294 research outputs found
The fermionic limit of the delta-function Bose gas: a pseudopotential approach
We use first-order perturbation theory near the fermionic limit of the
delta-function Bose gas in one dimension (i.e., a system of weakly interacting
fermions) to study three situations of physical interest. The calculation is
done using a pseudopotential which takes the form of a two-body
delta''-function interaction. The three cases considered are the behavior of
the system with a hard wall, with a point where the strength of the
pseudopotential changes discontinuously, and with a region of finite length
where the pseudopotential strength is non-zero (this is sometimes used as a
model for a quantum wire). In all cases, we obtain exact expressions for the
density to first order in the pseudopotential strength. The asymptotic
behaviors of the densities are in agreement with the results obtained from
bosonization for a Tomonaga-Luttinger liquid, namely, an interaction dependent
power-law decay of the density far from the hard wall, a reflection from the
point of discontinuity, and transmission resonances for the interacting region
of finite length. Our results provide a non-trivial verification of the
Tomonaga-Luttinger liquid description of the delta-function Bose gas near the
fermionic limit.Comment: LaTeX, 17 pages, no figure
A multispecies Calogero-Sutherland model
Motivated by the concept of ideal mutual statistics, we study a multispecies
Calogero-Sutherland model in which the interaction parameters and masses
satisfy some specific relations. The ground state is exactly solvable if those
relations hold, both on a circle and on a line with a simple harmonic
potential. In the latter case, the one-particle densities can be obtained using
a generalization of the Thomas-Fermi method. We calculate the second virial
coefficients in the high temperature expansion for the pressure. We show that
the low-energy excitations are the same as those of a Gaussian conformal field
theory. Finally, we discuss similar relations between the statistics parameters
and charges for a multispecies anyon model in a magnetic field.Comment: 27 pages, LaTeX, no figures; all sections have been significantly
expanded from the previous version of 13 pages; a new section on low-energy
excitations; to appear in Nucl. Phys.
Semiclassical analysis of two- and three-spin antiferromagnets and anyons on a sphere
We do a semiclassical analysis for two or three spins which are coupled
antiferromagnetically to each other. The semiclassical wave functions transform
correctly under permutations of the spins if one takes into account the
Wess-Zumino term present in the path integral for spins. The Wess-Zumino term
here is a total derivative which has no effect on the energy spectrum. The
semiclassical problem is related to that of anyons moving on a sphere with the
statistics parameter being for two spins and for
three spins. Finally, we present a novel way of deriving the semiclassical wave
functions from the spin wave functions.Comment: 16 pages, plain tex, 1 figure available on request, IISc-CTS-93-
Integers and Fractions
This article briefly reviews the quantum Hall effect and the contributions of
the winners of the 1998 Nobel Prize in Physics.Comment: LaTeX, 6 pages, no figures. On the 1998 Nobel Prize in Physics. To
appear in Current Scienc
Non-equilibrium Green's function formalism and the problem of bound states
The non-equilibrium Green's function formalism for infinitely extended
reservoirs coupled to a finite system can be derived by solving the equations
of motion for a tight-binding Hamiltonian. While this approach gives the
correct density for the continuum states, we find that it does not lead, in the
absence of any additional mechanisms for equilibration, to a unique expression
for the density matrix of any bound states which may be present. Introducing
some auxiliary reservoirs which are very weakly coupled to the system leads to
a density matrix which is unique in the equilibrium situation, but which
depends on the details of the auxiliary reservoirs in the non-equilibrium case.Comment: Revtex4, 32 pages including 5 figures; some corrections made, this is
the version published in Phys Rev
One-dimensional fermions with incommensurate hopping close to dimerization
We study the spectrum of fermions hopping on a chain with a weak
incommensuration close to dimerization; both q, the deviation of the wave
number from pi, and delta, the strength of the incommensuration, are small. For
free fermions, we use a continuum Dirac theory to show that there are an
infinite number of bands which meet at zero energy as q approaches zero. In the
limit that the ratio q/delta ---> 0, the number of states lying inside the q =
0 gap is nonzero and equal to 2 delta / pi^2. Thus the limit q ---> 0 differs
from q = 0; this can be seen clearly in the behavior of the specific heat at
low temperature. For interacting fermions or the XXZ spin-1/2 chain, we use
bosonization to argue that similar results hold.Comment: Revtex, 9 pages including 2 epsf figure
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