea. The treatment employs a semi-infinite wedge
product of Hilbert spaces. We also show that the construction is equivalent to
the standard Fock space construction.Comment: 7 page
The Integrals of Motion for the Deformed W-Algebra II: Proof of the commutation relations
We explicitly construct two classes of infinitly many commutative operators
in terms of the deformed W-algebra , and give proofs of the
commutation relations of these operators. We call one of them local integrals
of motion and the other nonlocal one, since they can be regarded as elliptic
deformation of local and nonlocal integrals of motion for the algebra.Comment: Dedicated to Professor Tetsuji Miwa on the occasion on the 60th
birthda
The structure of the hard sphere solid
We show that near densest-packing the perturbations of the HCP structure
yield higher entropy than perturbations of any other densest packing. The
difference between the various structures shows up in the correlations between
motions of nearest neighbors. In the HCP structure random motion of each sphere
impinges slightly less on the motion of its nearest neighbors than in the other
structures.Comment: For related papers see:
http://www.ma.utexas.edu/users/radin/papers.htm
Mutually Penetrating Motion of Self-Organized 2D Patterns of Soliton-Like Structures
Results of numerical simulations of a recently derived most general
dissipative-dispersive PDE describing evolution of a film flowing down an
inclined plane are presented. They indicate that a novel complex type of
spatiotemporal patterns can exist for strange attractors of nonequilibrium
systems. It is suggested that real-life experiments satisfying the validity
conditions of the theory are possible: the required sufficiently viscous
liquids are readily available.Comment: minor corrections, 4 pages, LaTeX, 6 figures, mpeg simulations
available upon or reques
Effective actions at finite temperature
This is a more detailed version of our recent paper where we proposed, from
first principles, a direct method for evaluating the exact fermion propagator
in the presence of a general background field at finite temperature. This can,
in turn, be used to determine the finite temperature effective action for the
system. As applications, we discuss the complete one loop finite temperature
effective actions for 0+1 dimensional QED as well as for the Schwinger model in
detail. These effective actions, which are derived in the real time (closed
time path) formalism, generate systematically all the Feynman amplitudes
calculated in thermal perturbation theory and also show that the retarded
(advanced) amplitudes vanish in these theories. Various other aspects of the
problem are also discussed in detail.Comment: 9 pages, revtex, 1 figure, references adde
Heat capacity at the glass transition
A fundamental problem of glass transition is to explain the jump of heat
capacity at the glass transition temperature without asserting the
existence of a distinct solid glass phase. This problem is also common to other
disordered systems, including spin glasses. We propose that if is defined
as the temperature at which the liquid stops relaxing at the experimental time
scale, the jump of heat capacity at follows as a necessary consequence
due to the change of system's elastic, vibrational and thermal properties. In
this picture, we discuss time-dependent effects of glass transition, and
identify three distinct regimes of relaxation. Our approach explains widely
observed logarithmic increase of with the quench rate and the correlation
of heat capacity jump with liquid fragility
The thickness of a liquid layer on the free surface of ice as obtained from computer simulation
Molecular dynamic simulations were performed for ice Ih with a free surface
by using four water models, SPC/E, TIP4P, TIP4P/Ice and TIP4P/2005. The
behavior of the basal plane, the primary prismatic plane and of the secondary
prismatic plane when exposed to vacuum was analyzed. We observe the formation
of a thin liquid layer at the ice surface at temperatures below the melting
point for all models and the three planes considered. For a given plane it was
found that the thickness of a liquid layer was similar for different water
models, when the comparison is made at the same undercooling with respect to
the melting point of the model. The liquid layer thickness is found to increase
with temperature. For a fixed temperature it was found that the thickness of
the liquid layer decreases in the following order: the basal plane, the primary
prismatic plane, and the secondary prismatic plane. For the TIP4P/Ice model, a
model reproducing the experimental value of the melting temperature of ice, the
first clear indication of the formation of a liquid layer appears at about -100
Celsius for the basal plane, at about -80 Celsius for the primary prismatic
plane and at about -70 Celsius for the secondary prismatic plane.Comment: 41 pages and 13 figure
A central extension of \cD Y_{\hbar}(\gtgl_2) and its vertex representations
A central extension of \cD Y_{\hbar}(\gtgl_2) is proposed. The bosonization
of level module and vertex operators are also given.Comment: 10 pages, AmsLatex, to appear in Lett. in Math. Phy
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