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In this paper, novel features offered by Resonant Tunneling Diode (RTD) are reviewed by simulating it under different conditions. GaAs/AlGaAs based RTD is used as the reference one to obtain the characteristics due to parametric variations. To fulfil this purpose a simple model of resonant electronic transport through a double-barrier structure is developed. I-V characteristics are studied by varying barrier parameters and well width. Different peak and valley currents are measured under these conditions. For the same set of parameters both symmetric and asymmetric cases are considered. Different materials of lower effective mass are also taken into consideration to improve Peak to Valley Ratio (PVR). The Indium (In) based materials are considered to compare the characteristics obtained from the conventional GaAs based RTD structure. All these proposed structures are simulated using Silvaco Atlas software.

Transfer matrix calculations of the critical two-point correlation function in 2D Ising model on a finite-size lattice with periodic boundaries along 〈11〉 direction are extended to L = 21. A refined analysis of the correlation function in 〈10〉 crystallographic direction at the distance r = L indicates the existence of a nontrivial finite-size correction of a very small amplitude with correction-to-scaling exponent ω < 2 in agreement with our foregoing study for L ≤ 20. Here we provide an additional evidence and show that amplitude a of the multiplicative correction term 1 + aL^-ω is about -3.5·10^-8 if ω = 1/4 (the expected value). We calculate also the susceptibility for L ≤ 18 in order to compare our numerical estimates for the constant background contribution with the known very precise value and to look for possible nontrivial corrections to scaling. The numerical analysis reveals a perfect agreement for the background term, as well as shows that the nontrivial correction term, detected by our analysis in the correlation function, likely cancels in the susceptibility.

A new family of superlattice structures modulated by the pseudo-Gaussian potential is proposed. The correlation between the configuration of minibands and the superlattice geometry is revealed using the transfer matrix approach.

The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a three-color problem. In this paper, we explicitly build the transfer matrix for the three-color problem in order to calculate the number of possible configurations for finite systems with free, periodic in one direction and toroidal boundary conditions (periodic in both directions)

The transfer matrix method to describe finite size effects due to tunneling are worked out for Z(2)- and Z(3)-symmetric models. We used this method to extract the surface tension σ in the SU(3) gauge theory at the finite temperature phase transition on lattices with an extent T=2 in the euclidean time direction. We also discuss if the confined phase completely wets the deconfined phase at this first order phase transition.

We use transfer-matrix methods to calculate free energies and specific heats on long, finite-width strips of Ising spins with randomly distributed ferromagnetic couplings. By implementation of our code on a highly parallel computer, we have managed to generate high-quality data for strip widths up to L = 18 sites. An unequivocal trend towards a divergency of the specific heat in the thermodynamic limit can be discerned. Finite-size data appear to behave halfway between a single- (ln L) and double- (lnln L) logarithmic dependence on strip width. This is in line with a crossover within the Dotsenko-Shalaev picture of logarithmic corrections to pure-system singularities.

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension x_σ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

We study the entanglement entropy (EE) for pure gauge theories in 1+1 dimensions with the lattice regularization. Using the definition of the EE for lattice gauge theories proposed in a previous paper,¹ we calculate the EE for arbitrary pure as well as mixed states in terms of eigenstates of the transfer matrix in (1+1)-dimensional lattice gauge theory. We find that the EE of an arbitrary pure state does not depend on the lattice spacing, thus giving the EE in the continuum limit, and show that the EE for an arbitrary pure state is independent of the real (Minkowski) time evolution. We also explicitly demonstrate the dependence of EE on the gauge fixing at the boundaries between two subspaces, which was pointed out for general cases in the paper. In addition, we calculate the EE at zero as well as finite temperature by the replica method, and show that our result in the continuum limit corresponds to the result obtained before in the continuum theory, with a specific value of the counterterm, which is otherwise arbitrary in the continuum calculation. We confirm the gauge dependence of the EE also for the replica method.

A transfer matrix formalism is employed to study the occurrence of the localized modes associated with an impurity cell embedded within a semi-infinite Heisenberg ferromagnetic superlattice with nearest-neighbor exchange interactions. The cell is at arbitrary distance from the deformed surface cell. We find that, in addition to bulk spin waves, there may arise localized modes associated both with the impurity cell and with the surface. Two situations were analyzed numerically: impurity is close to the surface and the impurity is practically in the bulk region. The modes influence each other when the impurity cell is near the surface, modifying spin wave energies.

We study the two-dimensional Ising model with competing nearest-neighbour and diagonal interactions and investigate the phase diagram of this model. We show that the ground state at low temperatures is ordered either as stripes or as the Néel antiferromagnet. However, we also demonstrate that the energy of defects and dislocations in the lattice is close to the ground state of the system. Therefore, many locally stable (or metastable) states associated with local energy minima separated by energy barriers may appear forming a glass-like state.

We discuss the results in connection with two physically different systems. First, we deal with planar clusters of loops including a Josephson π-junction (a π-rings). Each π-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments in the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. Second, we apply the model to the analysis of the structure of the newly discovered two-dimensional form of carbon, graphene. Carbon atoms in graphene form a planar honeycomb lattice. Actually, the graphene plane is not ideal but corrugated. The displacement of carbon atoms up and down from the plane can be also described in terms of Ising spins, the interaction of which determines the complicated shape of the corrugated graphene plane.

The obtained results may be verified in experiments and are also applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constant.

The water wave transmission properties and the frequency spectra of one-dimensional combination bottom of water and mercury with different filling fractions are studied by the transfer matrix method. For the periodic bottoms (PBs), the effect of the steps' numbers and the width on the band gaps are discussed. Each of whole band gaps is the juxtaposition of the gaps of three kinds of PBs, without covering. The numerical results show that the band gaps could be enlarged effectively by choosing the steps' width properly.

Quantum and classical components are blended together in this proposed theoretical model for describing multiple quantum well solar cells (MQWSC) in a p-i-n architecture. The model characteristics are: the use of transfer matrix as a quantum method for finding allowed energies in the coupled quantum wells, the connection of the absorption coefficient in the confined 2D structure to the one in the bulk semiconductor, and the treatment of the whole cell as a pseudo-homogeneous media to determine its reflectance. The resulted model is intended to be a working tool to assess electro-optical properties of MQWSC. Numerical results which relate the performance of the MQWSC to its structure are reported.

A detail study on the in-degree distribution (ID) of cellular automata is obtained by exact enumeration. The results indicate large deviation from multi-scaling and classification according to various IDs are discussed. We further augment the transfer matrix such that the distributions for more complicated rules are obtained. Dependence of ID on the lattice size have also been found for some rules including R50 and R77.

For the propagation of harmonic longitudinal stress wave in phononic crystal rod (PCR), transfer matrix of elastic wave in PCR was derived based on the wave equation and band structure of infinite PCR was calculated. For semi-infinite PCR, theoretical derivation of dynamic stress solutions of arbitrary section and internal interfaces was conducted with Bloch theorem. Inherent relationship between dynamic stress and surface wave modal frequency (SWMF) was analyzed. Afterwards, numerical computation mainly focusing on dynamic stress level of the internal interfaces of PCR was given in detail. Finally, numerical analysis for finite PCR was carried out and verified by finite element simulation. Our results show that SWMF has a significant influence on the dynamic stress, and exactly it is the formal pole of stress solution whose nature is directly determined by the sort order of the two materials constituting the PCR.

Based on the concept of generalized phononic crystals (GPCs), a type of 1D cylindrical shell of generalized phononic crystals (CS-GPCs) where two kinds of homogeneous materials are arranged periodically along radial direction was proposed in this paper. On the basis of radial, torsional shear and axial shear vibrational equations of cylindrical shell, the total transfer matrix of mechanical state vector were set up respectively, and the bandgap phenomena of these three type waves were disclosed by using the method of transfer matrix eigenvalue of mechanical state vector instead of the previous localized factor analyses and Bloch theorem. The characteristics and forming mechanism of these bandgaps of CS-GPCs, together with the influences of several important structure and material parameters on them were investigated and discussed in detail. Our results showed that, similar to the plane wave bandgaps, 1D CS-GPCs can also possess radial, torsional shear and axial shear wave bandgaps within high frequency region that conforms to the Bragg scattering effect; moreover, the radial vibration of CS-GPCs can generate low frequency bandgap (the start frequency near 0 Hz), as a result of the double effects of wavefront expansion and Bragg scattering effect, wherein the wavefront effect can be the main factor and directly determine the existence of the low frequency bandgaps, while the Bragg scattering effect has obvious enhancement effect to the attenuation. Additionally, the geometrical and material parameters of units have significant influences on the wave bandgaps of CS-GPCs.

Spin transport properties of a double-triangular quantum network with local magnetic moment on backbones and magnetic flux penetrating the network plane are studied. Numerical simulation results show that such a quantum network will be a good candidate for spin filter and spin switch. Local dispersion and density of states are considered in the framework of tight-binding approximation. Transmission coefficients are calculated by the method of transfer matrix. Spin transmission is regulated by substrate magnetic moment and magnetic flux piercing those triangles. Experimental realization of such theoretical research will be conducive to designing of new spintronic devices.

One-dimensional defective binary photonic crystal is considered with the structure (AB)${}^N$D(AB)${}^N$, where A (TiO${}_2)$ and B (SiO${}_2)$ are the layers constituting the photonic crystal and D is the defect layer. The temperature dependence of the defect mode is investigated by considering both thermo-optic and thermal expansion effects. As the refractive indices and thicknesses of the photonic crystal layers are varied by temperature, the properties of the photonic crystal, such as bandgap and defect mode, are modified. Thus, we propose a tunable transmission filter operating in the visible region of the spectrum. It is found that the transmittance peak shift of the defect mode can be enhanced with the increase of both thermo-optic and the thermal expansion coefficients of the defect mode. As an example, we consider a photonic crystal with the structure (TiO₂–SiO${}_2{)}^6$/SiOC/(TiO₂–SiO${}_2{)}^6$ and a transmittance peak shift of the defect mode of 1.51 nm is obtained for a temperature increase of $100^{\circ }$C.

Numerical calculations by a transfer matrix method have been performed to obtain the transmission coefficient of rectangular double barrier structures. The dependence of the well width, barrier width and the barrier height was systematically investigated. When the width ratio of the two barriers was varied on condition that a total width was fixed, the transmission coefficient at a resonance is varied while that at a valley region is not. It is concluded that the resonant tunneling is characterized by two parameters: total width and the width ratio. Our results clarify the transition of transmission spectrum from a single barrier to a double barrier structure.

Double barrier structures with a gradient have been studied by numerical calculations of transmission coefficient following a transfer matrix method. As the slope of the barriers becomes steep, the resonant energy is lowered. On the other hand, the full width at half maximum does not depend on the gradient.

Based on the tight-binding model of the single electron, the one-dimensional Anderson model with random binary distributed on-site energies is studied using the transfer-matrix approach. We calculate numerically the localization length, the density of the electronic states and the Lyapunov exponent. The results show that the localization length strongly depends on energies and is affected by disordered degrees to some extent. With finite size systems, the localization length presents obvious effect on the impurity concentration. While in the dilute limit there exist extended states, increasing the impurity concentration beyond a critical value destroys these extended states and the localization length over the entire energy range becomes smaller than the system size. By studying the scaling relation, we find that the localized states are stable in the thermodynamic limit. Transforming the random matrix product into a conformal map, we introduce the Lyapunov exponent, which is finite within the entire band in our model. Starting from the Lyapunov exponent, the localization length and the density of states may also be obtained.