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We present an algorithm to compute the exact critical probability h (n) for an n × ∞ helical square lattice with random and independent site occupancy. The algorithm has time complexity O (n 2 c n) and space complexity O (c n) with c = 2.7459... and allows us to compute h (n) up to n = 24. Since the extrapolation result of h (n) is inconsistent with the current best estimation of pc, we also compute and extend the exact critical probability p c (n) for an n × ∞ cylindrical square lattice to n = 24. Our calculation shows that the current best result of p c = 0.592 746 050 792 10 (2) by Jacobsen (2015 J. Phys. A: Math. Theor. 48 454003) is incorrect and the corrected value should be 0.592 746 050 7896 (1) . [ABSTRACT FROM AUTHOR]

In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in finite one-dimensional anisotropic periodic stratified media with an arbitrary number of cells. By invoking the Cayley–Hamilton theorem on the transfer matrix for the electromagnetic field in a periodic stratified media formed by N cells, we obtain a fourth-order recursive relation for the matrix coefficients that defines the so-called Tetranacci polynomials (TPs). In the symmetric case, corresponding to a unit-cell transfer matrix with a characteristic polynomial where the coefficients of the linear and cubic terms are equal, closed expressions for the solutions to the recursive relation, known as symmetric TPs, have recently been derived, allowing us to write the transfer matrix and transmittance in a closed form. We show as sufficient conditions that the 4 × 4 differential propagation matrix of each layer in the binary unit cell, Δ , a) has eigenvalues of the form ± p 1 , ± p 2 , with p 1 ≠ p 2 , and b) its off-diagonal 2 × 2 block matrices possess the same symmetric structure in both layers. Otherwise, the recursive relations are still solvable for any 4 × 4 matrix and provide an algorithm to compute the N th power of the transfer matrix without carrying out explicitly the matrix multiplication of N matrices. We obtain analytical expressions for the dispersion relation and transmittance, in closed form, for two finite periodic systems: the first one consists of two birefringent uniaxial media with their optical axis perpendicular to the z -axis, and the second consists of two isotropic media subject to an external magnetic field oriented along the z -axis and exhibiting the Faraday effect. Our formalism applies also to lossy media, magnetic anisotropy or optical activity. [ABSTRACT FROM AUTHOR]

The high longitudinal electric fields generated in plasma wakefields are very attractive for a new generation of high gradient plasma based accelerators. On the other hand, the strong transverse fields increase the demand for a proper matching device in order to avoid the spoiling of beam transverse quality. A solution can be provided by the use of a plasma ramp, a region at the plasma injection/extraction with smoothly increasing/decreasing plasma density. The transport of a beam inside a plasma ramp, beside its parameters, depends on the profile of the ramp itself. Establishing the transfer matrix for a plasma ramp represent a very useful tool in order to evaluate the beam evolution in the plasma. In this paper a study of a cosine squared ramp is presented. An approximate solution of the transverse equation of motion is evaluated and exploited to provide a simple transfer matrix for the plasma ramp. The transfer matrix is then employed to demonstrate that this kind of ramp has the effect to minimize the emittance growth due to betatron dephasing. The behavior of a squared cosine plasma ramp will be compared with an experimentally measured plasma ramp profile in order to validate the applicability of the transfer matrix to real cases. [ABSTRACT FROM AUTHOR]

We want to understand how relaxation process from an initial non-generic state proceeds towards a long-time typical state reached under unitary quantum evolution. One would expect that after some initial correlation time relaxation will be a simple exponential decay with constant decay rate. We show that this is not necessarily the case. Studying various Floquet systems with fixed two-qubit gates, and focusing on purity and out-of-time-ordered correlation functions, we find that in many situations relaxation proceeds in two phases of exponential decay having different relaxation rates. Namely, in the thermodynamic limit the relaxation rate exhibits a change at a critical time proportional to system's size. The initial thermodynamically relevant rate can be slower or faster than the asymptotic one, demonstrating that the recently discovered phantom relaxation, in which the decay is slower than predicted by a nonzero transfer matrix gap, is not limited to only random circuits. [ABSTRACT FROM AUTHOR]

Adsorption of a single AB random copolymer (RC) chain onto homogeneous and inhomogeneous ab surfaces with a regular periodic pattern is studied theoretically. For the averaging over disorder in the RC sequence, the constrained annealed approximation, known as the Morita approximation is employed. A general scheme for constructing the Morita approximation of an arbitrary order m is proposed; it is based on representation of the RC monomer sequence as a Markov chain of overlapping (m –1)-ads. The problem is solved within the framework of the generating functions approach for the two-dimensional partially directed walk model of the polymer on a square lattice. Temperature dependences of various adsorption characteristics are obtained. The accuracy of the Morita approximation is assessed by comparison with the numerical results for RC with quenched sequences obtained by the transfer matrix approach. It is shown that for RC adsorption on a homogeneous surface for AB -copolymers with adsorbing A and neutral B blocks, it is sufficient to use the Morita approximation of second or third order. If the non-adsorbing B block is repelled from the surface, then a higher order of the approximation (5th–6th) is required. An important indicator of validity of the Morita approximation is the entropy: if the order of the approximation is not high enough, the entropy becomes negative in the low-temperature regime which means that the Morita approximation is wrong in this order. In the case when the surface is periodically inhomogeneous, the Morita approximation works worse and very high orders are required, which can be beyond the computational capabilities. Moreover, the Morita approximations become degenerate: approximations of two or more consecutive orders give the same result. [ABSTRACT FROM AUTHOR]

The adsorption and diffusion of hydrogen atoms on Cu(001) are studied using first-principles calculations. By taking into account the contribution of zero-point energy (ZPE), the originally identical barriers are shown to be different for H and D, which are respectively calculated to be ∼158 meV and ∼139 meV in height. Using the transfer matrix method (TMM), we are able to calculate the accurate probability of transmission across the barriers. The crucial role of quantum tunneling is clearly demonstrated at low-temperature region. By introducing a temperature-dependent attempting frequency prefactor, the rate constants and diffusion coefficients are calculated. The results are in agreement with the experimental measurements at temperatures from ∼50 K to 80 K. [ABSTRACT FROM AUTHOR]

We propose magnetized gyromagnetic photonic crystals (MGPCs) composed of indium antimonide (InSb) and yttrium iron garnet ferrite (YIGF) layers, which possess the properties of nonreciprocal wide-angle bidirectional absorption. Periodical defects in the MGPCs work as filters. Absorption bands (ABs) for the positive and negative propagations arise from the optical Tamm state and resonance in cavities respectively, and they prove to share no overlaps in the studied frequency range. Given ω = 2.0138 THz, for the positive propagation, the ABs in the high-frequency range are localized in the interval between 0.66 ω and 0.88 ω. In the angular range, the ABs for the TE and TM waves reach 60° and 51°, separately. For the negative propagation, the ABs in the low-frequency range are localized in the interval between 0.13 ω and 0.3 ω. The ABs extend to 60° for the TE waves and 80.4° for the TM waves. There also exists a narrow frequency band in a lower frequency range. The relevant factors, which include the external temperature, the magnetic fields applied to the YIGF, the refractive index of the impedance matching layer, and the defect thickness, are adjusted to investigate the effects on the ABs. All the numerical simulations are based on the transfer matrix method. This work provides an approach to designs of isolators and so on. [ABSTRACT FROM AUTHOR]

Yang–Baxter integrable vertex models with a generic Z 2 -staggering can be expressed in terms of composite R -matrices given in terms of the elementary R -matrices. Similarly, integrable open boundary conditions can be constructed through generalized reflection algebras based on these objects and their representations in terms of composite boundary matrices K ± . We show that only two types of staggering yield a local Hamiltonian with integrable open boundary conditions in this approach. The staggering in the underlying model allows for a second hierarchy of commuting integrals of motion (in addition to the one including the Hamiltonian obtained from the usual transfer matrix), starting with the so-called quasi momentum operator. In this paper, we show that this quasi momentum operator can be obtained together with the Hamiltonian for both periodic and open models in a unified way from enlarged Yang–Baxter or reflection algebras in the composite picture. For the special case of the staggered six-vertex model, this allows constructing an integrable spectral flow between the two local cases. [ABSTRACT FROM AUTHOR]

Acoustic liners are the most commonly used dissipative muffler for aero-engines but remain a challenge to design a broadband acoustic liner under the grazing flow. In this work, a novel neck-embedded meta-liner is proposed for the broadband sound-absorbing under the grazing flow with a wide speed range. The meta-liner is composed of many neck-embedded Helmholtz Resonators, and the idea of bending the subsequent cavity is introduced to improve low-frequency sound absorption performance. The acoustic impedance model of the meta-liner with neck-embedded slit is first detailly established by analyzing the acoustic characteristics of the equivalent elliptical pipe and using the matrix transfer method. Then by designing the local coupling between channels, efficient broadband impedance modulation and broadband matching with air impedance under grazing flow conditions are realized. The proposed meta-liner exhibits the excellent sound attenuation capacity in the frequency domain of 500–3000 Hz under the grazing flow speeds from 0 m s−1 to 98 m s−1 and the sound absorption performance is greatly boosted compared with the traditional Double- Degree-Of-Freedom liner. Features mentioned above have been verified numerically and in a series of comparative experiments. Besides, the thickness of the meta-liner is only 50 mm. Our work provides a possible design reference for the new generation of acoustic liners and has potential applications in noise reduction engineering. [ABSTRACT FROM AUTHOR]

Evanescent waves are waves that decay or grow exponentially in regions of the space void of interaction. In potential scattering defined by the Schrödinger equation, (âˆ' ∇ 2 + v) ψ = k 2 ψ for a local potential v, they arise in dimensions greater than one and are generally present regardless of the details of v. The approximation in which one ignores the contributions of the evanescent waves to the scattering process corresponds to replacing v with a certain energy-dependent nonlocal potential V k ˆ . We present a dynamical formulation of the stationary scattering for V ˆ k in two dimensions, where the scattering data are related to the dynamics of a quantum system having a non-self-adjoint, unbounded, and nonstationary Hamiltonian operator. The evolution operator for this system determines a two-dimensional analog of the transfer matrix of stationary scattering in one dimension which contains the information about the scattering properties of the potential. Under rather general conditions on v, we establish the strong convergence of the Dyson series expansion of the evolution operator and prove the existence of the transfer matrix for V ˆ k as a densely-defined operator acting in C 2 ⊗ L 2 (âˆ' k , k). [ABSTRACT FROM AUTHOR]

In this paper, the bistable phenomenon with the coherent perfect absorption properties are studied through the nonlinear transfer matrix method in one-dimensional nonlinear photonic crystals doped with a defect. The focus is on the influences of the relative phase of coherent light on the bistable coherent absorption intensity, and the tuning of the bistable threshold by parameters such as angle and wavelength of incidence. The simulated results show that the coherent absorption intensity is very sensitive to the relative phase of coherent incidence. As the phase decreases, the absorption intensity also decreases, varying from 1 to âˆ'1 when the phase change is within 180°. The tuning of the relative phase to the absorption intensity provides great convenience for the application of bistable, and parameters such as the incident angle can also achieve sensitive tuning of the bistable threshold. The larger the incident angle, the larger the threshold, and the more obvious the bistable phenomenon at TE mode. The application of nonlinear optical devices has been expanded in the fields of filters, optical switches, optical power threshold devices, etc. [ABSTRACT FROM AUTHOR]

We present an algorithm to compute the exact probability R n (p) for a site percolation cluster to span an n × n square lattice at occupancy p. The algorithm has time and space complexity O (λ n ) with λ ≈ 2.6. It allows us to compute R n (p) up to n = 24. We use the data to compute estimates for the percolation threshold p c that are several orders of magnitude more precise than estimates based on Monte-Carlo simulations. [ABSTRACT FROM AUTHOR]

The dual-channel nearly perfect absorption is realized by the coupled modes of topological interface states (TIS) in the near-infrared range. An all-dielectric layered heterostructure composed of photonic crystals (PhC)/graphene/PhC/graphene/PhC on GaAs substrate is proposed to excite the TIS at the interface of adjacent PhC with opposite topological properties. Based on finite element method (FEM) and transfer matrix method (TMM), the dual-channel absorption can be modulated by the periodic number of middle PhC, Fermi level of graphene, and angle of incident light (TE and TM polarizations). Especially, by fine-tuning the Fermi level of graphene around 0.4 eV, the absorption of both channels can be switched rapidly and synchronously. This design is hopefully integrated into silicon-based chips to control light. [ABSTRACT FROM AUTHOR]

In two dimensions, the standard treatment of the scattering problem for a delta-function potential, v (r) = z δ (r) , leads to a logarithmic singularity which is subsequently removed by a renormalization of the coupling constant z. Recently, we have developed a dynamical formulation of stationary scattering (DFSS) which offers a singularity-free treatment of this potential. We elucidate the basic mechanism responsible for the implicit regularization property of DFSS that makes it avoid the logarithmic singularity one encounters in the standard approach to this problem. We provide an alternative interpretation of this singularity showing that it arises, because the standard treatment of the problem takes into account contributions to the scattered wave whose momentum is parallel to the detectors’ screen. The renormalization schemes used for removing this singularity has the effect of subtracting these unphysical contributions, while DFSS has a built-in mechanics that achieves this goal. [ABSTRACT FROM AUTHOR]

Mathematical analysis on the existence of eigenvalues is essential because it is deeply related to localization, which is an exceptionally crucial property of quantum walks (QWs). We construct the method for the eigenvalue problem via the transfer matrix for space-inhomogeneous three-state QWs in one dimension with a self-loop, which is an extension of the technique in a previous study (Kiumi and Saito 2021 Quantum Inf. Process. 20 171). This method reveals the necessary and sufficient condition for the eigenvalue problem of a two-phase three-state QW with one defect whose time evolution varies in the negative part, positive part, and at the origin. [ABSTRACT FROM AUTHOR]

In the context of tensor network states, we for the first time reformulate the corner transfer matrix renormalization group (CTMRG) method into a variational bilevel optimization algorithm. The solution of the optimization problem corresponds to the fixed-point environment pursued in the conventional CTMRG method, from which the partition function of a classical statistical model, represented by an infinite tensor network, can be efficiently evaluated. The validity of this variational idea is demonstrated by the high-precision calculation of the residual entropy of the dimer model, and is further verified by investigating several typical phase transitions in classical spin models, where the obtained critical points and critical exponents all agree with the best known results in literature. Its extension to three-dimensional tensor networks or quantum lattice models is straightforward, as also discussed briefly. [ABSTRACT FROM AUTHOR]

Leveraging the traditional transfer matrix and stationary phase methods, the nonreciprocal Goosâ€"Hänchen (GH) phenomena for the electromagnetic (EM) waves reflected at the surface of the one-dimensional photonic crystals with ferrite layers and dielectric layers are investigated numerically. The GH effect (the peak of the lateral shift value up to over 200 times the wavelength) produced by the forward and backward incidence of EM waves under the transverse electric wave is identified to arise at significantly different frequency positions in the terahertz (THz) regime, whereas the transverse magnetic wave produces almost no GH effect under the same condition. Based on such a nonreciprocal phenomenon, the effect of the incident angle on the nonreciprocal properties is covered initially, for every 20° increase in the angle of the incident TE wave, the frequency span at which the two GH shift peaks emerge will decrease by 0.1 THz. In addition, the thicknesses of dielectric layers are modified separately, and distinct sensitivities of them to the nonreciprocal phenomenon are displayed. Lastly, through the regulation of the external magnetic fields of ferrite layers, the nonreciprocal effect can be selectively presented in multiple forms, which provides a novel pathway to design nonreciprocal sensors. [ABSTRACT FROM AUTHOR]

Modern cosmic microwave background (CMB) analysis pipelines regularly employ complex time-domain filters, beam models, masking, and other techniques during the production of sky maps and their corresponding angular power spectra. However, these processes can generate couplings between multipoles from the same spectrum and from different spectra, in addition to the typical power attenuation. Within the context of pseudo- C â„" based, MASTER-style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function, F â„" , that can fail to capture mode mixing and is dependent on the spectrum of the signal. To address these shortcomings, we have developed a simulation-based spectral correction approach that constructs a two-dimensional transfer matrix, J â„" â„" ′ , which contains information about mode mixing in addition to mode attenuation. We demonstrate the application of this approach on data from the first flight of the Spider balloon-borne CMB experiment. [ABSTRACT FROM AUTHOR]

The present study demonstrates the tuning of optical characteristics of porous silicon (PSi)-based microcavities by N ion beam interactions. These optical microcavities are prepared by using electrochemical etching of heavily doped p+-type Si. The PSi microcavities were exposed to N ions of 200 keV and 1 MeV at an optimized ion fluence of 1 Ă— 1015 ions cmâˆ'2. A significant red-shifting of 32 ∼ 60 nm in the resonance cavity mode was observed due to ion interaction. The experimental results are in good agreement with the transfer matrix simulations. A substantial modification of the PSi microcavity surface states is visualized through Raman and x-ray photoelectron spectroscopy (XPS) techniques. The Raman spectral results show modifications from crystalline Si to nanostructured Si and subsequently to amorphous Si. The XPS indicates the modification of Siâ€"Si and Siâ€"O bonds and the formation of new Siâ€"N bonds, implying the presence of Si3N4. These experimental observations, along with analytical simulations and transfer-matrix method microcavity modeling, conclusively support the realization of cavity tunability and substantial modification in the optical field intensity and photon confinement within the spacer layer of the microcavity. These results suggest that ion beams are the effective tool to produce wider tunable optical properties in microcavities with highly stable designer optical structures suitable for photonic applications. [ABSTRACT FROM AUTHOR]

The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schrödinger equation. The fact that the potential term entering the latter is energy-dependent obstructs the application of the results on low-energy quantum scattering in the study of the low-frequency waves satisfying the Helmholtz equation. We use a recently developed dynamical formulation of stationary scattering to offer a comprehensive treatment of the low-frequency scattering of these waves for a general finite-range scatterer. In particular, we give explicit formulas for the coefficients of the low-frequency series expansion of the transfer matrix of the system which in turn allow for determining the low-frequency expansions of its reflection, transmission, and absorption coefficients. Our general results reveal a number of interesting physical aspects of low-frequency scattering particularly in relation to permittivity profiles having balanced gain and loss. [ABSTRACT FROM AUTHOR]

The influence of the off-resonant circularly polarized light on the Josephson current in the time-reversal broken superconducting Weyl semimetal junctions is investigated by using the Bogoliubov–de Gennes equation and the transfer matrix approach. Both the zero momentum BCS pairing states and the finite momentum Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing states are considered for the Weyl superconductors. When a circularly polarized light is applied, it is shown that the current phase relation remains unchanged for the BCS pairing with the increasing of incident radiation intensity A0. For FFLO pairing, the Josephson current exhibits the 0–π transition and periodic oscillation as a function of A0. The dependence of free energy and critical current on A0 are also investigated. [ABSTRACT FROM AUTHOR]

The adhesive contact problem between a rigid cylindrical punch and a gradient nanostructured (GNS) coating is investigated by considering the size effect. The laminated plate model is applied to characterize the material properties of a GNS coating in plane strain couple stress elasticity. By using the Fourier integral transform and transfer matrix method, the governing integral equation(s) for the two-dimensional adhesive contact problem are obtained. Numerically calculated results are presented to analyse the effect of characteristic material length, the adhesion parameter and nonhomogeneous parameters on the mechanical response of the GNS coating for the adhesive contact problem. We explore the nanoscale contact of a GNS coating with shear modulus varying as a function of depth according to an exponential function or the power-law function. The present results provide a way to improve the contact deformation and damage to nanoelectromechanical systems by adjusting the gradient index of the GNS coating. [ABSTRACT FROM AUTHOR]

As interconnects in very-large-scale-integration technology shrinks into the sub-22 nm regime, carbon nanotubes, graphene nanoribbons (GNRs), and Cu-GNRs are emerging as potential replacements for conventional copper on-chip interconnects. This paper presents an matrix-rational-approximation (MRA) model for the fast transient analysis of graphene-based on-chip interconnects. The proposed model's key feature is that it allows the mathematical representation of the transfer function matrix of on-chip graphene-based interconnect networks in the frequency-domain using closed-form rational functions. The network's rational functions coefficients are derived from per-unit-length parameters and predetermined coefficients of the Padé approximation. The graphene-based network's time-domain model is directly obtained from the rational function frequency-domain model without any numerical integration techniques. This makes the proposed MRA model more numerically efficient than conventional simulation program with integrated circuit emphasis (SPICE) models. The results obtained using the proposed model show less than 1% error when compared with HSPICE simulations, ensuring the proposed model's excellent accuracy. A wide eye-height of 0.8137 V and eye-width of 219.87 ps are obtained for the eye-diagram analysis of multilayer graphene nanoribbon lines at 4 Gbps. [ABSTRACT FROM AUTHOR]

As building blocks of acoustic metamaterials, resonant scatterers have demonstrated their ability to modulate the effective fluid parameters, which subsequently possess extreme properties such as negative bulk modulus or negative mass density. Promising applications have been shown such as extraordinary absorption, focusing, and abnormal refraction for instance. However, acoustic waves can be further controlled in Willis materials by harnessing the coupling parameters. In this work, we derive the closed forms of the effective parameters from the transfer matrix in three asymmetric and reciprocal one-dimensional resonant configurations and exhibit the differences in terms of coupling coefficients. The way in which Willis coupling occurs in spatially asymmetric unit cells is highlighted. In addition, the analysis shows the absence of odd Willis coupling for reciprocal configurations. These effective parameters are validated against experimental and numerical results in the three configurations. This article paves the way of a novel physical understanding and engineering use of Willis acoustic materials. [ABSTRACT FROM AUTHOR]

Wave demultiplexers transporting desired wavelengths towards proper directions or ports are attracting numerous interests and applications in both physical and engineering areas. In acoustics, there is still a lack of compact and simple designs to achieve demultiplexers in three-port systems. In this work, we propose such a design using Helmholtz resonators where the frequency selection is based on the phenomenon of acoustically induced transparency (AIT). First, a modified transfer matrix method is derived to analytically describe and analyze the AIT effect with Helmholtz resonators. Then, the good performances of wave routing in these designs are further demonstrated by both simulation and experiment. These AIT based demultiplexers are subwavelength and simple in their designs. Therefore, they are promising for various potential applications such as signal processing, information communication and sensing. [ABSTRACT FROM AUTHOR]

To accommodate different application requirements, resonances of microring resonator (MRR)-based devices have been developed into various lineshapes, such as electromagnetically induced transparency, electromagnetically induced absorption, and Fano lineshapes. However, these lineshapes are mainly achieved in large-footprint structures demanding precise control. Under such context, this work investigates the formation of various resonance lineshapes in a single MRR with two partially reflecting elements incorporated into the bus waveguide. The transfer matrix model of the compact structure is established with the reflective wave in the MRR included. It is revealed that the abundant resonance lineshapes originate from the mode-coupling between the Fabry–Perot cavity and the MRR. Based on this model, the formation of each resonance lineshape is analyzed. The conditions under which each resonance lineshape can occur are identified and the characteristics of these resonance lineshapes are studied. In addition, the significant role of the reflective wave in the formation of these lineshapes is emphasized. Under the theoretical guidance of the presented work, various resonance lineshapes can be achieved and designed flexibly in a single MRR. Thus, the lineshapes required for a range of applications can be realized in a simple and reproducible MRR. [ABSTRACT FROM AUTHOR]

Proton transfer plays a key role in the applications of advanced energy materials as well as in the functionalities of biological systems. In this work, based on the transfer matrix method, we study the quantum effects of proton transfer in a series of one-dimensional (1D) model potentials and numerically calculate the quantum probability of transferring across single and double barriers (wells). In the case of single barriers, when the incident energies of protons are above the barrier height, the quantum oscillations in the transmission coefficients depend on the geometric shape of the barriers. It is found that atomic resonant tunneling (ART) not only presents in the rectangular single well and rectangular double barriers as expected, but also exists in the other types of potential wells and double barriers. For hetero-structured double barriers, there is no resonant tunneling in the classical forbidden zone, i.e., in the case when the incident energy (Ei) is lower than the barrier height (Eb). Furthermore, we have provided generalized analysis on the characteristics of transmission coefficients of hetero-structured rectangular double barriers. [ABSTRACT FROM AUTHOR]

We discuss a general description of the solutions to the 1D time-independent Schrödinger equation that does not a priori distinguish between scattering states and bound states and emphasizes and reinforces their relationship and connection to each other. This manuscript also introduces the concept of transfer matrices, which it presents as a logical extension of the traditional approach to evaluating 1D potentials. Using the transfer matrix method and a finite step approximation allows for a simple and straight-forward numerical solution of arbitrary 1D potentials. It also separates the process of solving the Schrödinger equation from selecting physically relevant solutions, which is a critical skill in quantum mechanics and is at the core of physics problems in general. [ABSTRACT FROM AUTHOR]

The ice-type model proposed by Linus Pauling to explain its entropy at low temperatures is here approached in a didactic way. We first present a theoretically estimated low-temperature entropy and compare it with numerical results. Then, we consider the mapping between this model and the three-colour problem, i.e. colouring a regular graph with coordination equal to 4 (a two-dimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of N oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for the case N → ∞ which is compared with the exact solution by Lieb. [ABSTRACT FROM AUTHOR]

It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we give an efficient algorithm to explicitly compute a transfer matrix which realizes the simultaneous block diagonalization of unitary matrices whose decomposition in irreducible blocks (common invariant subspaces) is known from elsewhere. Our main motivation lies in particle physics, where the resulting transfer matrix must be known explicitly in order to unequivocally determine the action of outer automorphisms such as parity, charge conjugation, or time reversal on the particle spectrum. [ABSTRACT FROM AUTHOR]

The epoch of reionization (EoR) marks the end of the Cosmic Dawn and the beginning of large-scale structure formation in the universe. The impulsive ionization fronts (I-fronts) heat and ionize the gas within the reionization bubbles in the intergalactic medium (IGM). The temperature during this process is a key yet uncertain ingredient in current models. Typically, reionization simulations assume that all baryonic species are in instantaneous thermal equilibrium with each other during the passage of an I-front. Here we present a new model of the temperature evolution for the ionization front by studying nonequilibrium effects. In particular, we include the energy transfer between major baryon species (e−, H i , H ii , He i , and He ii) and investigate their impacts on the post-ionization front temperature Tre. For a better step-size control when solving the stiff equations, we implement an implicit method and construct an energy transfer rate matrix. We find that the assumption of equilibration is valid for a nonrelativistic ionization front (speed less than), but deviations from equilibrium occur for faster fronts. The post-front temperature Tre is lower by up to 19.7% (at s−1) or 30.8% (at 1010 cm s−1) relative to the equilibrium case. [ABSTRACT FROM AUTHOR]

Monolayer transition metal dichalcogenides (TMDCs) under the application of a magnetic exchange field carry the nontrivial optical Hall conductivity and thus exhibit the nonzero Faraday rotation (FR) angle. However, the tradeoff between the FR angle and transmission hinders their possible applications in magnetic-optical (MO) devices. Here, we theoretically show that a heterostructure of two photonic crystals with proximitized monolayer TMDCs enables the enhancement of the FR angle and transmission simultaneously through the combination of a four-band Hamiltonian model, Kubo formula and transfer matrix method. The MO improvement in the hybrid structure in both the FR angle and transmission is determined by the combined effects from the localized electromagnetic field at the interface between the two photonic crystals and the satisfaction of the phase match condition. Our work opens up an alternative opportunity to use TMDCs in two-dimensional MO fields in the visible frequency range. [ABSTRACT FROM AUTHOR]

We extend the notion of the transfer matrix of potential scattering to a large class of long-range potentials v(x) and derive its basic properties. We outline a dynamical formulation of the time-independent scattering theory for this class of potentials where we identify their transfer matrix with the S-matrix of a certain effective non-unitary two-level quantum system. For sufficiently large values of |x|, we express v(x) as the sum of a short-range potential and an exactly solvable long-range potential. Using this result and the composition property of the transfer matrix, we outline an approximation scheme for solving the scattering problem for v(x). To demonstrate the effectiveness of this scheme, we construct an exactly solvable long-range potential and compare the exact values of its reflection and transmission coefficients with those we obtain using our approximation scheme. [ABSTRACT FROM AUTHOR]

In this paper, the hyperbolic metamaterials (HMs) based on the one-dimensional (1D) plasma photonic crystals is proposed, whose dielectric constant and group index can be obtained through the effective medium theory. By adopting an improved Thue–Morse sequence structure and using the transfer matrix method, the tunable single-frequency reflection in absorption (SFRA) with angle stability is achieved. The effects of incident angle, filling rate, and plasma collision frequency on the refractive index of HM and the SFRA are also analyzed respectively. The simulated results show that the incident angle makes no difference in the frequency position of the SFRA. However, a larger filling rate means that SFRA will move quickly to the lower frequencies, and the greater plasma collision frequency indicates that SFRA will appear in the higher frequencies. The better performance of SFRA can be realized in the cases of a smaller filling rate, plasma collision frequency, and θ (less than 60°). When the incident angle is about 60°, a perfect single-frequency reflection in the absorption region can be found for the transverse magnetic wave. These computed results can provide ideas for designing the new angle stability anti-dispersion waveguide structures, single-frequency filter with reflection, and absorber. [ABSTRACT FROM AUTHOR]

We present a theory for terahertz (THz) wave emission in a cavity containing a graphene-based asymmetric hyperbolic metamaterial (AHMM), and the results of the calculation of the output power of the THz laser. An asymmetry appears in the spatial spectrum of the eigenmodes due to a tilt of an anisotropy axis with respect to the interfaces of the AHMM that results in a difference in the wave vector components for waves propagating in opposite directions. This AHMM is an active medium in the THz region due to an inverted population of charge carriers in graphene. The theory is based on the analysis of eigenwaves in the cavity containing the graphene-based AHMM and the use of the transfer matrix method. The components of the Poynting vector, normal to the interface of the AHMM, have been calculated for different eigenmodes, taking into account the gain saturation. The gain saturation manifests itself as a decrease of the negative imaginary part of the effective permittivity of the metamaterial. This gain saturation results from the dependence of the chemical potential in graphene on the component of the electric field transverse to the graphene sheets. Here, the balance of gain versus loss predicts the intensity of the AHMM THz laser emission. [ABSTRACT FROM AUTHOR]

To obtain the adjustable photonic crystals (PCs), we numerically investigate one-dimensional (1D) PCs with alternating VO2 and SiO2 layers through transfer matrix method. The dispersion relation agrees well with the transmittance obtained by the finite element calculation. Tunable band gaps are achieved with the thermal stimuli of VO2, which has two crystal structures. The monoclinic crystal structure VO2 (R) at low temperature exhibits insulating property, and the high temperature square rutile structure VO2 (M) presents metal state. Concretely, the bandwidth is getting narrower and red shift occurs with the higher temperature in VO2 (R)/SiO2 PCs structure. Based on the phase change characteristics of VO2, we can flexibly adjust the original structure as VO2 (R)/VO2 (M)/SiO2. By increasing the phase ratio of VO2 (R) to VO2 (M), the band gap width gradually becomes wider and blue shift occurs. The discrete layers of gradient composites on the dispersion of 1D PCs are also investigated, which enhances the feasibility in practical operation. Thus, our proposed thermal modulation PCs structure paves a new way to realize thermal tunable optical filters and sensors. [ABSTRACT FROM AUTHOR]

We study the fused currents of the deformed Virasoro algebra. By constructing a homotopy operator we show that for special values of the parameter of the algebra fused currents pairwise coincide on the cohomologies of the Felder resolution. Within the algebraic approach to lattice models these currents are known to describe neutral excitations of the solid-on-solid (SOS) models in the transfer-matrix picture. It allows us to prove the closeness of the system of excitations for a special nonunitary series of restricted SOS models. Though the results of the algebraic approach to lattice models were consistent with the results of other methods, the lack of such proof had been an essential gap in its construction. [ABSTRACT FROM AUTHOR]

Coupling between the optical Tamm states (OTS) and microcavity mode in one-dimensional photonic crystal (1DPhC) structures is investigated experimentally and numerically with the help of transfer matrix method in resonant and non-resonant conditions, as a function of the distance between the 1DPhC-metal interface and the cavity layer (in terms of number of bilayers, Ntop, between the Tamm cavity and the microcavity). The system under study comprised of twelve bi-layers of alternating SiO2/TiO2 thin films, a half-wave thick TiO2 microcavity region and a layer of silver metal on top of the structure. It is observed that the microcavity mode and the OTS repel each other when Ntop is reduced indicating strong coupling between the two modes. In the resonant condition, wherein the individual structure consisting of either microcavity alone or Tamm cavity alone are tuned for the configuration Ntop = 2, the coupled modes in the hybrid structures are simultaneously localized at metal-1DPhC interface and at the microcavity. In the non-resonant condition when the microcavity mode and the OTS in the individual structure are not tuned, the coupling between the modes for the hybrid structure with Ntop = 2 leads to an enhanced electric field intensity of the microcavity mode compared to that from the uncoupled microcavity mode. Consequently, four different configurations corresponding to the non-resonant condition, having different Ntop are studied experimentally. The last four TiO2 layers and the microcavity layer of all the fabricated samples were incorporated with carbon quantum dots (CQDs). Comparison of photoluminescence enhancement as a function of Ntop in coupled and uncoupled conditions is discussed. [ABSTRACT FROM AUTHOR]

The spin-1/2 Heisenberg chain coupled to a spin-S impurity moment with anti-periodic boundary condition is studied via the off-diagonal Bethe ansatz method. The twisted boundary breaks the U(1) symmetry of the system, which leads to that the spin ring with impurity can not be solved by the conventional Bethe ansatz methods. By combining the properties of the R-matrix, the transfer matrix, and the quantum determinant, we derive the T–Q relation and the corresponding Bethe ansatz equations. The residual magnetizations of the ground states and the impurity specific heat are investigated. It is found that the residual magnetizations in this model strongly depend on the constraint of the topological boundary condition, the inhomogeneity of the impurity comparing with the hosts could depress the impurity specific heat in the thermodynamic limit. This method can be expand to other integrable impurity models without U(1) symmetry. [ABSTRACT FROM AUTHOR]

We cast diffraction-based interferometry in the framework of post-selected unitary description towards enabling it as a platform for quantum information processing (QIP). We express slit-diffraction as an infinite-dimensional transformation and truncate it to a finite-dimensional transfer matrix by post-selecting modes. Using such a framework with classical fields we show that a customized double-slit setup is effectively a lossy beam splitter in a post-selected sense. Diffraction optics provides a robust alternative to conventional multi-beam interferometry with scope for miniaturization, and also has applications in matter wave interferometry. In this work, the classical treatment of slit-diffraction sets the stage for quantization of fields and implementing higher-dimensional QIP like that done with other platforms such as orbital angular momentum. [ABSTRACT FROM AUTHOR]

In this paper, we present a theoretical model for the optimization of multilayer anti-reflection coatings for PEDOT:PSS/c-Si heterojunction solar cell based on optical interference transfer-matrix theory. A comprehensive idea of designing multilayer anti-reflection coatings (ARCs) on the solar cell and minimization of the overall reflectance is provided in this work. Optical reflectance values for various single, double and three layer anti-reflection coatings on PEDOT:PSS deposited c-Si substrate have been deduced using a MATLAB program and compared with that of the measured value. The reflectance value is calculated to be lower than 4% in the visible wavelength spectra for ARC by alternately using high and low refractive index materials. This low value of reflectance suggests that the anti-reflection coating layers proposed in this study can be employed as the standard ARC materials for optical coatings of the PEDOT:PSS/c-Si heterojunction solar cells.

The aim of this article is to provide some Matlab scripts to the teaching community in quantum physics. The scripts are based on the transfer-matrix formalism and offer a very efficient and versatile tool to solve problems of a physical object (electron, proton, neutron, etc) with one-dimensional (1D) stationary potential energy. Resonant tunnelling through a multiple-barrier or confinement in wells of various shapes is particularly analysed. The results are quantitatively discussed with semiconductor heterostructures, harmonic and anharmonic molecular vibrations, or neutrons in a gravity field. Scripts and other examples (hydrogen-like ions and transmission by a smooth variation of potential energy) are available freely at http://www-loa.univ-lille1.fr/∼pujol in three languages: English, French and Spanish. [ABSTRACT FROM AUTHOR]

Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long-range interactions, whose properties can be tailored by the choice of injected laser powers, frequencies, and polarizations. We use a transfer matrix approach to study the forces induced by non-interfering fields of orthogonal polarization or different frequencies in a 1D geometry, and find long-range self-ordering of particles without a prescribed order. Adjusting the laser frequencies and powers allows one to tune the inter-particle distances and provides a wide range of possible dynamical couplings not accessible in usual standing wave geometries with prescribed order. In this work, we restrict the examples to two frequencies and polarizations, but the framework also allows one to treat multicolour light beams with random phases. These dynamical effects should be observable in existing experimental setups with effective 1D geometries, such as atoms or nanoparticles coupled to the field of an optical nanofibre or transversely trapped in counter-propagating Gaussian beams. [ABSTRACT FROM AUTHOR]

The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the S-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(τ). We show that the application of the adiabatic approximation to H(τ) corresponds to the semiclassical description of the original scattering problem. In particular, the geometric part of the phase of the evolving eigenvectors of H(τ) gives the pre-exponential factor of the WKB wave functions. We use these observations to give an explicit semiclassical expression for the transfer matrix. This allows for a detailed study of the semiclassical unidirectional reflectionlessness and invisibility. We examine concrete realizations of the latter in the realm of optics. [ABSTRACT FROM AUTHOR]

We study the phase diagram and critical properties of the two-dimensional disordered O(n) loop model. The renormalization group (RG) flow is extracted from the landscape of the effective central charge c obtained by the transfer matrix method. We find a line of multicritical fixed points (FPs) at strong randomness for n > nc ∼ 0.5. We also find a line of stable random FPs for nc < n < 1, whose c and critical exponents agree well with the 1 − n expansion results. The multicritical FP at n = 1 has c = 0.4612(4), which suggests that it belongs to the universality class of the Nishimori point in the random-bond Ising model. For n > 2, we find another critical line that connects the hard-hexagon FP in the pure model to a finite-randomness zero-temperature FP . [ABSTRACT FROM AUTHOR]

The analysis of the transfer matrices associated with the most general representations of the 8-vertex reflection algebra on spin-1/2 chains is here implemented by introducing a quantum separation of variables (SOV) method, which generalizes to these integrable quantum models the method first introduced by Sklyanin. For representations reproducing in their homogeneous limits the open XYZ spin-1/2 quantum chains with the most general integrable boundary conditions, we explicitly construct representations of the 8-vertex reflection algebras, for which the transfer matrix spectral problem is separated. Then, in these SOV representations we get the complete characterization of the transfer matrix spectrum (eigenvalues and eigenstates) and its non-degeneracy. Moreover, we present the first fundamental step toward the characterization of the dynamics of these models by deriving determinant formulae for the matrix elements of the identity on separated states, which particularly apply to transfer matrix eigenstates. A comparison of our analysis of the 8-vertex reflection algebra with that of (Niccoli G 2012 J. Stat. Mech. P10025, Faldella S et al 2014 J. Stat. Mech. P01011) for the 6-vertex leads to an interesting remark in that there is a profound similarity in both the characterization of the spectral problems and the scalar products, which exists for these two different realizations of the reflection algebra once they are described by the SOV method. As will be shown in a future publication, this remarkable similarity will be the basis of a simultaneous determination of the form factors of local operators of integrable quantum models associated with general reflection algebra representations of both 8-vertex and 6-vertex type. [ABSTRACT FROM AUTHOR]

Thermal noise in a cellular automaton (CA) refers to a random perturbation in its function which eventually leads the automaton to an equilibrium state controlled by a temperature parameter. We study the one-dimensional majority-3 CA under this model of noise. Without noise, each cell in the automaton decides its next state by majority voting among itself and its left and right neighbour cells. Transfer matrix analysis shows that the automaton always reaches a state in which every cell is in one of its two states with probability 1/2 and thus cannot remember even one bit of information. Numerical experiments, however, support the possibility of reliable computation for a long but finite time. [ABSTRACT FROM AUTHOR]

Theoretical description of the wave propagation in an elliptical cylinder multilayer structure under the conditions of H polarization and E polarization is presented. A transfer matrix method has been developed for elliptical cylinder waves. The formulas of reflection and transmission coefficients for an elliptical cylinder multilayer structure are driven. Reflection and transmission coefficients of elliptical cylinder waves by a single elliptical cylinder interface is presented. The obtained formulas can be generalized to the cold plasma filled structures and thus the obtained results in the limit of circular cylinder structures are investigated. [ABSTRACT FROM AUTHOR]