Fermionic R-operator approach for the small-polaron model with open boundary condition

Exact integrability and algebraic Bethe ansatz of the small-polaron model with the open boundary condition are discussed in the framework of the quantum inverse scattering method (QISM). We employ a new approach where the fermionic R-operator which consists of fermion operators is a key object. It satisfies the Yang-Baxter equation and the reflection equation with its corresponding K-operator. Two kinds of 'super-transposition' for the fermion operators are defined and the dual reflection equation is obtained. These equations prove the integrability and the Bethe ansatz equation which agrees with the one obtained from the graded Yang-Baxter equation and the graded reflection equations.Comment: 10 page

Correlation length of the 1D Hubbard Model at half-filling : equal-time one-particle Green's function

The asymptotics of the equal-time one-particle Green's function for the half-filled one-dimensional Hubbard model is studied at finite temperature. We calculate its correlation length by evaluating the largest and the second largest eigenvalues of the Quantum Transfer Matrix (QTM). In order to allow for the genuinely fermionic nature of the one-particle Green's function, we employ the fermionic formulation of the QTM based on the fermionic R-operator of the Hubbard model. The purely imaginary value of the second largest eigenvalue reflects the k_F (= pi/2) oscillations of the one-particle Green's function at half-filling. By solving numerically the Bethe Ansatz equations with Trotter numbers up to N=10240, we obtain accurate data for the correlation length at finite temperatures down into the very low temperature region. The correlation length remains finite even at T=0 due to the existence of the charge gap. Our numerical data confirm Stafford and Millis' conjecture regarding an analytic expression for the correlation length at T=0.Comment: 7 pages, 6 figure

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

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

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

Fast and stable method for simulating quantum electron dynamics

A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several computational techniques such as Suzuki's exponential product, Cayley's form, the finite differential method and an operator named adhesive operator. This method conserves the norm of the wavefunction, manages periodic conditions and adaptive mesh refinement technique, and is suitable for vector- and parallel-type supercomputers. Applying this method to some simple electron dynamics, we confirmed the efficiency and accuracy of the method for simulating fast time-dependent quantum phenomena.Comment: 10 pages, 35 eps figure

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

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, $T(x)$, is an extended solution of the Schr\"oder functional equation, $q(T(x))=\lambda q(x)$, 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 $\wp$ 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

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 $\approx$ 10$^{-4}$ 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

Finding Exponential Product Formulas of Higher Orders

In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves important symmetries of the system dynamics. We focuse on two algorithms of constructing higher-order exponential product formulas. The first is the fractal decomposition, where we construct higher-order formulas recursively. The second is to make use of the quantum analysis, where we compute higher-order correction terms directly. As interludes, we also have described the decomposition of symplectic integrators, the approximation of time-ordered exponentials, and the perturbational composition.Comment: 22 pages, 9 figures. To be published in the conference proceedings ''Quantum Annealing and Other Optimization Methods," eds. B.K.Chakrabarti and A.Das (Springer, Heidelberg