6,328 research outputs found
Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons
We calculate the exact dynamical magnetic structure factor S(Q,E) in the
ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2
spinon excitations, the Haldane-Shastry model with inverse-square exchange,
which is in the same low-energy universality class as Bethe's nearest-neighbor
exchange model. Only two-spinon excited states contribute, and S(Q,E) is found
to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903
Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
One-dimensional model of non-relativistic particles with inverse-square
interaction potential known as Calogero-Sutherland Model (CSM) is shown to
possess fractional statistics. Using the theory of Jack symmetric polynomial
the exact dynamical density-density correlation function and the one-particle
Green's function (hole propagator) at any rational interaction coupling
constant are obtained and used to show clear evidences of the
fractional statistics. Motifs representing the eigenstates of the model are
also constructed and used to reveal the fractional {\it exclusion} statistics
(in the sense of Haldane's ``Generalized Pauli Exclusion Principle''). This
model is also endowed with a natural {\it exchange } statistics (1D analog of
2D braiding statistics) compatible with the {\it exclusion} statistics.
(Submitted to PRL on April 18, 1994)Comment: Revtex 11 pages, IASSNS-HEP-94/27 (April 18, 1994
Universal Level dynamics of Complex Systems
. We study the evolution of the distribution of eigenvalues of a
matrix subject to a random perturbation drawn from (i) a generalized Gaussian
ensemble (ii) a non-Gaussian ensemble with a measure variable under the change
of basis. It turns out that, in the case (i), a redefinition of the parameter
governing the evolution leads to a Fokker-Planck equation similar to the one
obtained when the perturbation is taken from a standard Gaussian ensemble (with
invariant measure). This equivalence can therefore help us to obtain the
correlations for various physically-significant cases modeled by generalized
Gaussian ensembles by using the already known correlations for standard
Gaussian ensembles.
For large -values, our results for both cases (i) and (ii) are similar to
those obtained for Wigner-Dyson gas as well as for the perturbation taken from
a standard Gaussian ensemble. This seems to suggest the independence of
evolution, in thermodynamic limit, from the nature of perturbation involved as
well as the initial conditions and therefore universality of dynamics of the
eigenvalues of complex systems.Comment: 11 Pages, Latex Fil
Energy absorption in time-dependent unitary random matrix ensembles: dynamic vs Anderson localization
We consider energy absorption in an externally driven complex system of
noninteracting fermions with the chaotic underlying dynamics described by the
unitary random matrices. In the absence of quantum interference the energy
absorption rate W(t) can be calculated with the help of the linear-response
Kubo formula. We calculate the leading two-loop interference correction to the
semiclassical absorption rate for an arbitrary time dependence of the external
perturbation. Based on the results for periodic perturbations, we make a
conjecture that the dynamics of the periodically-driven random matrices can be
mapped onto the one-dimensional Anderson model. We predict that in the regime
of strong dynamic localization W(t) ln(t)/t^2 rather than decays exponentially.Comment: 6 pages, 1 figur
Theory of localization and resonance phenomena in the quantum kicked rotor
We present an analytic theory of quantum interference and Anderson
localization in the quantum kicked rotor (QKR). The behavior of the system is
known to depend sensitively on the value of its effective Planck's constant
\he. We here show that for rational values of \he/(4\pi)=p/q, it bears
similarity to a disordered metallic ring of circumference and threaded by
an Aharonov-Bohm flux. Building on that correspondence, we obtain quantitative
results for the time--dependent behavior of the QKR kinetic energy, (this is an observable which sensitively probes the system's localization
properties). For values of smaller than the localization length , we
obtain scaling , where is
the quasi--energy level spacing on the ring. This scaling is indicative of a
long time dynamics that is neither localized nor diffusive. For larger values
, the functions saturates (up to exponentially
small corrections ), thus reflecting essentially localized
behavior.Comment: 27 pages, 3 figure
Measurement of the charged pion mass using X-ray spectroscopy of exotic atoms
The transitions in pionic nitrogen and muonic oxygen were measured
simultaneously by using a gaseous nitrogen-oxygen mixture at 1.4\,bar. Due to
the precise knowledge of the muon mass the muonic line provides the energy
calibration for the pionic transition. A value of
(139.57077\,\,0.00018)\,MeV/c (\,1.3ppm) is derived for the
mass of the negatively charged pion, which is 4.2ppm larger than the present
world average
Quantum Mechanics with Random Imaginary Scalar Potential
We study spectral properties of a non-Hermitian Hamiltonian describing a
quantum particle propagating in a random imaginary scalar potential. Cast in
the form of an effective field theory, we obtain an analytical expression for
the ensemble averaged one-particle Green function from which we obtain the
density of complex eigenvalues. Based on the connection between non-Hermitian
quantum mechanics and the statistical mechanics of polymer chains, we determine
the distribution function of a self-interacting polymer in dimensions .Comment: 10 pages, 1 eps figur
Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization
The explicit analytical expression for the distribution function of
parametric derivatives of energy levels ("level velocities") with respect to a
random change of scattering potential is derived for the chaotic quantum
systems belonging to the quasi 1D universality class (quantum kicked rotator,
"domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.
Laughlin Wave Function and One-Dimensional Free Fermions
Making use of the well-known phase space reduction in the lowest Landau
level(LLL), we show that the Laughlin wave function for the
case can be obtained exactly as a coherent state representation of an one
dimensional wave function. The system consists of copies of
free fermions associated with each of the electrons, confined in a common
harmonic well potential. Interestingly, the condition for this exact
correspondence is found to incorporate Jain's parton picture. We argue that,
this correspondence between the free fermions and quantum Hall effect is due to
the mapping of the system under consideration, to the Gaussian unitary
ensemble in the random matrix theory.Comment: 7 pages, Latex , no figure
Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
We show that the particles in the Calogero-Sutherland Model obey fractional
exclusion statistics as defined by Haldane. We construct anyon number densities
and derive the energy distribution function. We show that the partition
function factorizes in the form characteristic of an ideal gas. The virial
expansion is exactly computable and interestingly it is only the second virial
coefficient that encodes the statistics information.Comment: 10pp, REVTE
- …