3,326 research outputs found
Super Rogers-Szeg\"o polynomials associated with type of Polychronakos spin chains
As is well known, multivariate Rogers-Szeg\"o polynomials are closely
connected with the partition functions of the type of Polychronakos
spin chains having long-range interactions. Applying the `freezing trick', here
we derive the partition functions for a class of type of Polychronakos
spin chains containing supersymmetric analogues of polarized spin reversal
operators and subsequently use those partition functions to obtain novel
multivariate super Rogers-Szeg\"o (SRS) polynomials depending on four types of
variables. We construct the generating functions for such SRS polynomials and
show that these polynomials can be written as some bilinear combinations of the
type of SRS polynomials. We also use the above mentioned generating
functions to derive a set of recursion relations for the partition functions of
the type of Polychronakos spin chains involving different numbers of
lattice sites and internal degrees of freedom.Comment: 33 pages, minor typos corrected, journal reference give
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
A General Relativistic study of the neutrino path and calculation of minimum photosphere for different stars
A detailed general relativistic (GR) calculation of the neutrino path for a
general metric describing a rotating star is studied. We have calculated the
neutrino path along a plane, with the consideration that the neutrino does not
at any time leave the plane. The expression for the minimum photosphere radius
(MPR) is obtained and matched with the Schwarzschild limit. The MPR is
calculated for the stars with two different equations of state (EOS) each
rotating with two different velocities. The results shows that the MPR for the
hadronic star is much greater than the quark star and the MPR increases as the
rotational velocity of the star decreases. The MPR along the polar plane is
larger than that along the equatorial plane.Comment: 13 pages, 5 figures and 1 tabl
Rational quantum integrable systems of D_N type with polarized spin reversal operators
We study the spin Calogero model of D_N type with polarized spin reversal
operators, as well as its associated spin chain of Haldane-Shastry type, both
in the antiferromagnetic and ferromagnetic cases. We compute the spectrum and
the partition function of the former model in closed form, from which we derive
an exact formula for the chain's partition function in terms of products of
partition functions of Polychronakos-Frahm spin chains of type A. Using a
recursion relation for the latter partition functions that we derive in the
paper, we are able to numerically evaluate the partition function, and thus the
spectrum, of the D_N-type spin chain for relatively high values of the number
of spins N. We analyze several global properties of the chain's spectrum, such
as the asymptotic level density, the distribution of consecutive spacings of
the unfolded spectrum, and the average degeneracy. In particular, our results
suggest that this chain is invariant under a suitable Yangian group, and that
its spectrum coincides with that of a Yangian-invariant vertex model with
linear energy function and dispersion relation.Comment: 26 pages, 5 figures, typeset in LaTe
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