318 research outputs found
Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model
The quantum transfer matrix (QTM) approach to integrable lattice Fermion
systems is presented. As a simple case we treat the spinless Fermion model with
repulsive interaction in critical regime. We derive a set of non-linear
integral equations which characterize the free energy and the correlation
length of for arbitrary particle density at any finite
temperatures. The correlation length is determined by solving the integral
equations numerically. Especially in low temperature limit this result agrees
with the prediction from conformal field theory (CFT) with high accuracy.Comment: 17 page
Fermionisation of the Spin-S Uimin-Lai-Sutherland Model: Generalisation of Supersymmetric t-J Model to Spin-S
The spin-1 Uimin-Lai-Sutherland (ULS) isotropic chain model is expressed in
terms of fermions and the equivalence of the fermionic representation to the
supersymmetric t-J model is established directly at the level of
Hamiltonians.The spin-S ULS model is fermionized and the Hamiltonian of the
corresponding generalisation of the t-J model is written down.Comment: 16 page
Fermionic R-Operator and Algebraic Structure of 1D Hubbard Model: Its application to quantum transfer matrix
The algebraic structure of the 1D Hubbard model is studied by means of the
fermionic R-operator approach. This approach treats the fermion models directly
in the framework of the quantum inverse scattering method. Compared with the
graded approach, this approach has several advantages. First, the global
properties of the Hamiltonian are naturally reflected in the algebraic
properties of the fermionic R-operator. We want to note that this operator is a
local operator acting on fermion Fock spaces. In particular, SO(4) symmetry and
the invariance under the partial particle hole transformation are discussed.
Second, we can construct a genuinely fermionic quantum transfer transfer matrix
(QTM) in terms of the fermionic R-operator. Using the algebraic Bethe Ansatz
for the Hubbard model, we diagonalize the fermionic QTM and discuss its
properties.Comment: 22 pages, no figure
Solution of the quantum inverse problem
We derive a formula that expresses the local spin and field operators of
fundamental graded models in terms of the elements of the monodromy matrix.
This formula is a quantum analogue of the classical inverse scattering
transform. It applies to fundamental spin chains, such as the XYZ chain, and to
a number of important exactly solvable models of strongly correlated electrons,
such as the supersymmetric t-J model or the the EKS model.Comment: 37 pages, AMS-Latex, AMS-Font
Madelung Fluid Model for The Most Likely Wave Function of a Single Free Particle in Two Dimensional Space with a Given Average Energy
We consider spatially two dimensional Madelung fluid whose irrotational
motion reduces into the Schr\"odinger equation for a single free particle. In
this respect, we regard the former as a direct generalization of the latter,
allowing a rotational quantum flow. We then ask for the most likely wave
function possessing a given average energy by maximizing the Shannon
information entropy over the quantum probability density. We show that there
exists a class of solutions in which the wave function is self-trapped,
rotationally symmetric, spatially localized with finite support, and spinning
around its center, yet stationary. The stationarity comes from the balance
between the attractive quantum force field of a trapping quantum potential
generated by quantum probability density and the repulsive centrifugal force of
a rotating velocity vector field. We further show that there is a limiting case
where the wave function is non-spinning and yet still stationary. This special
state turns out to be the lowest stationary state of the ordinary Schr\"odinger
equation for a particle in a cylindrical tube classical potential.Comment: 19 page
The Schr\"oder functional equation and its relation to the invariant measures of chaotic maps
The aim of this paper is to show that the invariant measure for a class of
one dimensional chaotic maps, , is an extended solution of the Schr\"oder
functional equation, , induced by them. Hence, we give an
unified treatment of a collection of exactly solved examples worked out in the
current literature. In particular, we show that these examples belongs to a
class of functions introduced by Mira, (see text). Moreover, as a new example,
we compute the invariant densities for a class of rational maps having the
Weierstrass functions as an invariant one. Also, we study the relation
between that equation and the well known Frobenius-Perron and Koopman's
operators.Comment: 9 page
Praktična sinteza regulatora za precizno pozicioniranje sustava pomične podloge
This paper presents a practical feedback controller design of a ball screw-driven table system for the microdisplacement positioning. Friction of the mechanism in the micro-displacement region has nonlinear elastic properties, unlike Coulomb and/or viscous friction in the macro-displacement, resulting in different positioning responses and frequency characteristics of the plant depending on the regions. In this paper, at first, a numerical simulator with a rolling friction model is adopted to reproduce the positioning behaviors in the micro-displacement region. Based on the simulator, the stability condition of positioning in the region is clarified on the basis of frequency characteristics and, then, appropriate parameters of feedback controller are practically designed to satisfy the required positioning performance. Effectiveness of the proposed design has been verified by a series of experiments using a prototype of ball screw-driven table positioning device.U radu je prikazana sinteza regulatora s povratnom vezom u sustavu za precizno linearno pozicioniranje pomične podloge pomoću kugličnih ležajeva. Za razliku od uobičajenih modela Coulombova i/ili viskoznog trenja, trenje razmatranog sustava ima izrazito nelinearna svojstva u području mikro-pomaka, što za posljedicu ima različite odzive pozicioniranja i frekvencijski karakteristike, ovisno o radnom području. U radu je prvo razvijeno numeričko simulacijsko okruženje zasnovano na modelu trenja kotrljanja u svrhu simuliranja ponašanja sustava pozicioniranja u području mikropomaka. Potom je, zasnivajući se na simulacijskom okruženju, pomoću frekvencijske karakteristike razjašnjen problem stabilnosti sustava u promatranom radnom području te su odabrani odgovarajući parametri regulatora koji poštuju uvjet stabilnosti i zadovoljavaju željenu kvalitetu odziva. Sinteza regulatora provedena je vodeći računa o praktičnoj primjenjivosti postupka. Učinkovitost predložene sinteze potvr.ena je nizom eksperimenata na prototipu sustava za precizno linearno pozicioniranje pomične podloge pomoću kugličnih ležajeva
Exact solutions to chaotic and stochastic systems
We investigate functions that are exact solutions to chaotic dynamical
systems. A generalization of these functions can produce truly random numbers.
For the first time, we present solutions to random maps. This allows us to
check, analytically, some recent results about the complexity of random
dynamical systems. We confirm the result that a negative Lyapunov exponent does
not imply predictability in random systems. We test the effectiveness of
forecasting methods in distinguishing between chaotic and random time-series.
Using the explicit random functions, we can give explicit analytical formulas
for the output signal in some systems with stochastic resonance. We study the
influence of chaos on the stochastic resonance. We show, theoretically, the
existence of a new type of solitonic stochastic resonance, where the shape of
the kink is crucial. Using our models we can predict specific patterns in the
output signal of stochastic resonance systems.Comment: 31 pages, 18 figures (.eps). To appear in Chaos, March 200
Light emission from a scanning tunneling microscope: Fully retarded calculation
The light emission rate from a scanning tunneling microscope (STM) scanning a
noble metal surface is calculated taking retardation effects into account. As
in our previous, non-retarded theory [Johansson, Monreal, and Apell, Phys. Rev.
B 42, 9210 (1990)], the STM tip is modeled by a sphere, and the dielectric
properties of tip and sample are described by experimentally measured
dielectric functions. The calculations are based on exact diffraction theory
through the vector equivalent of the Kirchoff integral. The present results are
qualitatively similar to those of the non-retarded calculations. The light
emission spectra have pronounced resonance peaks due to the formation of a
tip-induced plasmon mode localized to the cavity between the tip and the
sample. At a quantitative level, the effects of retardation are rather small as
long as the sample material is Au or Cu, and the tip consists of W or Ir.
However, for Ag samples, in which the resistive losses are smaller, the
inclusion of retardation effects in the calculation leads to larger changes:
the resonance energy decreases by 0.2-0.3 eV, and the resonance broadens. These
changes improve the agreement with experiment. For a Ag sample and an Ir tip,
the quantum efficiency is 10 emitted photons in the visible
frequency range per tunneling electron. A study of the energy dissipation into
the tip and sample shows that in total about 1 % of the electrons undergo
inelastic processes while tunneling.Comment: 16 pages, 10 figures (1 ps, 9 tex, automatically included); To appear
in Phys. Rev. B (15 October 1998
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Biases in the perceived timing of perisaccadic perceptual and motor events
Subjects typically experience the temporal interval immediately following a saccade as longer than a comparable control interval. One explanation of this effect is that the brain antedates the perceptual onset of a saccade target to around the time of saccade initiation. This could explain the apparent continuity of visual perception across eye movements. Thisantedating account was tested in three experiments in which subjects made saccades of differing extents and then judged either the duration or the temporal order of key events. Postsaccadic stimuli underwent subjective temporal lengthening and had early perceived onsets. A temporally advanced awareness of saccade completion was also found, independently of antedating effects. These results provide convergent evidence supporting antedating and differentiating it from other temporal biases
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