Finite size and boundary effects in critical two-dimensional free-fermion models

Here we will consider the finite-size scaling, finite-size corrections and boundary effects for the critical two-dimensional free-fermion models. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We derive the exact finite-size corrections for the set of free models of statistical mechanics, including Ising model, dimer model, resistor network and spanning tree model under different boundary conditions. We have shown that the partition functions of all these models can be written in terms of the only object, namely, the partition function with twisted boundary conditions.     

细胞丛状化分布对二维耦合体系尺度选择效应的影响

采用随机模拟方法对体系的化学朗之万方程进行了数值模拟，考察了二维耦合细胞体系中，细胞的丛状化分布对于因内噪声作用而产生的尺度选择效应所带来的影响.研究发现，当体系处于Hopf分岔点附近时，由于耦合作用使得处于最佳状态的一定数目的细胞呈现丛状化聚集在一起，而这种丛状化分布的“团队精神”可以极大地提高体系的工作效率，表现为体系对外界刺激信号的响应能力(信噪比)达到极大值.同时还观察到，体系对外界刺激最为敏感时对应的最佳细胞丛尺度大小不随耦合强度的改变而变化，而体系输出信号的信噪比，随着耦合强度的增加有增大趋势.这些现象表明，细胞的丛状化分布将极大地增强细胞中钙离子信号对外界刺激的响应效果.生物体系本身可能具有这种特性，并利用它来改善和提高感受外界信息的能力.     

Electric field patterns in finite two-dimensional wire photonic lattices

Electric field patterns in finite two-dimensional wire photonics lattices are investigated by means of electromagnetic simulations. These studies reveal a strong analogy with the envelope wavefunction approach extensively used for semiconductor superlattices. Several propagating eigenmodes in the pass-band of the periodic structure as well as evanescent modes in the stop-bands are clearly identified. They are interpreted on the basis of the matching of the wavelength of electromagnetic field to the lattice dimensions with an envelope wavefunction resulting of a Fabry–Pérot effect in the cavity formed by the periodic structure. In terms of transmission coefficient, the calculated frequency dependence are in agreement with those measured in finite metallic rod arrays between 50 and 110 GHz.     

Exchange and correlation effects in a semiconductor quantum-well wire

The exchange and correlation effects of a quasi-one-dimensional electron gas are investigated by using the self-consistent-field approximation theory proposed by Singwi, Tosi, Land and Sjölander for the response function of the electron system. The present results are applied to GaAs-GaAlAs rectangular quantum-well-wires with the appropriate form factors that take into account the influence of the finite width of the electron layer. The plasmon dispersion relation and structure factor are calculated as a function of electron density and thickness of the wire. Results for the total energy per electron including kinetic, exchange and correlation energies and electron effective mass are presented. The Hartree-Fock and the random-phase approximation (RPA) results are also presented for comparison. We have found that exchange and correlation effects are more evident in wires of reduced dimensions.     

Dynamical exchange effects in a two-dimensional many-polaron gas

We calculate the influence of dynamical exchange effects on the response properties and the static properties of a two-dimensional many-polaron gas. These effects are not manifested in the random-phase approximation which is widely used in the analysis of the many-polaron system. Here they are taken into account by using a dielectric function derived in the time-dependent Hartree-Fock formalism. At weak electron-phonon coupling, we find that dynamical exchange effects lead to substantial corrections to the random-phase approximation results for the ground state energy, the effective mass, and the optical conductivity of the polaron system. Furthermore, we show that the reduction of the spectral weight of the optical absorption spectrum at frequencies above the longitudinal optical phonon frequency, due to many-body effects, is overestimated by the random-phase approximation.Received: 24 December 2003, Published online: 9 April 2004PACS: 71.45.Gm Exchange, correlation, dielectric and magnetic response functions, plasmons - 71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) - 71.38.Fp Large or Fröhlich polarons     

Magnetic ratchet effects in a two-dimensional electron gas

The effect of the magnetic field on the generation of an electric current in a two-dimensional electronic ratchet is theoretically studied. Mechanisms of the formation of magnetically induced photocurrent are proposed for a structure with a two-dimensional electron gas (quantum well, graphene, or topological insulator) with a lateral asymmetric superlattice consisting of metallic strips on the external surface of the structure. The ratchet with the spatially oscillating magnetic field generated by the ferromagnetic lattice, as well as the nonmagnetic ratchet placed in the uniform magnetic field both classically weak and strong quantizing, is considered. It is established that the ratio of the amplitude of the magnetic oscillations of photocurrent to the ratchet photocurrent in zero field can exceed two orders of magnitude.     

Optical coherent transient effects in a magnetized semiconductor quantum wire

Effects of an external magnetic field on free induction decay (FID) and the Stark effect in GaAs/GaAlAs quantum wires have been investigated analytically. Our results show that both FID and the Stark effect become enhanced due to the presence of a magnetic field. We have also seen that the magnetic field plays an important role in wider wires while in thinner wires, the geometric confinement dominates over the magnetic effects. The results are found to be in good qualitative agreement with that available in the literature.     

Primarily nonlinear effects observed in a driven asymmetrical vibrating wire

The purpose of the work reported here is to further experimentally explore the wide variety of behaviors exhibited by driven vibrating wires, primarily in the nonlinear regime. When the wire is driven near a resonant frequency, it is found that most such behaviors are significantly affected by the splitting of the resonant frequency and by the existence of a "characteristic" axis associated with each split frequency. It is shown that frequency splitting decreases with increasing wire tension and can be altered by twisting. Two methods are described for determining the orientation of characteristic axes. Evidence is provided, with a possible explanation, that each axis has the same orientation everywhere along the wire. Frequency response data exhibiting nonlinear generation of transverse motion perpendicular to the driving direction, hysteresis, linear generation of perpendicular motion (sometimes tubular), and generation of motion at harmonics of the driving frequency are exhibited and discussed. Also reported under seemingly unchanging conditions are abrupt large changes in the harmonic content of the motion that sometimes involve large subharmonics and harmonics thereof. Slow transitions from one stable state of vibration to another and quasiperiodic motions are also exhibited. Possible musical significance is discussed.     

Intersecting veins effects of a two-dimensional photonic crystal with a large two-dimensional complete bandgap

Optimal design of a two-dimensional photonic crystal with a square lattice of dielectric rods with intersecting veins in GaAs is investigated numerically using plane wave expansion method. It is shown how a maximum complete two-dimensional bandgap is obtained by optimally connecting the dielectric rods with intersecting veins. The complete two-dimensional photonic bandgap (PBG) of our optimal design reaches Δω = 0.10664(2πc/a) (where a is the lattice constant and c is the speed of light in vacuum) when the radius of dielectric rod is 280.1 nm and the half-vein width is 60 nm. Our result shows 40% the width of PBG higher than that obtained from Ref. [M. Qiu, S. He, J. Opt. Soc. Am. B 17 (2000) 1027] (Δω = 0.0762(2πc/a)). In addition, we found that the complete bandgap can be obtained in a large range of radius R of dielectric rod when the half width of intersecting veins d is larger than 65 nm.     

Renormalization and quantum effects in a two-dimensional planar model

We examine the influence of the charging energy on the vortex unbinding transition in two-dimensional arrays of Josephson junctions. The fluctuations of the phase about the time-dependent vortex solutions are treated within the self-consistent harmonic approximation. A new relation between the renormalized vortex unbinding temperature T_c and the charging energy U is derived. We predict a continuous drop of T_c at a critical value of U well below the spurious first order transition of the rigidity constant. The results are interpreted as a quantum assisted dissociation of vortex pairs.     

Competing effects of interactions and spin-orbit coupling in a quantum wire

We study the interplay of electron-electron interactions and Rashba spin-orbit coupling in one-dimensional ballistic wires. Using the renormalization group approach we construct the phase diagram in terms of Rashba coupling, Tomonaga-Luttinger stiffness and backward scattering strength. We identify the parameter regimes with a dynamically generated spin gap and show where the Luttinger liquid prevails. We also discuss the consequences for the operation of the Datta-Das transistor.     

GaAs抛物量子线中弱耦合极化子的磁场效应

应用变分法和改进的线性组合算符法,研究了磁场对抛物量子线中弱耦合极化子振动频率和相互作用能的影响.给出了GaAs抛物量子线中弱耦合极化子的振动频率和相互作用能与磁场和约束强度的依赖关系.对GaAs晶体作了数值计算,结果显示:极化子振动频率和相互作用能都随约束强度和外磁场的增加而增大.     

Typical cluster size for two-dimensional percolation processes

The typical cluster size for two-dimensional percolation models is discussed. It is shown that, forW ₀={xZ ²0x}, [–lim _n(1/n) logP _p (W ₀=n)]^–1p–p _c ^– aspp _c , provided thatE _p (W ₀²)/E _p (W ₀)p–P _c ^– aspp _c . Furthermore, we introduce a new quantityf _s (p), which may be thought of as the singular part of the free energy, and show thatf _s (p)¦p–p _c ¦^2v provided that the correlation length ¦p–p _c ¦^–v aspp _c .     

Hot-electron effects in two-dimensional hopping with a large localization length

We have studied nonlinear effects in the resistance of a two-dimensional system with a large localization length on both sides of the crossover from weak to strong localization. It is shown that nonlinearity in the hopping regime is due to electron overheating rather than the field effects. This qualitatively new behavior is a signature of a two-dimensional hopping transport with a large localization length.     

Nonequilibrium relaxations and aging effects in a two-dimensional Coulomb glass

The relaxations of conductivity have been studied in the glassy regime of a strongly disordered two-dimensional electron system in Si after a temporary change of carrier density during the waiting time tw. Two types of response have been observed: (a) monotonic, where relaxations exhibit aging, i.e., dependence on history, determined by tw and temperature; (b) nonmonotonic, where a memory of the sample history is lost. The conditions that separate the two regimes also have been determined.     

Screening effects in two-dimensional electron gas

The potential produced by a charged impurity at the interface of a highly doped GaAlAs and GaAs is calculated at a finite temperature. The electron gas formed at the interface is described as a two dimensional gas in which the impurity is assumed to be dipped. Temperature dependence of the impurity potential is calculated in the random phase approximation (R.P.A.) as well as in the modified temperature dependent Thomas-Fermi (M.T.T.F.) approximation which is defined to include temperature effects and to reduce to Thomas-Fermi result at zero temperature. The binding energy of the impurity for the ground state is calculated in R.P.A. and in M.T.T.F.. It is shown that at temperature T, much larger than the Fermi temperature, T_F, M.T.T.F. gives binding energies close to R.P.A. results.