213 research outputs found
The excitation spectrum for weakly interacting bosons in a trap
We investigate the low-energy excitation spectrum of a Bose gas confined in a
trap, with weak long-range repulsive interactions. In particular, we prove that
the spectrum can be described in terms of the eigenvalues of an effective
one-particle operator, as predicted by the Bogoliubov approximation.Comment: LaTeX, 32 page
Some exact results for the multicomponent t-J model
We present a generalization of the Sutherland's multicomponent model. Our
extension includes both the ferromagnetic and the antiferromagnetic t-J model
for any value of the exchange coupling J and the hopping parameter t. We prove
rigorously that for one dimensional chains the ground-state of the generalized
model is non-degenerate. As a consequence, the ordering of energy levels of the
antiferromagnetic t-J model is determined. Our result rigorously proves and
extends the analysis carried out by Sutherland in establishing the phase
diagram of the model as a function of the number of components.Comment: 11 pages, RevTeX 3.0, no figure
Exact solution of the six-vertex model with domain wall boundary condition. Critical line between ferroelectric and disordered phases
This is a continuation of the papers [4] of Bleher and Fokin and [5] of
Bleher and Liechty, in which the large asymptotics is obtained for the
partition function of the six-vertex model with domain wall boundary
conditions in the disordered and ferroelectric phases, respectively. In the
present paper we obtain the large asymptotics of on the critical line
between these two phases.Comment: 22 pages, 6 figures, to appear in the Journal of Statistical Physic
Effective lattice actions for correlated electrons
We present an exact, unconstrained representation of the electron operators
in terms of operators of opposite statistics. We propose a path--integral
representation for the - model and introduce a parameter controlling the
semiclassical behaviour. We extend the functional approach to the Hubbard model
and show that the mean--field theory is equivalent to considering, at
Hamiltonian level, the Falikov--Kimball model. Connections with a bond-charge
model are also discussed.Comment: 12 pages, REVTeX 3.0, no figure
Listening and learning : the reciprocal relationship between worker and client
The relationship between worker and client has for the best part of 100 years been the mainstay of probation, and yet has recently been eroded by an increased emphasis on punishment, blame and managerialism. The views of offenders are in direct contradiction to these developments within the criminal justice system and this article argues that only by taking account of the views of those at the 'coal face' will criminologists, policy makers and practitioners be able to effect real change in crime rates. The article thus focuses on the views of a sample of previously persistent offenders in Scotland about offending, desistance and how the system can help them. It explores not only their need for friendship and support in youth but also the close association between relationships and the likelihood of offending. It also demonstrates the views of offenders themselves about the importance of the working relationship with supervising officers in helping them desist from crime. The article concludes that the most effective way of reducing offending is to re-engage with the message of the Probation Act of 100 years ago, namely, to 'advise, assist and befriend' offenders rather than to 'confront, challenge and change' offending behaviour
Lieb-Schultz-Mattis in Higher Dimensions
A generalization of the Lieb-Schultz-Mattis theorem to higher dimensional
spin systems is shown. The physical motivation for the result is that such spin
systems typically either have long-range order, in which case there are gapless
modes, or have only short-range correlations, in which case there are
topological excitations. The result uses a set of loop operators, analogous to
those used in gauge theories, defined in terms of the spin operators of the
theory. We also obtain various cluster bounds on expectation values for gapped
systems. These bounds are used, under the assumption of a gap, to rule out the
first case of long-range order, after which we show the existence of a
topological excitation. Compared to the ground state, the topologically excited
state has, up to a small error, the same expectation values for all operators
acting within any local region, but it has a different momentum.Comment: 14 pages, 3 figures, final version in pres
Evaluation of the BCS Approximation for the Attractive Hubbard Model in One Dimension
The ground state energy and energy gap to the first excited state are
calculated for the attractive Hubbard model in one dimension using both the
Bethe Ansatz equations and the variational BCS wavefunction. Comparisons are
provided as a function of coupling strength and electron density. While the
ground state energies are always in very good agreement, the BCS energy gap is
sometimes incorrect by an order of magnitude, particularly at half-filling.
Finite size effects are also briefly discussed for cases where an exact
solution in the thermodynamic limit is not possible. In general, the BCS result
for the energy gap is poor compared to the exact result.Comment: 25 pages, 5 Postscript figure
Finite one dimensional impenetrable Bose systems: Occupation numbers
Bosons in the form of ultra cold alkali atoms can be confined to a one
dimensional (1d) domain by the use of harmonic traps. This motivates the study
of the ground state occupations of effective single particle states
, in the theoretical 1d impenetrable Bose gas. Both the system on a
circle and the harmonically trapped system are considered. The and
are the eigenvalues and eigenfunctions respectively of the one body
density matrix. We present a detailed numerical and analytic study of this
problem. Our main results are the explicit scaled forms of the density
matrices, from which it is deduced that for fixed the occupations
are asymptotically proportional to in both the circular
and harmonically trapped cases.Comment: 22 pages, 8 figures (.eps), uses REVTeX
Exact solution of the six-vertex model with domain wall boundary conditions. Antiferroelectric phase
We obtain the large asymptotics of the partition function of the
six-vertex model with domain wall boundary conditions in the antiferroelectric
phase region, with the weights a=\sinh(\ga-t), b=\sinh(\ga+t), c=\sinh(2\ga),
|t|<\ga. We prove the conjecture of Zinn-Justin, that as ,
Z_n=C\th_4(n\om) F^{n^2}[1+O(n^{-1})], where \om and are given by
explicit expressions in \ga and , and is the Jacobi theta
function. The proof is based on the Riemann-Hilbert approach to the large
asymptotic expansion of the underlying discrete orthogonal polynomials and on
the Deift-Zhou nonlinear steepest descent method.Comment: 69 pages, 10 figure
Universality class of S=1/2 quantum spin ladder system with the four spin exchange
We study s=1/2 Heisenberg spin ladder with the four spin exchange. Combining
numerical results with the conformal field theory(CFT), we find a phase
transition with central charge c=3/2. Since this system has an SU(2) symmetry,
we can conclude that this critical theory is described by k=2 SU(2)
Wess-Zumino-Witten model with Z symmetry breaking
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