3,422 research outputs found
Bethe Ansatz and Classical Hirota Equation
We discuss an interrelation between quantum integrable models and classical
soliton equations with discretized time. It appeared that spectral
characteristics of quantum integrable systems may be obtained from entirely
classical set up. Namely, the eigenvalues of the quantum transfer matrix and
the scattering -matrix itself are identified with a certain -functions
of the discrete Liouville equation. The Bethe ansatz equations are obtained as
dynamics of zeros. For comparison we also present the Bethe ansatz equations
for elliptic solutions of the classical discrete Sine-Gordon equation. The
paper is based on the recent study of classical integrable structures in
quantum integrable systems, hep-th/9604080.Comment: 15 pages, Latex, special World Scientific macros include
Hidden Integrability of a Kondo Impurity in an Unconventional Host
We study a spin-1/2 Kondo impurity coupled to an unconventional host in which
the density of band states vanishes either precisely at (``gapless'' systems)
or on some interval around the Fermi level (``gapped''systems). Despite an
essentially nonlinear band dispersion, the system is proven to exhibit hidden
integrability and is diagonalized exactly by the Bethe ansatz.Comment: 4 pages, RevTe
On the singular spectrum of the Almost Mathieu operator. Arithmetics and Cantor spectra of integrable models
I review a recent progress towards solution of the Almost Mathieu equation
(A.G. Abanov, J.C. Talstra, P.B. Wiegmann, Nucl. Phys. B 525, 571, 1998), known
also as Harper's equation or Azbel-Hofstadter problem. The spectrum of this
equation is known to be a pure singular continuum with a rich hierarchical
structure. Few years ago it has been found that the almost Mathieu operator is
integrable. An asymptotic solution of this operator became possible due
analysis the Bethe Ansatz equations.Comment: Based on the lecture given at 13th Nishinomiya-Yukawa Memorial
Symposium on Dynamics of Fields and Strings, Nishinomiya, Japan, 12-13 Nov
1998, and talk given at YITP Workshop on New Aspects of Strings and Fields,
Kyoto, Japan, 16-18 Nov 199
Geometric adiabatic transport in quantum Hall states
We argue that in addition to the Hall conductance and the nondissipative
component of the viscous tensor, there exists a third independent transport
coefficient, which is precisely quantized. It takes constant values along
quantum Hall plateaus. We show that the new coefficient is the Chern number of
a vector bundle over moduli space of surfaces of genus 2 or higher and
therefore cannot change continuously along the plateau. As such, it does not
transpire on a sphere or a torus. In the linear response theory, this
coefficient determines intensive forces exerted on electronic fluid by
adiabatic deformations of geometry and represents the effect of the
gravitational anomaly. We also present the method of computing the transport
coefficients for quantum Hall states.Comment: 6 pages, discussion of angular momentum formulas in sec. 7 is amende
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