21,676 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
Global monopoles and scalar fields as the electrogravity dual of Schwarzschild spacetime
We prove that both global monopole and minimally coupled static zero mass
scalar field are electrogravity dual of the Schwarzschild solution or flat
space and they share the same equation of state, . This
property was however known for the global monopole spacetime while it is for
the first time being established for the scalar field. In particular, it turns
out that the Xanthopoulos - Zannias scalar field solution is dual to flat
space.Comment: 5 pages, RevTe
Identification of delays and discontinuity points of unknown systems by using synchronization of chaos
In this paper we present an approach in which synchronization of chaos is
used to address identification problems. In particular, we are able to
identify: (i) the discontinuity points of systems described by piecewise
dynamical equations and (ii) the delays of systems described by delay
differential equations. Delays and discontinuities are widespread features of
the dynamics of both natural and manmade systems. The foremost goal of the
paper is to present a general and flexible methodology that can be used in a
broad variety of identification problems.Comment: 11 pages, 3 figure
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