57 research outputs found
Dissipation and Topologically Massive Gauge Theories in Pseudoeuclidean Plane
In the pseudo-euclidean metrics Chern-Simons gauge theory in the infrared
region is found to be associated with dissipative dynamics. In the infrared
limit the Lagrangian of 2+1 dimensional pseudo-euclidean topologically massive
electrodynamics has indeed the same form of the Lagrangian of the damped
harmonic oscillator. On the hyperbolic plane a set of two damped harmonic
oscillators, each other time-reversed, is shown to be equivalent to a single
undamped harmonic oscillator. The equations for the damped oscillators are
proven to be the same as the ones for the Lorentz force acting on two particles
carrying opposite charge in a constant magnetic field and in the electric
harmonic potential. This provides an immediate link with Chern-Simons-like
dynamics of Bloch electrons in solids propagating along the lattice plane with
hyperbolic energy surface. The symplectic structure of the reduced theory is
finally discussed in the Dirac constrained canonical formalism.Comment: 22 pages, LaTe
Degenerate Four Virtual Soliton Resonance for KP-II
By using disipative version of the second and the third members of AKNS
hierarchy, a new method to solve 2+1 dimensional Kadomtsev-Petviashvili (KP-II)
equation is proposed. We show that dissipative solitons (dissipatons) of those
members give rise to the real solitons of KP-II. From the Hirota bilinear form
of the SL(2,R) AKNS flows, we formulate a new bilinear representation for
KP-II, by which, one and two soliton solutions are constructed and the
resonance character of their mutual interactions is studied. By our bilinear
form, we first time created four virtual soliton resonance solution for KP-II
and established relations of it with degenerate four-soliton solution in the
Hirota-Satsuma bilinear form for KP-II.Comment: 10 pages, 5 figures, Talk on International Conference Nonlinear
Physics. Theory and Experiment. III, 24 June-3 July, 2004, Gallipoli(Lecce),
Ital
Integrable Hierarchies and Information Measures
In this paper we investigate integrable models from the perspective of
information theory, exhibiting various connections. We begin by showing that
compressible hydrodynamics for a one-dimesional isentropic fluid, with an
appropriately motivated information theoretic extension, is described by a
general nonlinear Schrodinger (NLS) equation. Depending on the choice of the
enthalpy function, one obtains the cubic NLS or other modified NLS equations
that have applications in various fields. Next, by considering the integrable
hierarchy associated with the NLS model, we propose higher order information
measures which include the Fisher measure as their first member. The lowest
members of the hiearchy are shown to be included in the expansion of a
regularized Kullback-Leibler measure while, on the other hand, a suitable
combination of the NLS hierarchy leads to a Wootters type measure related to a
NLS equation with a relativistic dispersion relation. Finally, through our
approach, we are led to construct an integrable semi-relativistic NLS equation.Comment: 11 page
Young diagrams and N-soliton solutions of the KP equation
We consider -soliton solutions of the KP equation,
(-4u_t+u_{xxx}+6uu_x)_x+3u_{yy}=0 . An -soliton solution is a solution
which has the same set of line soliton solutions in both
asymptotics and . The -soliton solutions include
all possible resonant interactions among those line solitons. We then classify
those -soliton solutions by defining a pair of -numbers with , which labels line solitons in the solution. The
classification is related to the Schubert decomposition of the Grassmann
manifolds Gr, where the solution of the KP equation is defined as a
torus orbit. Then the interaction pattern of -soliton solution can be
described by the pair of Young diagrams associated with . We also show that -soliton solutions of the KdV equation obtained by
the constraint cannot have resonant interaction.Comment: 22 pages, 5 figures, some minor corrections and added one section on
the KdV N-soliton solution
Pecularities of Hall effect in GaAs/{\delta}<Mn>/GaAs/In\timesGa1-\timesAs/GaAs (\times {\approx} 0.2) heterostructures with high Mn content
Transport properties of GaAs/{\delta}/GaAs/In\timesGa1-\timesAs/GaAs
structures containing InxGa1-xAs (\times {\approx} 0.2) quantum well (QW) and
Mn delta layer (DL) with relatively high, about one Mn monolayer (ML) content,
are studied. In these structures DL is separated from QW by GaAs spacer with
the thickness ds = 2-5 nm. All structures possess a dielectric character of
conductivity and demonstrate a maximum in the resistance temperature dependence
Rxx(T) at the temperature {\approx} 46K which is usually associated with the
Curie temperature Tc of ferromagnetic (FM) transition in DL. However, it is
found that the Hall effect concentration of holes pH in QW does not decrease
below TC as one ordinary expects in similar systems. On the contrary, the
dependence pH(T) experiences a minimum at T = 80-100 K depending on the spacer
thickness, then increases at low temperatures more strongly than ds is smaller
and reaches a giant value pH = (1-2)\cdot10^13 cm^(-2). Obtained results are
interpreted in the terms of magnetic proximity effect of DL on QW, leading to
induce spin polarization of the holes in QW. Strong structural and magnetic
disorder in DL and QW, leading to the phase segregation in them is taken into
consideration. The high pH value is explained as a result of compensation of
the positive sign normal Hall effect component by the negative sign anomalous
Hall effect component.Comment: 19 pages, 6 figure
Abelian Chern-Simons Vortices and Holomorphic Burgers' Hierarchy
The Abelian Chern-Simons Gauge Field Theory in 2+1 dimensions and its
relation with holomorphic Burgers' Hierarchy is considered. It is shown that
the relation between complex potential and the complex gauge field as in
incompressible and irrotational hydrodynamics, has meaning of the analytic
Cole-Hopf transformation, linearizing the Burgers Hierarchy in terms of the
holomorphic Schr\"odinger Hierarchy. Then the motion of planar vortices in
Chern-Simons theory, appearing as pole singularities of the gauge field,
corresponds to motion of zeroes of the hierarchy. Using boost transformations
of the complex Galilean group of the hierarchy, a rich set of exact solutions,
describing integrable dynamics of planar vortices and vortex lattices in terms
of the generalized Kampe de Feriet and Hermite polynomials is constructed. The
results are applied to the holomorphic reduction of the Ishimori model and the
corresponding hierarchy, describing dynamics of magnetic vortices and
corresponding lattices in terms of complexified Calogero-Moser models.
Corrections on two vortex dynamics from the Moyal space-time non-commutativity
in terms of Airy functions are found.Comment: 15 pages, talk presented in Workshop `Nonlinear Physics IV: Theory
and Experiment`, 22-30 June 2006, Gallipoli, Ital
Structural and transport properties of GaAs/delta<Mn>/GaAs/InxGa1-xAs/GaAs quantum wells
We report results of investigations of structural and transport properties of
GaAs/Ga(1-x)In(x)As/GaAs quantum wells (QWs) having a 0.5-1.8 ML thick Mn
layer, separated from the QW by a 3 nm thick spacer. The structure has hole
mobility of about 2000 cm2/(V*s) being by several orders of magnitude higher
than in known ferromagnetic two-dimensional structures. The analysis of the
electro-physical properties of these systems is based on detailed study of
their structure by means of high-resolution X-ray diffractometry and
glancing-incidence reflection, which allow us to restore the depth profiles of
structural characteristics of the QWs and thin Mn containing layers. These
investigations show absence of Mn atoms inside the QWs. The quality of the
structures was also characterized by photoluminescence spectra from the QWs.
Transport properties reveal features inherent to ferromagnetic systems: a
specific maximum in the temperature dependence of the resistance and the
anomalous Hall effect (AHE) observed in samples with both "metallic" and
activated types of conductivity up to ~100 K. AHE is most pronounced in the
temperature range where the resistance maximum is observed, and decreases with
decreasing temperature. The results are discussed in terms of interaction of
2D-holes and magnetic Mn ions in presence of large-scale potential fluctuations
related to random distribution of Mn atoms. The AHE values are compared with
calculations taking into account its "intrinsic" mechanism in ferromagnetic
systems.Comment: 15 pages, 9 figure
Chern - Simons Gauge Field Theory of Two - Dimensional Ferromagnets
A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the
continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets
can be analyzed whithin the anyon theory. Thus, we show that static magnetic
vortices correspond to the self-dual Chern - Simons solitons and are described
by the Liouville equation. The related magnetic topological charge is
associated with the electric charge of anyons. Furthermore, vortex - antivortex
configurations are described by the sinh-Gordon equation and its conformally
invariant extension. Physical consequences of these results are discussed.Comment: 15 pages, Plain TeX, Lecce, June 199
- …