962 research outputs found
Hyperbolic Supersymmetric Quantum Hall Effect
Developing a non-compact version of the SUSY Hopf map, we formulate the
quantum Hall effect on a super-hyperboloid. Based on group
theoretical methods, we first analyze the one-particle Landau problem, and
successively explore the many-body problem where Laughlin wavefunction,
hard-core pseudo-potential Hamiltonian and topological excitations are derived.
It is also shown that the fuzzy super-hyperboloid emerges in the lowest Landau
level.Comment: 14 pages, two columns, no figures, published version, typos correcte
Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry
We construct a supersymmetric quantum Hall liquid with a deformed
supersymmetry. One parameter is introduced in the supersymmetric Laughlin
wavefunction to realize the original Laughlin wavefunction and the Moore-Read
wavefunction in two extremal limits of the parameter. The introduced parameter
corresponds to the coherence factor in the BCS theory. It is pointed out that
the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed
supersymmetry. Based on the deformed supersymmetry, we construct a
pseudo-potential Hamiltonian whose groundstate is exactly the
parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY
pseudo-potential Hamiltonian is parameter-dependent and non-Hermitian, its
eigenvalues are parameter-independent and real.Comment: 14 pages, contribution to the proceedings of the Group 27 conference,
Yerevan, Armenia, August 13-19, 2008, published versio
Time-Reversal Symmetry in Non-Hermitian Systems
For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy
when the system has a half-odd-integer spin and the time reversal operator
obeys \Theta^2=-1, but no such a degeneracy exists when \Theta^2=+1. Here we
point out that for non-hermitian systems, there exists a degeneracy similar to
Kramers even when \Theta^2=+1. It is found that the new degeneracy follows from
the mathematical structure of split-quaternion, instead of quaternion from
which the Kramers degeneracy follows in the usual hermitian cases. Furthermore,
we also show that particle/hole symmetry gives rise to a pair of states with
opposite energies on the basis of the split quaternion in a class of
non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN
Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2
Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.Comment: 40 pages, 2 figures; typos fixed, references adde
SU(4) Coherent Effects to the Canted Antiferromagnetic Phase in Bilayer Quantum Hall Systems at =2
In bilayer quantum Hall (BLQH) systems at =2, three different kinds of
ground states are expected to be realized, i.e. a spin polarized phase (spin
phase), a pseudospin polarized phase (ppin phase) and a canted
antiferromagnetic phase (C-phase). An SU(4) scheme gives a powerful tool to
investigate BLQH systems which have not only the spin SU(2) but also the layer
(pseudospin) SU(2) degrees of freedom. In this paper, we discuss an origin of
the C-phase in the SU(4) context and investigate SU(4) coherent effects to it.
We show peculiar operators in the SU(4) group which do not exist in
SU(2)SU(2) group play a key role to
its realization. It is also pointed out that not only spins but also
pseudospins are ``canted'' in the C-phase.Comment: 8 pages, 4 figures and 1 tabl
SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry
We review the recent developments of the SUSY quantum Hall effect [hep-th/0409230, hep-th/0411137, hep-th/0503162, hep-th/0606007, arXiv:0705.4527]. We introduce a SUSY formulation of the quantum Hall effect on supermanifolds. On each of supersphere and superplane, we investigate SUSY Landau problem and explicitly construct SUSY extensions of Laughlin wavefunction and topological excitations. The non-anti-commutative geometry naturally emerges in the lowest Landau level and brings particular physics to the SUSY quantum Hall effect. It is shown that SUSY provides a unified picture of the original Laughlin and Moore-Read states. Based on the charge-flux duality, we also develop a Chern-Simons effective field theory for the SUSY quantum Hall effect
Exact shock solution of a coupled system of delay differential equations: a car-following model
In this paper, we present exact shock solutions of a coupled system of delay
differential equations, which was introduced as a traffic-flow model called
{\it the car-following model}. We use the Hirota method, originally developed
in order to solve soliton equations. %While, with a periodic boundary
condition, this system has % a traveling-wave solution given by elliptic
functions. The relevant delay differential equations have been known to allow
exact solutions expressed by elliptic functions with a periodic boundary
conditions. In the present work, however, shock solutions are obtained with
open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure
Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems
In a certain class of differential-difference equations for dissipative
systems, we show that hyperbolic tangent model is the only the nonlinear system
of equations which can admit some particular solutions of the Toda lattice. We
give one parameter family of exact solutions, which include as special cases
the Toda lattice solutions as well as the Whitham's solutions in the Newell's
model. Our solutions can be used to describe temporal-spatial density patterns
observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur
- …