9,517 research outputs found
Exact solution of type quantum Calogero model through a mapping to free harmonic oscillators
We solve the eigenvalue problem of the type of Calogero model by
mapping it to a set of decoupled quantum harmonic oscillators through a
similarity transformation. In particular, we construct the eigenfunctions of
this Calogero model from those of bosonic harmonic oscillators having either
all even parity or all odd parity. It turns out that the eigenfunctions of this
model are orthogonal with respect to a nontrivial inner product, which can be
derived from the quasi-Hermiticity property of the corresponding conserved
quantities.Comment: 16 page
Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
We derive the exact spectra as well as partition functions for a class of
type of spin Calogero models, whose Hamiltonians are constructed by
using supersymmetric analogues of polarized spin reversal operators (SAPSRO).
The strong coupling limit of these spin Calogero models yields type of
Polychronakos-Frahm (PF) spin chains with SAPSRO. By applying the freezing
trick, we obtain an exact expression for the partition functions of such PF
spin chains. We also derive a formula which expresses the partition function of
any type of PF spin chain with SAPSRO in terms of partition functions of
several type of supersymmetric PF spin chains, where .
Subsequently we show that an extended boson-fermion duality relation is obeyed
by the partition functions of the type of PF chains with SAPSRO. Some
spectral properties of these spin chains, like level density distribution and
nearest neighbour spacing distribution, are also studied.Comment: 36 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1402.275
Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
We study a system of electrons moving on a noncommutative plane in the
presence of an external magnetic field which is perpendicular to this plane.
For generality we assume that the coordinates and the momenta are both
noncommutative. We make a transformation from the noncommutative coordinates to
a set of commuting coordinates and then we write the Hamiltonian for this
system. The energy spectrum and the expectation value of the current can then
be calculated and the Hall conductivity can be extracted. We use the same
method to calculate the phase shift for the Aharonov-Bohm effect. Precession
measurements could allow strong upper limits to be imposed on the
noncommutativity coordinate and momentum parameters and .Comment: 9 pages, RevTeX4, references added, small changes in the tex
Multi-parameter deformed and nonstandard Yangian symmetry in integrable variants of Haldane-Shastry spin chain
By using `anyon like' representations of permutation algebra, which pick up
nontrivial phase factors while interchanging the spins of two lattice sites, we
construct some integrable variants of Haldane-Shastry (HS) spin chain. Lax
equations for these spin chains allow us to find out the related conserved
quantities. However, it turns out that such spin chains also possess a few
additional conserved quantities which are apparently not derivable from the Lax
equations. Identifying these additional conserved quantities, and the usual
ones related to Lax equations, with different modes of a monodromy matrix, it
is shown that the above mentioned HS like spin chains exhibit multi-parameter
deformed and `nonstandard' variants of Yangian symmetry.Comment: 18 pages, latex, no figure
Solution of a Cauchy singular fractional integro-differential equation in Bernstein polynomial basis
This article proposes a simple method to obtain approximate numerical solution of a singular fractional order integro-differential equation with Cauchy kernel by using Bernstein polynomials as basis. The fractional derivative is described in Caputo sense. The properties of Bernstein polynomials are used to reduce the fractional order integro-differential equation to the solution of algebraic equations. The numerical results obtained by the present method compares favorably with those obtained earlier for the first order integro-differential equation. Also the convergence of the method is established rigorously
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