Gauge symmetry as symmetry of matrix coordinates

We propose a new point of view on gauge theories, based on taking the action of symmetry transformations directly on the space coordinates. Via this approach the gauge fields are not introduced at the first step, and they can be interpreted as fluctuations around some classical solutions of the model. The new point of view is connected to the lattice formulation of gauge theories, and the parameter of the non-commutativity of the coordinates appears as the lattice spacing parameter. Through the statements concerning the continuum limit of lattice gauge theories, the suggestion arises that the non-commutative spaces are the natural ones to formulate gauge theories at strong coupling. Via this point of view, a close relation between the large-N limit of gauge theories and string theory can be made manifest. Received: 16 June 2000 / Published online: 8 September 2000     

Linearized tensor renormalization group algorithm for the calculation of thermodynamic properties of quantum lattice models

A linearized tensor renormalization group algorithm is developed to calculate the thermodynamic properties of low-dimensional quantum lattice models. This new approach employs the infinite time-evolving block decimation technique, and allows for treating directly the transfer-matrix tensor network that makes it more scalable. To illustrate the performance, the thermodynamic quantities of the quantum XY spin chain as well as the Heisenberg antiferromagnet on a honeycomb lattice are calculated by the linearized tensor renormalization group method, showing the pronounced precision and high efficiency.     

Zur Berechnung der Matrixelemente des Dichteoperators für die überlagerung Zweier Elektromagnetischer Felder

A method for calculation matrix-elements of the density operator for the superposition of two electromagnetic fields from the matrix-elements of the two components is developed. In the special case of superposition of a stationary coherent field and a stationary chaotic field results are compared with Peina's results.     

Some comments refering to the definition of the position-operator case of the Born-von Kármán boundary condition

A new position operator is defined obeying the Born-von Kármán boundary conditions. It is hermitian and satisfies the common operator calculus. Its matrix-elements with respect to Bloch functions are derived and expressed by a generalized function.     

Interplay between spin frustration and thermal entanglement in the exactly solved Ising–Heisenberg tetrahedral chain

The spin-1/2 Ising–Heisenberg tetrahedral chain is exactly solved using its local gauge symmetry (the total spin of the Heisenberg bonds is locally conserved) and the transfer-matrix approach. Exact results derived for spin–spin correlation functions are employed to obtain the frustration temperature. In addition, we have exactly calculated a concurrence quantifying thermal entanglement. It is shown that the frustration and threshold temperature coincide at sufficiently low temperatures, while they exhibit a very different behavior in the high-temperature region when tending towards completely different asymptotic limits. The threshold temperature additionally shows a notable reentrant behavior when it extends over a narrow temperature region above the classical ground state without any quantum correlations.     

Markov and stability properties of equilibrium states for nearest-neighbor interactions

Consider models on the lattice ^d with finite spin space per lattice point and nearest-neighbor interaction. Under the condition that the transfer matrix is invertible we use a transfer-matrix formalism to show that each Gibbs state is determined by its restriction to any pair of adjacent (hyper)planes. Thus we prove that (also in multiphase regions) translationally invariant states have a global Markov property. The transfer-matrix formalism permits us to view the correlation functions of a classicald-dimensional system as obtained by a linear functional on a noncommutative (quantum) system in (d – 1)-dimensions. More precisely, for reflection positive classical states and an invertible transfer matrix the linear functional is a state. For such states there is a decomposition theory available implying statements on the ergodic decompositions of the classical state ind dimensions. In this way we show stability properties of _ev ^d -ergodic states and the absence of certain types of breaking of translational invariance.     

Partial diagonality of stress trace

The trace of the stress energy tensor is shown to be diagonal between two states whose total four-momenta are equal. Additional comments are made on certain matrix-elements of the time-derivative of the dilation charge.     

Statistics of adsorption on top and bridge sites of a square lattice: Transfer-matrix approach

Statistics of particles adsorbed on the lattice with a complex elementary cell are analyzed by employing the transfer-matrix technique. The results obtained are compared with those given by the cluster approximation and also with the experimental data for the CO/Ni(100) system. The transfer-matrix technique is shown to be very effective for studies of two-dimensional systems with complex lattices.     

Comparative study of optical analysis methods for thin films

Three popular optical analysis methods (the transfer-matrix method, the Tinkham formula, and Beer's law) have been used for analyzing the optical spectra of thin films. While the transfer-matrix method is an accurate method, the Tinkham formula and Beer's law are approximate methods. Here we investigated the three methods using measured transmittance spectra of insulating transition-metal dichalcogenide (TMD) thin films on a quartz substrate. Three different semiconducting 2H-TMD systems (MoS₂, MoSe₂, and MoTe₂) were measured and analyzed. The optical conductivities obtained from the measured transmittance spectra using the transfer-matrix method and Tinkham formula and the absorption coefficients obtained using the transfer-matrix method and Beer's law were compared. The comparisons show some discrepancies. The reasons for the discrepancies between the results obtained via the two different methods were examined and the application limitations of the Tinkham formula and Beer's law were discussed.     

空间载频干涉法全场测量长度技术

 在研究二维快速傅里叶变换法进行干涉测试基本原理的基础上,提出一种基于二维快速傅里叶变换的长度测量法.以量块长度的测量为对象,被测量块置于泰曼-格林干涉仪测试光路中,参考光波分别与待测长度的量块表面和辅助平面反射的测试光波形成干涉条纹,条纹由图像采集系统采集.利用编制的算法处理软件,通过处理干涉条纹图中量块边缘识别、区域延拓、滤波、波面统一,获得了量块全场表面的空间长度分布,实现了对量块长度的自动化测量.结果表明：该测量法不仅具有较高的测量准确度,而且具有全场测试和非接触测量等优点.     

应用移相干涉术测量量块长度和长度变动量

研究了应用移相干涉术测量新的一等量块的方法。对于干涉图像进行多幅图的采样，由移相法计算量块测量面和与其研全的辅助平晶表面的波面面形，着重研究了在量块干涉图中有阶跃不连续的波面复原运算的原理与技术，得到一幅表征它们表面的离散滤差值，并给出量块工作面长度和长度变动量的测量结果。     

Leading Branches of the Transfer-Matrix Spectrum for Lattice Spin Systems (Quasi-Particles of Different Species)

For lattice systems under high temperatures T with compact or finite spin we construct three invariant subspaces of the transfer-matrix, which can be interpreted as the spaces of states for quasi-particles of two different species and the space of states for two particles of the first species. We formulate a condition on a priori distribution guaranteeing that the spectrum of the transfer-matrix on these subspaces are not overlapping.     

Fixed point action for the massless lattice Schwinger model

We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gausian measure. The resulting action has 123 independent couplings, is bilinear in the Grassmann fields, gauge invariant by the compact gauge transporters considered, and localized within a 7 × 7 lattice centered around one of the fermions. We then simulate the model at various values of β and compare with results obtained with the Wilson fermion action. We find excellent improvement for the observables studied (propagators and masses).     

Geometric phasea la Pancharatnam

In mid-1950s, Pancharatnam [1] encountered the geometric phase associated with the evolution along a geodesic triangle on the Poincaré sphere. We generalize his 3-vertex phase and employ it as the fundamental building block, to geometrically construct a general ray-space expression for geometric phase. In terms of a reference ray used to specify geometric phase, we delineate clear geometric meanings for gauge transformations and gauge freedom, which are generally regarded as mere mathematical abstractions.     

Gauge bosons at zero and finite temperature

Gauge theories of the Yang–Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang–Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.     

Modelling of strong coupling regime in bulk GaN microcavities using transfer matrix and quasiparticle formalisms

The evolution of the polaritonic Rabi splitting versus the excitonic broadenings is analyzed within two different formalisms: the transfer-matrix and the quasiparticle models. The splittings are deduced from angle-resolved reflectivity measurements performed at 5 K and 300 K on two GaN microcavities grown on silicon. Although the quasiparticle model allows a qualitative analysis when the quality factor of the cavity is high, the transfer-matrix formalism is more appropriate for the interpretation of the reflectivity spectra, whatever the configuration of the structure.     

金属/C2H2/金属结构中的电子输运

在紧束缚近似下,利用转移矩阵法对“金属/C2H2/金属”结构的分子导线的电子输运性质进行了研究。通过转移矩阵法求出转移矩阵和散射矩阵,从而解析地得到体系的透射系数和态密度的变化,并详细分析了透射系数对C2H2与金属的耦合强度及两个(CH)间的耦合强度的依赖关系。我们的结果显示这种结构的分子导线有着较好的开关特性。     

Gauge identities and the Dirac conjecture

The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonian or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first class constraints. In the latter approach such local symmetries are reflected in the existence of so called gauge identities. The connection between the two becomes apparent, if one works with a first order Lagrangean formulation. Our analysis applies to purely first class systems. We show that Dirac's conjecture applies to first class constraints which are generated in a particular iterative way, regardless of the possible existence of bifurcations or multiple zeroes of these constraints. We illustrate these statements in terms of several examples.     

Fractional Fringe Order Method Using Fourier Analysis for Absolute Measurement of Block Gauge Thickness

A fringe analysis method, which combines the Fourier transform with the fractional fringe order method for measuring the absolute thickness of a block gauge, is presented. An approximate integer part of the fringe order is estimated by mechanical measurements, and the fractional part is determined by Fourier analysis of the interferometric fringe patterns. The fringe patterns are obtained with a Michelson interferometer by illumination of several selected wavelengths, respectively. The use of the fractional fringe order method can determine accurately more than 2ϖ phase jumps. The measured thickness of a block gauge is 5999115.0 ± 0.7 nm, which is comparable with the standard thickness of 6 mm. The influence of wavelength and approximate integer part of fringe order on the measurement accuracy is discussed.     

Magnetotransport in a graphene monolayer with two tunable magnetic barriers

The magnetotransport property for a monolayer graphene with two turnable magnetic barriers has been investigated by the transfer-matrix method. We show that the parameters of barrier height, width, and interval between two barriers affect the electron wave decaying length, which determine the conductance with parallel or antiparallel magnetization configuration, and consequently the tunneling magnetoresistance (TMR) for the system. Interestingly, a graphene attached by two barriers with different heights can produce a resonant TMR peak at low energy region one order of magnitude larger than that for the system with two same height barriers because that the asymmetry of magnetic barriers block the electron transmission in the case of antiparallel magnetization configuration. The results obtained here may be useful in understanding of electron tunneling in graphene and in designing of graphene-based nanodevices.