1,696 research outputs found
Lattice two-body problem with arbitrary finite range interactions
We study the exact solution of the two-body problem on a tight-binding
one-dimensional lattice, with pairwise interaction potentials which have an
arbitrary but finite range. We show how to obtain the full spectrum, the bound
and scattering states and the "low-energy" solutions by very efficient and
easy-to-implement numerical means. All bound states are proven to be
characterized by roots of a polynomial whose degree depends linearly on the
range of the potential, and we discuss the connections between the number of
bound states and the scattering lengths. "Low-energy" resonances can be located
with great precission with the methods we introduce. Further generalizations to
include more exotic interactions are also discussed.Comment: 6 pages, 3 figure
Quasiparticles governing the zero-temperature dynamics of the 1D spin-1/2 Heisenberg antiferromagnet in a magnetic field
The T=0 dynamical properties of the one-dimensional (1D)
Heisenberg antiferromagnet in a uniform magnetic field are studied via Bethe
ansatz for cyclic chains of sites. The ground state at magnetization
, which can be interpreted as a state with spinons or as a
state of magnons, is reconfigured here as the vacuum for a different
species of quasiparticles, the {\em psinons} and {\em antipsinons}. We
investigate three kinds of quantum fluctuations, namely the spin fluctuations
parallel and perpendicular to the direction of the applied magnetic field and
the dimer fluctuations. The dynamically dominant excitation spectra are found
to be sets of collective excitations composed of two quasiparticles excited
from the psinon vacuum in different configurations. The Bethe ansatz provides a
framework for (i) the characterization of the new quasiparticles in relation to
the more familiar spinons and magnons, (ii) the calculation of spectral
boundaries and densities of states for each continuum, (iii) the calculation of
transition rates between the ground state and the dynamically dominant
collective excitations, (iv) the prediction of lineshapes for dynamic structure
factors relevant for experiments performed on a variety of quasi-1D
antiferromagnetic compounds, including KCuF,
Cu(CHN, and CuGeO.Comment: 13 pages, 12 figure
Spectrum and transition rates of the XX chain analyzed via Bethe ansatz
As part of a study that investigates the dynamics of the s=1/2 XXZ model in
the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz
equations for the case Delta=0 (XX model). We identify the general structure of
the Bethe ansatz solutions for the entire XX spectrum, which include states
with real and complex magnon momenta. We discuss the relation between the
spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions
(Jordan-Wigner representation). We present determinantal expressions for
transition rates of spin fluctuation operators between Bethe wave functions and
reduce them to product expressions. We apply the new formulas to two-spinon
transition rates for chains with up to N=4096 sites.Comment: 11 pages, 4 figure
Lineshape predictions via Bethe ansatz for the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field
The spin fluctuations parallel to the external magnetic field in the ground
state of the one-dimensional (1D) s=1/2 Heisenberg antiferromagnet are
dominated by a two-parameter set of collective excitations. In a cyclic chain
of N sites and magnetization 0<M_z<N/2, the ground state, which contains 2M_z
spinons, is reconfigured as the physical vacuum for a different species of
quasi-particles, identifiable in the framework of the coordinate Bethe ansatz
by characteristic configurations of Bethe quantum numbers. The dynamically
dominant excitations are found to be scattering states of two such
quasi-particles. For N -> \infty, these collective excitations form a continuum
in (q,\omega)-space with an incommensurate soft mode. Their matrix elements in
the dynamic spin structure factor S_{zz}(q,\omega) are calculated directly from
the Bethe wave functions for finite N. The resulting lineshape predictions for
N -> \infty complement the exact results previously derived via algebraic
analysis for the exact 2-spinon part of S_{zz}(q,\omega) in the zero-field
limit. They are directly relevant for the interpretation of neutron scattering
data measured in nonzero field on quasi-1D antiferromagnetic compounds.Comment: 10 page
Toward a Science of Effective Cognitive Training
A long-standing question in the behavioral sciences is whether cognitive functions can be improved through dedicated training. It is uncontested that training programs can lead to near transfer, meaning increased performance on untrained tasks involving similar cognitive functions. However, whether training also leads to far transfer, meaning increased performance on loosely related untrained tasks or even activities of daily living, is still hotly debated. Here, we review the extant literature and, in particular, the most recent meta-analytic evidence and argue that the ongoing crisis in the field of cognitive-training research may benefit from taking a more mechanistic approach to studying the effectiveness of training. We propose that (a) adopting a more rigorous theoretical framework that builds on a process-based account of training and transfer, (b) considering the role of individual differences in the responsiveness to training, and (c) drawing on Bayesian models of development may help to solve controversial issues in the field and lead the way to designing and implementing more effective training protocols
Quantum chaos: an introduction via chains of interacting spins-1/2
We introduce aspects of quantum chaos by analyzing the eigenvalues and the
eigenstates of quantum many-body systems. The properties of quantum systems
whose classical counterparts are chaotic differ from those whose classical
counterparts are not chaotic. The spectrum of the first exhibits repulsion of
the energy levels. This is one of the main signatures of quantum chaos. We show
how level repulsion develops in one-dimensional systems of interacting spins
1/2 which are devoid of random elements and involve only two-body interactions.
In addition to the statistics of the eigenvalues, we analyze how the structure
of the eigenstates may indicate chaos. The programs used to obtain the data are
available online.Comment: 7 pages, 3 figure
Interaction effects between impurities in low dimensional spin-1/2 antiferromagnets
We are considering the interplay between several non-magnetic impurities in
the spin-1/2 Heisenberg antiferromagnet in chains, ladders and planes by
introducing static vacancies in numerical quantum Monte Carlo simulations. The
effective potential between two and more impurities is accurately determined,
which gives a direct measure of the quantum correlations in the systems. Large
effective interaction potentials are an indication of strong quantum
correlations in the system and reflect the detailed nature of the valence bond
ground states. In two-dimensions (2D) the interactions are smaller, but can
still be analyzed in terms of valence bonds.Comment: 8 pages, 6 figures, accepted by Europhys. Lett. The latest pdf file
is available at http://www.physik.uni-kl.de/eggert/papers/interact2d.pd
Line shapes of dynamical correlation functions in Heisenberg chains
We calculate line shapes of correlation functions by use of complete
diagonalization data of finite chains and analytical implications from
conformal field theory, density of states, and Bethe ansatz. The numerical data
have different finite size accuracy in case of the imaginary and real parts in
the frequency and time representations of spin-correlation functions,
respectively. The low temperature, conformally invariant regime crosses over at
to a diffusive regime that in turn connects continuously to
the high temperature, interacting fermion regime. The first moment sum rule is
determined.Comment: 13 pages REVTEX, 18 figure
Self-adjoint symmetry operators connected with the magnetic Heisenberg ring
We consider symmetry operators a from the group ring C[S_N] which act on the
Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We
investigate such symmetry operators a which are self-adjoint (in a sence
defined in the paper) and which yield consequently observables of the
Heisenberg model. We prove the following results: (i) One can construct a
self-adjoint idempotent symmetry operator from every irreducible character of
every subgroup of S_N. This leads to a big manifold of observables. In
particular every commutation symmetry yields such an idempotent. (ii) The set
of all generating idempotents of a minimal right ideal R of C[S_N] contains one
and only one idempotent which ist self-adjoint. (iii) Every self-adjoint
idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k
which are also self-adjoint and pairwise orthogonal. We give a computer
algorithm for the calculation of such decompositions. Furthermore we present 3
additional algorithms which are helpful for the calculation of self-adjoint
operators by means of discrete Fourier transforms of S_N. In our investigations
we use computer calculations by means of our Mathematica packages PERMS and
HRing.Comment: 13 page
Thermodynamics of ideal quantum gas with fractional statistics in D dimensions
We present exact and explicit results for the thermodynamic properties
(isochores, isotherms, isobars, response functions, velocity of sound) of a
quantum gas in dimensions D>=1 and with fractional exclusion statistics 0<=g<=1
connecting bosons (g=0) and fermions (g=1). In D=1 the results are equivalent
to those of the Calogero-Sutherland model. Emphasis is given to the crossover
between boson-like and fermion-like features, caused by aspects of the
statistical interaction that mimic long-range attraction and short-range
repulsion. The full isochoric heat capacity and the leading low-T term of the
isobaric expansivity in D=2 are independent of g. The onset of Bose-Einstein
condensation along the isobar occurs at a nonzero transition temperature in all
dimensions. The T-dependence of the velocity of sound is in simple relation to
isochores and isobars. The effects of soft container walls are accounted for
rigorously for the case of a pure power-law potential.Comment: 15 pages, 31 figure
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