Full Transfer Matrix Research Articles

Fast reconstruction of programmable interferometers with intensity-only measurements

Programmable linear optical interferometers are promising for classical and quantum applications. Their integrated design makes it possible to create more scalable and stable devices. To use them in practice, one has to reconstruct the whole device model taking the manufacturing errors into account. The inability to address individual interferometer elements complicates the reconstruction problem. A naive approach is to train the model via some complex optimization procedure. A faster optimization-free algorithm has been recently proposed (Bantysh et al 2023 Opt. Express 31 16729–42). However, it requires the full transfer matrix tomography while a more practical setup measures only the fields intensities at the interferometer output. In this paper, we propose the modification of the fast algorithm, which uses additional set of interferometer configurations in order to reconstruct the model in the case of intensity-only measurements. We show that it performs slightly worse than the original fast algorithm but it is more practical and still does not require intensive numerical optimization.

Chordal Graphs and Partial Positive Passivity Assessment

This paper presents a novel approach to passivity assessment of multiport frequency-dependent rational models. The strategy exploits the interlacing properties relating the eigenvalues of a full transfer matrix and those of its submatrices plus some additional concepts from graph theory. Contrary to many existing approaches in which passivity assessment applies only to the full system, this novel scheme aims at identifying passive subsystems embedded into a non-passive system so that a partial positive system could be specified. This enables the identification of parameters contributing to passivity violations and how these are distributed across the system ports. We also propose an index to quantify how passivity violations permeate into the system and take as cases studies actual transformer data to demostrate its applicability.

Channel Correlation-Based Approach for Feedback Overhead Reduction in Massive MIMO

For frequency-division duplex multiple-input–multiple-output (MIMO) systems, the channel state information at the transmitter is usually obtained by sending pilots or reference signals from all elements of the antenna array. The channel is then estimated by the receiver and communicated back to the transmitter. However, for massive MIMO, this periodical estimation of the full transfer matrix can lead to prohibitive overhead. To reduce the amount of data, we propose to estimate the updated channel matrix from the knowledge of the full correlation matrix at the transmitter made during some initialization time and the instantaneous measured channel matrix of smaller size, characterizing the link between the user and a limited number of reference array elements. The proposed algorithm is validated with measured massive MIMO channel transfer functions at 3.5 GHz between a $9 \times 9$ uniform rectangular array and different user positions. Since measurements were made in static conditions, the criteria chosen for evaluating the performance of the algorithm are based on a comparison of the predicted channel capacity calculated from either the measured or estimated channel matrix.

Classifying parafermionic gapped phases using matrix product states

In the Fock representation, we construct matrix product states (MPS) for one-dimensional gapped phases for $\mathbb{Z}_{p}$ parafermions. From the analysis of irreducibility of MPS, we classify all possible gapped phases of $\mathbb{Z}_{p}$ parafermions without extra symmetry other than $\mathbb{Z}%_{p}$ charge symmetry, including topological phases, spontaneous symmetry breaking phases and a trivial phase. For all phases, we find the irreducible forms of local matrices of MPS, which span different kinds of graded algebras. The topological phases are characterized by the non-trivial simple $\mathbb{Z}_{p}$ graded algebras with the characteristic graded centers, yielding the degeneracies of the full transfer matrix spectra uniquely. But the spontaneous symmetry breaking phases correspond to the trivial semisimple $\mathbb{Z}_{p/n}$ graded algebras, which can be further reduced to the trivial simple $\mathbb{Z}_{p/n}$ graded algebras, where $n$ is the divisor of $p$. So the present results deepen our understanding of topological phases in one dimension from the viewpoints of MPS.

Mapping of surface plasmon dispersion in thin Ag–Au layered composite films

Propagating surface plasmon polaritons (SPPs) at metal–dielectric interfaces allow extreme light confinement enabling important technologies such as label-free real-time sensing and nanoscale optical wave guiding. In this work, we experimentally and theoretically map the surface plasmon dispersion of thin films of sequentially deposited silver and gold based on the Kretschmann–Raether configuration using spectroscopic ellipsometry. The results show efficient excitation of SPP modes related to the symmetric and antisymmetric modes of an insulator–metal–insulator waveguide. Since the symmetric modes have a larger electric field inside the bimetallic layer than the antisymmetric modes, we show that the dispersion for both modes can be tuned independently by controlling the thickness ratio and deposition order of metals in the film. This behavior is fundamentally different than modes in a single film or a thin film alloy. Results are in agreement with the analytical eigenmode dispersion of these modes and with a full transfer matrix model. Our results provide a complete understanding of surface plasmon modes in thin bilayer or multilayer metallic films and their ability to influence the propagation of surface plasmon waves.

The Eight-Vertex Model and Lattice Supersymmetry

We show that the XYZ spin chain along the special line of couplings J_xJ_y+J_xJ_z+J_yJ_z=0 possesses a hidden N=(2,2) supersymmetry. This lattice supersymmetry is non-local and changes the number of sites. It extends to the full transfer matrix of the corresponding eight-vertex model. In particular, it is shown how to derive the supercharges from Baxter's Bethe ansatz. This analysis leads to new conjectures concerning the ground state for chains of odd length. We also discuss a correspondence between the spectrum of this XYZ chain and that of a manifestly supersymmetric staggered fermion chain.

Normal incidence sound transmission loss in impedance tube – Measurement and prediction methods using perforated plates

Abstract For the determination of the transmission loss of samples in an impedance tube, two different approaches is found in the literature, one based on determining the full transfer matrix (TM method) of the acoustic element, the other based on the wavefield decomposition theory (WD method). In this paper both methods are implemented and measured results are compared using samples which includes different types of perforated plates, also combined with porous material. Measurements are conducted in a tube of square cross section with dimensions 200 × 200 mm, thereby limiting the workable frequency range upwards to approximately 850 Hz. The main purpose of the paper is, however, to compare measured results with predictions using the transfer matrix method. For a bare plate with cylindrical apertures two models are compared as well; a “classical” one and another based on modeling the perforated plate as a porous material having a rigid frame. As for these transmission loss measurements, the two measurement approaches turn out to give identical results within the numerical accuracy. The fit between measured and predicted results are reasonably good with a maximum deviation mostly within 2 dB.

Separation of variables for integrable spin–boson models

We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang–Baxter algebra. The main deviation from the standard approach consists in a half infinite Sklyanin lattice made of the eigenvalues of the operator zeros of the Bethe annihilation operator. By a separation of variables, functional TQ -equations are obtained for this half infinite lattice. They provide valuable information about the spectrum of a given Hamiltonian model. We apply this procedure to integrable spin–boson models subject to both twisted and open boundary conditions. In the case of general twisted and certain open boundary conditions polynomial solutions to these TQ -equations are found and we compute the spectrum of both the full transfer matrix and its quasi-classical limit. For generic open boundaries we present a two-parameter family of Bethe equations, derived from TQ -equations that are compatible with polynomial solutions for Q. A connection of these parameters to the boundary fields is still missing.

Boundary Element Computations in the Forward and Inverse Problems of Electrocardiography: Comparison of Collocation and Galerkin Weightings

In electrocardiographic imaging, epicardial potentials are reconstructed computationally from electrocardiographic measurements. The reconstruction is typically done with the help of the boundary element method (BEM), using the point collocation weighting and constant or linear basis functions. In this paper, we evaluated the performance of constant and linear point collocation and Galerkin BEMs in the epicardial potential problem. The integral equations and discretizations were formulated in terms of the single- and double-layer operators. All inner element integrals were calculated analytically. The computational methods were validated against analytical solutions in a simplified geometry. On the basis of the validation, no method was optimal in all testing scenarios. In the forward computation of the epicardial potential, the linear Galerkin (LG) method produced the smallest errors. The LG method also produced the smallest discretization error on the epicardial surface. In the inverse computation of epicardial potential, the electrode-specific transfer matrix performed better than the full transfer matrix. The Tikhonov 2 regularization outperformed the Tikhonov 0. In the optimal modeling conditions, the best BEM technique depended on electrode positions and chosen error measure. When large modeling errors such as omission of the lungs were present, the choice of the basis and weighting functions was not significant.

Structure‐borne modeling of a vehicle in the mid‐frequency range using Virtual SEA: experimental validation

Virtual SEA is a modeling process using FE computations to build an SEA model including equivalent masses, modal densities, and CLF, but excluding DLF since damping modeling in the mid‐high frequency range is still an open issue. This technique, previously proposed by some of the authors, is applied to a production vehicle in the range 200‐1000 Hz. The actual vehicle is simultaneously measured at a subset of the FE nodes. The automated sub‐structuring provided by Virtual SEA (20 subsystems at 630Hz) is used to favorably position 64 sensors on the body. Next, an experimental SEA procedure is performed: a full transfer matrix is measured between more than 1000 excitation (hammer) locations and the sensors. In order to compensate for structural heterogeneity, input mobilities are measured at every point and used to normalize the transfer matrix As all measurement points are associated to FE nodes, computed input mobilities can be compared to measurements. Finally, the SEA model identification is carried out for both experimental and virtual SEA. As far as damping (DLF) can only be known experimentally, comparisons of the numerical and experimental approach only concern the orher SEA parameters (CLFs, modal densities ...) and transfer functions.

On the choice of the density matrix in the stochastic TMRG

In applications of the density matrix renormalization group to nonhermitean problems, the choice of the density matrix is not uniquely prescribed by the algorithm. We demonstrate that for the recently introduced stochastic transfer matrix DMRG (stochastic TMRG) the necessity to use open boundary conditions makes asymmetrical reduced density matrices, as used for renormalization in quantum TMRG, an inappropriate choice. An explicit construction of the largest left and right eigenvectors of the full transfer matrix allows us to show why symmetrical density matrices are the correct physical choice.

Elastic waves in graded-composition systems

We study the transverse and sagittal elastic waves in graded-composition systems, having a parabolic or linear grading, by means of the full transfer matrix technique and the surface Green function matching method. We obtain the velocities of the different waves as a function of the thickness of the structure, and we compare the variation of the velocities of these waves for the different profiles employed in our calculations. The spatial localization of the different modes is also considered.

Study of the eight-band Kane model by full transfer matrix and surface Green function matching

Full Transfer Matrix and Surface Green Function Matching are applied to the practical study of layered semiconductor systems described, within the Envelope Function Approximation, by the eight-band Kane model. A practical procedure is given to sor out the numerical difficulties often arising on integrating across thick constituent layers. A numerical application for the case of HgTe/CdTe superlattice is presented. The results agree quite well with the experimental and theoretical results obtained by other methods.

Effective transfer matrix for low-lying glueball states in lattice gauge theory

Abstract In four-dimensional lattice gauge theory without quarks the lowest particle states in the strong coupling region correspond to a spin-zero and a spin-two glueball. They are degenerate in the lowest order of the strong coupling expansion. There exists an effective transfer matrix, acting in the lowest order eigenspace, whose eigenvalues are identical with the corresponding ones of the full transfer matrix to all orders in the strong coupling expansion. It is constructed here up to the eighth nontrivial order for different gauge groups. Diagonalization yields the energy-momentum dispersion relations for glueball states.