1,184 research outputs found
Integrable Chern-Simons Gauge Field Theory in 2+1 Dimensions
The classical spin model in planar condensed media is represented as the U(1)
Chern-Simons gauge field theory. When the vorticity of the continuous flow of
the media coincides with the statistical magnetic field, which is necessary for
the model's integrability, the theory admits zero curvature connection. This
allows me to formulate the model in terms of gauge - invariant fields whose
evolution is described by the Davey-Stewartson (DS) equations. The Self-dual
Chern-Simons solitons described by the Liouville equation are subjected to
corresponding integrable dynamics. As a by-product the 2+1-dimensional
zero-curvature representation for the DS equation is obtained as well as the
new reduction conditions related to the DS-I case. Some possible applications
for the statistical transmutation in the anyon superfluid and TQFT are briefly
discussed.Comment: 16 pages, plain Te
Special functions with mod n symmetry and kaleidoscope of quantum coherent states
The set of mod functions associated with primitive roots of unity and
discrete Fourier transform is introduced. These functions naturally appear in
description of superposition of coherent states related with regular polygon,
which we call kaleidoscope of quantum coherent states. Displacement operators
for kaleidoscope states are obtained by mod exponential functions with
operator argument and non-commutative addition formulas. Normalization
constants, average number of photons, Heinsenberg uncertainty relations and
coordinate representation of wave functions with mod n symmetry are expressed
in a compact form by these functions.Comment: 12 pages, 4 figures, talk in The 32nd International Colloquium on
Group Theoretical Methods in Physics (Group32), Prague, Czech Republic, 9-13
July 201
The Lax Pair by Dimensional Reduction of Chern-Simons Gauge Theory
We show that the Nonlinear Schr\"odinger Equation and the related Lax pair in
1+1 dimensions can be derived from 2+1 dimensional Chern-Simons Topological
Gauge Theory. The spectral parameter, a main object for the Loop algebra
structure and the Inverse Spectral Transform, has appear as a homogeneous part
(condensate) of the statistical gauge field, connected with the compactified
extra space coordinate. In terms of solitons, a natural interpretation for the
one-dimensional analog of Chern-Simons Gauss law is given.Comment: 27 pages, Plain Te
q-Shock Soliton Evolution
By generating function based on the Jackson's q-exponential function and
standard exponential function, we introduce a new q-analogue of Hermite and
Kampe-de Feriet polynomials. In contrast to standard Hermite polynomials, with
triple recurrence relation, our polynomials satisfy multiple term recurrence
relation, derived by the q-logarithmic function. It allow us to introduce the
q-Heat equation with standard time evolution and the q-deformed space
derivative. We found solution of this equation in terms of q-Kampe-de Feriet
polynomials with arbitrary number of moving zeros, and solved the initial value
problem in operator form. By q-analog of the Cole-Hopf transformation we find a
new q-deformed Burgers type nonlinear equation with cubic nonlinearity. Regular
everywhere single and multiple q-Shock soliton solutions and their time
evolution are studied. A novel, self-similarity property of these q-shock
solitons is found. The results are extended to the time dependent
q-Schr\"{o}dinger equation and the q-Madelung fluid type representation is
derived.Comment: 15 pages, 6 figure
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