State vector evolution localized over the edges of a square tight-binding lattice

We study the time evolution of a state vector in a square tight-binding lattice, focusing on its evolution localized over the system surfaces. In this tight-binding lattice, the energy of atomic orbital centred at surface site is different from that at the interior (bulky) site by an energy shift U. It is shown that for the state vector initially localized on a surface, there exists an exponential law (y=a\e^x/b+y₀) determined by the absolute value of the energy shift, |U|, which describes the transition of the state evolving on the square tight-binding lattice, from delocalized over the whole lattice to localized over the surfaces.     

Magneto-electronic properties of rhombohedral trilayer graphene: Peierls tight-binding model

Magneto-electronic properties of rhombohedral (ABC-stacked) trilayer graphene are investigated by the tight-binding (TB) model with all important interlayer interactions taken into account. A numerical strategy, band-like matrix, is applied to solve the huge Hamiltonian matrix and thus the eigenvalues and eigenvectors of Landau levels (LLs) are well defined. Based on the characteristics of the wave functions, the LLs are divided into three groups. These LLs are strongly affected by the stacking configuration and interlayer interactions. The LL spectra do reflect the main features of the zero-field subbands, i.e., the existence of three LL groups, specified onset energies of the three groups, and asymmetric electronic structure. In an ABC-stacked structure, the LL wave functions are each composed of six magnetic TB Bloch functions for six sublattices. Each magnetic TB Bloch function exhibits the spatial symmetry, localization feature, and oscillation modes. Three sets of effective quantum numbers are defined to index the LLs of the three groups based on the oscillation modes in specific sublattices. These effective quantum numbers are useful for defining the optical selection rules of the optical absorption spectra.     

Driven state transfer and state storage in a tight-binding chain using two local barriers

A theoretical scheme to realize quantum state transfer and state storage in a uniformly coupled tight-binding chain is introduced in this paper. Two controllable gate voltages acting as local barriers are applied onto specific sites of the system, which separate the chain into three regions. By setting two gate voltages being equal, we show that an initially localized quantum wave packet undergoes perfect periodic revivals, allowing for perfect quantum state transfer between two nonadjacent spatial regions of the system. We also show that the wave packet can be trapped in its initial region by setting two gate voltages being unequal, which relates to the problem of storing quantum information. Moreover an efficient time-dependent quantum state transfer protocol is presented by smoothly varying the two gate voltages. Significantly, in our setup, the transferred state can be trapped, with a high fidelity of storage, at the end of the transfer protocol.     

Unit cell dependence of optical matrix elements in tight-binding theory: The case of zigzag graphene nanoribbons

In the tight-binding theory, momentum matrix elements (MMEs) needed to calculate the optical properties are normally computed using a formulation based on the gradient of the Hamiltonian in the k space. We demonstrate the inadequacy of this formulation by considering the case of zigzag graphene nanoribbons. We show that one obtains wrong values of MMEs, in violation of the well-known selection rules, if the unit cell chosen in the calculations does not incorporate the symmetries of the bulk. This is in spite of the fact that the band structure is insensitive to the choice of the unit cell. We substantiate our results based on group-theoretic arguments. Our observations will open an avenue for proper formulation of MMEs.     

石墨烯能带中的重叠矩阵效应:Tight-Binding方法在模拟中的研究

采用紧束缚方法计算了石墨烯的价带(π)和导带(π*),考虑了非正交基矢下重叠矩阵效应,重叠积分参量s越小,导带越靠近费米面,而价带越远离费米面.在重叠积分参量s≤0.1时,基本保持了原子在实际空间中重叠所引起的能带的改变,太大(s=0.4)则会导致物理上失效.计算了石墨烯的能态密度,在费米面ε=0处(对应Dirac点)的能态密度为零,并且在Dirac点附近呈线性变化.     

Distribution of resonance widths in localized tight-binding models

We numerically analyze the distribution of scattering resonance widths in one- and quasi-one dimensional tight binding models, in the localized regime. We detect and discuss an algebraic decay of the distribution, similar, though not identical, to recent theoretical predictions. Received 14 April 2000 and Received in final form 27 July 2000     

Entropic, LES and boundary conditions in lattice Boltzmann simulations of turbulence

Large scale (1600³-grid) entropic lattice Boltzmann (ELB) simulations are performed on the 27-bit model at sufficiently high Reynolds numbers to find intermittency corrections to the Kolmogorov k ^-5/3 inertial spectrum. Even though the transport coefficients in ELB and in the Large Eddy Simulation (LES) lattice Boltzmann schemes have very different origins, there are strong similarities in their turbulence statistics from 512³-grid simulations. A new LB moment-space boundary condition algorithm is tested on the 2D backstep problem, with excellent agreement with experimental data even up to a Reynolds number of 800.     

Combinatorial computational chemistry approach of tight-binding quantum chemical molecular dynamics method to the design of the automotive catalysts

Recently, we have developed a new tight-binding quantum chemical molecular dynamics program “Colors” for combinatorial computational chemistry approach. This methodology is based on our original tight-binding approximation and realized over 5000 times acceleration compared to the conventional first-principles molecular dynamics method. In the present study, we applied our new program to the simulations on various realistic large-scale models of the automotive three-way catalysts, ultrafine Pt particle/CeO₂(111) support. Significant electron transfer from the Pt particle to the CeO₂(111) surface was observed and it was found to strongly depend on the size of the Pt particle. Furthermore, our simulation results suggest that the reduction of the Ce atom due to the electron transfer from the Pt particle to the CeO₂ surface is a main reason for the strong interaction of the Pt particle and CeO₂(111) support.     

Entropic and conformational study of isolated double-tethered chains by three-dimensional lattice simulations

Double-tethered polymers are a kind of linear polymer with a peculiar topological constraint; that is, both of its end-points are attached to a plane which the polymer segments cannot penetrate. The effects of the constraint on the polymer's configurational and entropic properties were investigated by means of a three-dimensional lattice simulation that combined a previously proposed idea with a very efficient chain generation algorithm. In particular, the value of a topology-dependent critical exponent was estimated for the double-tethered configurations. This data is the first report on isolated and double-tethered chains. Also, two optional types of tethered-polymer were investigated as asymptotes of the double- and single-tethered configurations.     

熵测不准关系与光场的熵压缩

用熵作为光场量子涨落的量度,根据熵测不准关系,建立了熵压缩的概念,具体研究了光场与原子相互作用时的熵压缩,结果显示,熵压缩实现了对光场压缩效应的高灵敏量度。     

Phase controllable dynamical localization of a quantum particle in a driven optical lattice

The Dunlap–Kenkre (DK) result states that dynamical localization of a driven quantum particle in a periodic lattice happens when the ratio of the field magnitude to the field frequency of the diagonal drive is a root of the ordinary Bessel function of order 0. This has been experimentally verified. A generalization of the DK result is presented here. The hitherto considered DK model contains only the diagonal forcing. In the present extended version of the DK model we consider both off-diagonal and diagonal driving fields with different frequencies and a definite relative phase between them. We analytically show that new dynamical localizations conditions exist where an important role is played by the relative phase. In appropriate limits our results reduce to DK result.     

Quasi-equilibrium mixture of itinerant and localized bose atoms in optical lattice

Conditions are studied under which there can exist a quasi-equilibrium mixture of itinerant and localized bosonic atoms in an optical lattice, even at zero temperature and at integer filling factor, when such a coexistence is impossible for an equilibrium lattice. The consideration is based on a model having the structure of a two-band, or two-component, boson Hubbard Hamiltonian. The minimal value for the ratio of onsite repulsion to tunneling parameter, necessary for the occurrence of such a mixture, is found.     

Holes localized on a Skyrmion in a doped antiferromagnet on the honeycomb lattice: Symmetry analysis

Using the low-energy effective field theory for hole-doped antiferromagnets on the honeycomb lattice, we study the localization of holes on Skyrmions, as a potential mechanism for the preformation of Cooper pairs. In contrast to the square lattice case, for the standard radial profile of the Skyrmion on the honeycomb lattice, only holes residing in one of the two hole pockets can get localized. This differs qualitatively from hole pairs bound by magnon exchange, which is most attractive between holes residing in different momentum space pockets. On the honeycomb lattice, magnon exchange unambiguously leads to f$f$-wave pairing, which is also observed experimentally. Using the collective-mode quantization of the Skyrmion, we determine the quantum numbers of the localized hole pairs. Again, f$f$-wave symmetry is possible, but other competing pairing symmetries cannot be ruled out.     

Temperature evolution of electronic and lattice configurations in highly ordered trans-polyacetylene

We have studied the temperature evolution of the optical absorption and Raman scattering spectra of a trans-cis blend of “soluble” polyacetylene in a polyvinylbutyral/butanol mixture. On decreasing temperature a reversible restructuring of the electronic and lattice systems of trans-(CH)_x occurs: the electronic energy gap contracts at the high rate of 0.4 meV/K, and the vibrational modes are modified. The experimental data obtained are interpreted in terms of a peculiar interaction of π-conjugated electrons with lattice fluctuations. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 613–617 (10 November 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On the characterization of the higgs phase in lattice gauge theories

We consider Higgs models on a lattice in 3 or 4 dimensions. Higgs scalars are assumed to transform trivially under a finite subgroup Γ of the compact gauge groupG. We adopt 't Hooft's definition of the Higgs phase, it is characterized by a nonvanishing free energy per unit length (area) of a vortex in 3 (4) dimensions. By using a Peierls argument we show that the models are in the Higgs phase in this sense for suitable coupling constants.     

Entropic stochastic resonance: the constructive role of the unevenness

We demonstrate the existence of stochastic resonance (SR) in confined systems arising from entropy variations associated to the presence of irregular boundaries. When the motion of a Brownian particle is constrained to a region with uneven boundaries, the presence of a periodic input may give rise to a peak in the spectral amplification factor and therefore to the appearance of the SR phenomenon. We have proved that the amplification factor depends on the shape of the region through which the particle moves and that by adjusting its characteristic geometric parameters one may optimize the response of the system. The situation in which the appearance of such entropic stochastic resonance (ESR) occurs is common for small-scale systems in which confinement and noise play an prominent role. The novel mechanism found could thus constitute an important tool for the characterization of these systems and can put to use for controlling their basic properties.