4,031 research outputs found
The exactly solvable spin Sutherland model of B_N type and its related spin chain
We compute the spectrum of the su(m) spin Sutherland model of B_N type,
including the exact degeneracy of all energy levels. By studying the large
coupling constant limit of this model and of its scalar counterpart, we
evaluate the partition function of their associated spin chain of
Haldane-Shastry type in closed form. With the help of the formula for the
partition function thus obtained we study the chain's spectrum, showing that it
cannot be obtained as a limiting case of its BC_N counterpart. The structure of
the partition function also suggests that the spectrum of the Haldane-Shastry
spin chain of B_N type is equivalent to that of a suitable vertex model, as is
the case for its A_{N-1} counterpart, and that the density of its eigenvalues
is normally distributed when the number of sites N tends to infinity. We
analyze this last conjecture numerically using again the explicit formula for
the partition function, and check its validity for several values of N and m.Comment: Typeset in LaTeX (24 pages, 4 figures). arXiv admin note: text
overlap with arXiv:0909.296
Pseudo-hermitian interaction between an oscillator and a spin half particle in the external magnetic field
We consider a spin half particle in the external magnetic field which couples
to a harmonic oscillator through some pseudo-hermitian interaction. We find
that the energy eigenvalues for this system are real even though the
interaction is not PT invariant.Comment: Latex, no figs, 8 pages. (To appear in Mod. Phys. Lett. A
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
Non-equilibrium fluctuations and mechanochemical couplings of a molecular motor
We investigate theoretically the violations of Einstein and Onsager
relations, and the efficiency for a single processive motor operating far from
equilibrium using an extension of the two-state model introduced by Kafri {\em
et al.} [Biophys. J. {\bf 86}, 3373 (2004)]. With the aid of the Fluctuation
Theorem, we analyze the general features of these violations and this
efficiency and link them to mechanochemical couplings of motors. In particular,
an analysis of the experimental data of kinesin using our framework leads to
interesting predictions that may serve as a guide for future experiments.Comment: 4 pages, 4 figures, accepted to Phys. Rev. Let
Quantum bound states for a derivative nonlinear Schrodinger model and number theory
A derivative nonlinear Schrodinger model is shown to support localized N-body
bound states for several ranges (called bands) of the coupling constant eta.
The ranges of eta within each band can be completely determined using number
theoretic concepts such as Farey sequences and continued fractions. For N > 2,
the N-body bound states can have both positive and negative momentum. For eta >
0, bound states with positive momentum have positive binding energy, while
states with negative momentum have negative binding energy.Comment: Revtex, 7 pages including 2 figures, to appear in Mod. Phys. Lett.
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