27,066 research outputs found
Generalised Calogero-Moser models and universal Lax pair operators
Calogero-Moser models can be generalised for all of the finite reflection
groups. These include models based on non-crystallographic root systems, that
is the root systems of the finite reflection groups, H_3, H_4, and the dihedral
group I_2(m), besides the well-known ones based on crystallographic root
systems, namely those associated with Lie algebras. Universal Lax pair
operators for all of the generalised Calogero-Moser models and for any choices
of the potentials are constructed as linear combinations of the reflection
operators. The consistency conditions are reduced to functional equations for
the coefficient functions of the reflection operators in the Lax pair. There
are only four types of such functional equations corresponding to the
two-dimensional sub-root systems, A_2, B_2, G_2, and I_2(m). The root type and
the minimal type Lax pairs, derived in our previous papers, are given as the
simplest representations. The spectral parameter dependence plays an important
role in the Lax pair operators, which bear a strong resemblance to the Dunkl
operators, a powerful tool for solving quantum Calogero-Moser models.Comment: 37 pages, LaTeX2e, no macro, no figur
Numerical Tests of the Chiral Luttinger Liquid Theory for Fractional Hall Edges
We report on microscopic numerical studies which support the chiral Luttinger
liquid theory of the fractional Hall edge proposed by Wen. Our calculations are
based in part on newly proposed and accurate many-body trial wavefunctions for
the low-energy edge excitations of fractional incompressible states.Comment: 12 pages + 1 figure, Revte
Quantitative Probe of Pairing Correlations in a Cold Fermionic Atom Gas
A quantitative measure of the pairing correlations present in a cold gas of
fermionic atoms can be obtained by studying the dependence of RF spectra on
hyperfine state populations. This proposal follows from a sum rule that relates
the total interaction energy of the gas to RF spectrum line positions. We argue
that this indicator of pairing correlations provides information comparable to
that available from the spin-susceptibility and NMR measurements common in
condensed-matter systems.Comment: 5 pages, 1 figur
Thermally-Assisted Current-Driven Domain Wall Motion
Starting from the stochastic Landau-Lifschitz-Gilbert equation, we derive
Langevin equations that describe the nonzero-temperature dynamics of a rigid
domain wall. We derive an expression for the average drift velocity of the
domain wall as a function of the applied current, and find qualitative
agreement with recent magnetic semiconductor experiments. Our model implies
that at any nonzero temperature the average domain-wall velocity initially
varies linearly with current, even in the absence of non-adiabatic spin
torques.Comment: 4 pages, 2 figure
Phase Separation of a Fast Rotating Boson-Fermion Mixture in the Lowest-Landau-Level Regime
By minimizing the coupled mean-field energy functionals, we investigate the
ground-state properties of a rotating atomic boson-fermion mixture in a
two-dimensional parabolic trap. At high angular frequencies in the
mean-field-lowest-Landau-level regime, quantized vortices enter the bosonic
condensate, and a finite number of degenerate fermions form the
maximum-density-droplet state. As the boson-fermion coupling constant
increases, the maximum density droplet develops into a lower-density state
associated with the phase separation, revealing characteristics of a
Landau-level structure
A Quantum Theory of Cold Bosonic Atoms in Optical Lattices
Ultracold atoms in optical lattices undergo a quantum phase transition from a
superfluid to a Mott insulator as the lattice potential depth is increased. We
describe an approximate theory of interacting bosons in optical lattices which
provides a qualitative description of both superfluid and insulator states. The
theory is based on a change of variables in which the boson coherent state
amplitude is replaced by an effective potential which promotes phase coherence
between different number states on each lattice site. It is illustrated here by
applying it to uniform and fully frustrated lattice cases, but is simple enough
that it can easily be applied to spatially inhomogeneous lattice systems
Cauchy's residue theorem for a class of real valued functions
Let be an interval in and let be a real valued
function defined at the endpoints of and with a certain number of
discontinuities within . Having assumed to be differentiable on a
set to the derivative , where is a subset of at whose points can take values or not be defined at all,
we adopt the convention that and are equal to 0 at all points of
and show that %, where
denotes the total value of the \textit{% Kurzweil-Henstock} integral. The
paper ends with a few examples that illustrate the theory.Comment: 6 page
Magnons and skyrmions in fractional Hall ferromagnets
Recent experiments have established a qualitative difference between the
magnetization temperature-dependences of quantum Hall ferromagnets at
integer and fractional filling factors. We explain this difference in terms of
the relative energies of collective magnon and particle-hole excitations in the
two cases. Analytic calculations for hard-core model systems are used to
demonstrate that, in the fractional case, interactions suppress the
magnetization at finite temperatures and that particle-hole excitations rather
than long-wavelength magnons control at low .Comment: 4 pages, no figure
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