Matrix Elements Research Articles

UNTANGLING THE VALLEY STRUCTURE OF STATES FOR INTRAVALLEY EXCHANGE ANISOTROPY IN LEAD CHALCOGENIDES QUANTUM DOTS

We put forward a generalized procedure which allows to restore the bulk-like electron and hole wave functions localized in certain valleys from the wave functions of quantum confined electron/hole states obtained in atomistic calculations of nanostructures. The procedure is applied to the lead chalcogenide quantum dots to accurately extract the intravalley velocity matrix elements and the constants of the effective intravalley Hamiltonian of the exchange interaction for the ground exciton state in PbS and PbSe quantum dots. Our results suggest that intravalley parameters in PbS quantum dots are much more anisotropic than the ones in PbSe. Renormalization of the velocity matrix elements, forbidden band gap, valley and exchange splittings of exciton and exciton binding energy are also calculated.

A windowed mean trajectory approximation for condensed phase dynamics.

We propose a trajectory-based quasi-classical method for approximating dynamics in condensed phase systems. Building upon the previously developed optimized mean trajectory approximation that has been used to compute linear and nonlinear spectra, we borrow some ideas from filtering trajectory methods to obtain a novel semiclassical method for the dynamical propagation of density matrices. This new approximation is tested rigorously against standard multistate electronic models, spin-boson models, and models of the Fenna-Matthews-Olson complex. For dissipative systems, the current method is significantly better or as good as many other semiclassical methods available, especially at low temperatures and for off-diagonal density matrix elements, whereas for scattering models, the current method bears similar limitations as mean-field propagation schemes. All results are tested against the numerically exact hierarchical equations of motion method. The new method shows excellent agreement across various parameter regimes with numerically exact results, highlighting the robustness and accuracy of our approach.

Exploring the Influence of Approximations for Simulating Valence Excited X-ray Spectra.

First-principles simulations of excited-state X-ray spectra are becoming increasingly important to interpret the wealth of electronic and geometric information contained within femtosecond X-ray absorption spectra recorded at X-ray Free Electron Lasers (X-FELs). However, because the transition dipole matrix elements must be calculated between two excited states (i.e., the valence excited state and the final core excited state arising from the initial valence excited state) of very different energies, this can be challenging and time-consuming to compute. Herein using two molecules, protonated formaldimine and cyclobutanone, we assess the ability of n-electron valence-state perturbation theory (NEVPT2), equation-of-motion coupled-cluster theory (EOM-CCSD), linear-response time-dependent density functional theory (LR-TDDFT) and the maximum overlap method (MOM) to describe excited state X-ray spectra. Our study focuses in particular on the behavior of these methods away from the Franck-Condon geometry and in the vicinity of important topological features of excited-state potential energy surfaces, namely, conical intersections. We demonstrate that the primary feature of excited-state X-ray spectra is associated with the core electron filling the hole created by the initial valence excitation, a process that all of the methods can capture. Higher energy states are generally weaker, but importantly much more sensitive to the nature of the reference electronic wave function. As molecular structures evolve away from the Franck-Condon geometry, changes in the spectral shape closely follow the underlying valence excitation, highlighting the importance of accurately describing the initial valence excitation to simulate the excited-state X-ray absorption spectra.

Tetrahedron equation and Schur functions

Abstract The tetrahedron equation introduced by Zamolodchikov is a three-dimensional generalization of the Yang–Baxter equation. Several types of solutions to the tetrahedron equation that have connections to quantum groups can be viewed as q-oscillator valued vertex models with matrix elements of the L-operators given by generators of the q-oscillator algebra acting on the Fock space. Using one of the q = 0-oscillator valued vertex models introduced by Bazhanov–Sergeev, we introduce a family of partition functions that admits an explicit algebraic presentation using Schur functions. Our construction is based on the three-dimensional realization of the Zamolodchikov–Faddeev algebra provided by Kuniba–Maruyama–Okado. Furthermore, we investigate an inhomogeneous generalization of the three-dimensional lattice model. We show that the inhomogeneous analog of (a certain subclass of) partition functions can be expressed as loop elementary symmetric functions.

Forced vibration assessment of moderately thick carbon nanotube-reinforced composite plates

Carbon nanotubes, distributed in composite sheets with various arrangements, can lead to the development of materials with functionally graded properties. In the present study, the method of spectral components was used to investigate the free vibration frequencies and dynamic responses of single-layer sheets reinforced with carbon nanotubes. The spectral component method offers significant advantages for high-frequency dynamic problems, as it requires fewer fine elements to solve boundary conditions. Based on the first-order shear theory, the governing equations of sheet vibration are derived. The discrete Fourier transform is applied to convert the differential equations from the time domain to the frequency domain. Using dynamic shape functions obtained from the exact solutions, the stiffness matrix of the spectral element is constructed. Dynamic frequency responses are then derived, and time-domain responses are obtained using the inverse Fourier transform. The study extracted the exact natural frequencies of functionally graded sheets and verified them with results from the literature, showing high accuracy with a minimal number of elements. The spectral finite element method of fundamental natural frequencies for different ratios of modulus of elasticity and width-to-thickness ratios obtained were investigated and compared with the results of research. The forced vibration was addressed, demonstrating that the method efficiently captures dynamic responses under different carbon nanotube distributions, with spectral displacements verified through numerical comparison. These findings demonstrate the capability and efficiency of the spectral finite element method for analyzing carbon nanotube-reinforced composite plates.

Optical properties of rutile TiO[formula omitted] with Zr, Mo, Zn, Cd impurities

To explore quasiparticle (QP) energy gaps and photoabsorption spectra of rutile TiO2 with nonmagnetic transition metal (Zr, Mo, Zn, Cd) impurities, we conducted a Γ-point only GW ＋ Bethe–Salpeter equation (BSE) calculation on a 72 (or 71) atom supercell. Our findings reveal that Zn and Cd impurities must coexist, at least partly, with oxygen vacancies to maintain charge neutrality. Among the systems considered, Mo, Zn, or Cd doped rutile TiO2 may exhibit optical absorption and catalytic activity under visible light. The resulting QP energy gaps (ΔɛQP) and photoabsorption energies (PAEs) are fairly in good agreement with both experimental and theoretical data currently available. The necessary conditions for the applicability of the Γ-point only approach in the GW ＋ BSE framework were found to be: (1) The Γ-point only GW calculation should reproduce a reasonable band gap. (2) The “superficial” exciton binding energy (the diagonal element of Wvc;vc−2Xvc;vc between v= VBM and c= CBM, where W and X are the direct and exchange terms of the BSE matrix elements, respectively) must be positive or marginally negative. (3) The “real” exciton binding energy (ΔɛQP− the lowest PAE) should be positive, even if it is exceptionally small.

Realization of low-frequency omnidirectional curve beam resonator (OCBR): Analytical spectral formulation and experimental characterization

The primary contribution of this study lies in the strong alignment between analytical, numerical, and experimental results, underscoring the validity and practical applicability of the Omnidirectional Curved Beam Resonator (OCBR) design in diverse structural configurations. This research encompasses the realization, characterization, and development of a spectral element formulation for the OCBR, a novel device engineered for vibration control within hollow structures. The spectral element matrix for the curved beam elements is formulated considering all six degrees of freedom using rigid body dynamics and mass inertia, enabling accurate dynamic analysis. Analytical solutions for the Frequency Response Function (FRF), derived using the spectral matrix and fixed boundary conditions, exhibited a close match with experimental results, validating the accuracy of the proposed model. Experimental setups with different orientations consistently observed resonant frequencies at 26 Hz, 32 Hz, 72 Hz, and 78 Hz, corresponding to the OCBR’s axial, in-plane, and out-of-plane vibrations, further affirming the theoretical predictions. Additionally, numerical simulations performed in COMSOL provided detailed insights into the system’s behavior, with deflected shapes at resonant frequencies corroborating the analytically predicted resonances. This study demonstrates the OCBR’s potential as a highly effective solution for vibration control, particularly in attenuating vibrations in the lower frequency range, representing a significant advancement in structural vibration mitigation techniques.

Single-shot 3 × 3 Mueller matrix microscopy with color polarization encoding.

Snapshot retrieval of linear Stokes parameters in polarized light microscopy has benefited from recent advances in nanotechnology which have made polarization image sensors commercially available. However, real-time retrieval of the 3 × 3 Mueller matrix (MM) is limited by the need for time-sequential change in polarization states in the input. In the present Letter, we propose a cost-effective technique for the real-time retrieval of the 3 × 3 Mueller matrix by encoding linear polarization states in each of the three color channels of the source and analyzing light passing through the sample using a color polarization sensor placed in the imaging plane of a transmission microscope. Validation experiments for samples under real-time imaging conditions are presented. To the best of our knowledge, this is the first report on the snapshot 3 × 3 Mueller matrix element retrieval in polarized light microscopy by combining division of focal plane (DoFP) color polarimetric sensing and polarization color encoding of the source.

Characterizing coherent errors using matrix-element amplification

Repeating a gate sequence multiple times amplifies systematic errors coherently, making it a useful tool for characterizing quantum gates. However, the precision of such an approach is limited by low-frequency noise, while its efficiency is hindered by time-consuming scans required to match up the phases of the off-diagonal matrix elements being amplified. Here, we overcome both challenges by interleaving the gate of interest with dynamical decoupling sequences in a protocol we call Matrix-Element Amplification using Dynamical Decoupling (MEADD). Using frequency-tunable superconducting qubits from a Google Sycamore quantum processor, we experimentally demonstrate that MEADD surpasses the accuracy and precision of existing characterization protocols for estimating systematic errors in single- and two-qubit gates. We use MEADD to estimate coherent parameters of CZ gates with 5 to 10 times the precision of existing methods and to characterize previously undetectable coherent crosstalk, reaching a precision below one milliradian.

Spin-Hall effect in topological materials: evaluating the proper spin current in systems with arbitrary degeneracies

The spin-Hall effect underpins some of the most active topics in modern physics, including spin torques and the inverse spin-Hall effect, yet it lacks a proper theoretical description. This makes it difficult to differentiate the SHE from other mechanisms, as well as differentiate band structure and disorder contributions. Here, by exploiting recent analytical breakthroughs in the understanding of the intrinsic spin-Hall effect, we devise a density functional theory method for evaluating the conserved (proper) spin current in a generic system. Spin non-conservation makes the conventional spin current physically meaningless, while the conserved spin current has been challenging to evaluate since it involves the position operator between Bloch bands. The novel method we introduce here can handle band structures with arbitrary degeneracies and incorporates all matrix elements of the position operator, including the notoriously challenging diagonal elements, which are associated with Fermi surface, group velocity, and dipolar effects but often diverge if not treated correctly. We apply this method to the most important classes of spin-Hall materials: topological insulators, 2D quantum spin-Hall insulators, non-collinear antiferromagnets, and strongly spin-orbit coupled metals. We demonstrate that the torque dipole systematically suppresses contributions to the conventional spin current such that, the proper spin current is generally smaller in magnitude and often has a different sign. Remarkably, its energy-dependence is relatively flat and featureless, and its magnitude is comparable in all classes of materials studied. These findings will guide the experiment in characterizing charge-to-spin interconversion in spintronic and orbitronic devices. We also discuss briefly a potential generalization of the method to calculate extrinsic spin currents generated by disorder scattering.

Investigation of pion-nucleon contributions to nucleon matrix elements

We investigate contributions of excited states to nucleon matrix elements computed in lattice QCD by employing, in addition to the standard nucleon interpolating operator, pion-nucleon (π−N) operators. We solve a generalized eigenvalue problem (GEVP) to obtain an optimal interpolating operator that minimizes overlap with the π−N states. We derive a variant of the standard application of the GEVP method, which allows for constructing 3-point correlation functions using the optimized interpolating operator without requiring the computationally demanding combination that includes π−N operators in both sink and source. We extract nucleon matrix elements using two twisted mass fermion ensembles, one ensemble generated using pion mass of 346 MeV and one ensemble tuned to reproduce the physical value of the pion mass. Especially, we determine the isoscalar and isovector scalar, pseudoscalar, vector, axial, and tensor matrix elements. We include results obtained using a range of kinematic setups, including momentum in the sink. Our results using this variational approach are compared with previous results obtained using the same ensembles and multistate fits without GEVP improvement. We find that for the physical mass point ensemble, the improvement, in terms of suppression of excited states using this method, is most significant for the case of the matrix elements of the isovector axial and pseudoscalar currents. Published by the American Physical Society 2024

Direct quarkonium production in DIS from a joint CGC and NRQCD framework

We compute the differential cross section for direct quarkonium production in high-energy electron-nucleus collisions at small x. Our computation is performed within the nonrelativistic QCD factorization formalism that separates the calculation into short distance coefficients and long distance matrix elements that depend on the color and spin of the state. We obtain the short distance coefficients of the production of the heavy quark pair within the framework of the color glass condensate effective field theory, which resums coherent multiple interactions of the heavy quark pair with the nucleus to all orders. Our results are expressed as the convolution of perturbatively calculable functions with multipoint lightlike Wilson line correlators. In the correlation limit, we establish the correspondence between our color glass condensate formulation with calculations employing the transverse momentum dependent (TMD) framework. We extend this correspondence by resumming kinematic power corrections within the improved TMD framework, which interpolates between the TMD formalism and k⊥-factorization formalism. We present a detailed numerical analysis, focusing on J/ψ production in the kinematics accessible at the future Electron-Ion Collider, highlighting the importance of genuine higher-order saturation contributions when the electron collides with a large nucleus. Our results are also valid in the photoproduction limit where we expect the largest contribution from genuine higher-order saturation contributions which could be accessed in ultraperipheral collisions of relativistic heavy ions. Published by the American Physical Society 2024

A spectral element-based reduced order model for thermoacoustic stability analysis in waveguides

A novel approach to perform linear stability analysis using a spectral element-based reduced order model is proposed, thereby facilitating the comprehensive study of (thermo)acoustic (in)stability across complex waveguide configurations. Providing a generalization of a wave-based method (e.g. spectral element method) to the Laplace domain, this study is offering not only a new methodology for analyzing thermoacoustic systems but also expanding the application of the spectral element method and other wave-based techniques to a broader class of problems. By solving the wave equation in the Laplace domain, spectral elementary matrices can be defined in the complex plane in both wavenumber and frequency domains, allowing for an examination of system stability. This technique supports a wide range of waveguide investigations, whether using an analytical description to get the spectral matrix or a numerical method to determine the dispersion curves and eigenvectors in the cross-section. Additionally, the proposed method simplifies the implementation of parametric optimization procedures due to its low computational cost, thus offering significant advancements in the study of waveguide behavior of thermoacoustic systems.

De Sitter S matrix for the masses

We define an S matrix for massive scalar fields on a fixed de Sitter spacetime, in the expanding patch coordinates relevant for early Universe cosmology. It enjoys many of the same properties as its Minkowski counterpart, for instance: it is insensitive to total derivatives and field redefinitions in the action; it can be extracted as a particular “on shell” limit of time-ordered correlation functions; and for low-point scattering, kinematics strongly constrains its possible structures. We present explicit formulas relating inflationary observables—namely in-in equal-time correlators and wavefunction coefficients at the conformal boundary—to these S matrix elements. This new formalism will allow modern amplitude methods to be applied directly in cosmology and hence provide a wider range of more accurate theoretical predictions for upcoming sky surveys. Published by the American Physical Society 2024

Quasi-periodic breathers and their dynamics to the Fokas system in nonlinear optics

The Fokas system is widely applied in nonlinear optics which can be used to describe the propagation behavior of optical solitons. An effective method for constructing the quasi-periodic breathers of the Fokas system is presented by combining the Hirota’s bilinear method with the theta function. The solvable problem of the quasi-periodic breathers is successfully transformed into a least squares problem whose numerical solutions ultimately are obtained through the Gauss–Newton method and the Levenberg–Marquardt method. Theoretical inference and numerical results show that when the real part of the diagonal elements of the Riemann matrix tends to positive infinity, the quasi-periodic breathers can be reduced to regular breathers. By analyzing the propagation characteristics of the quasi-periodic breathers, these quasi-periodic breathers are divided into three categories, general quasi-periodic breathers, quasi-periodic approximate Kuznetsov–Ma breathers and quasi-periodic Akhmediev breathers. Furthermore, by using an analytical method related to the characteristic lines for the quasi-periodic breathers, the dynamic characteristics including the periods and wave velocities of the quasi-periodic breathers are analyzed.

Laser-Assisted Scattering With Screened Diatomic Potential

This study explores the differential cross section (DCS) for laser-assisted scattering of diatomic molecules, considering various polarization conditions (linear, circular, elliptical) and potential parameters. The primary objective is to understand how polarization, screening effects, and potential parameters influence the scattering behavior. Utilizing a model that incorporates the Morse potential with screening effects, the analysis treats the laser field classically as a time-dependent, spatially homogeneous electric field, while the electron dynamics are described quantum mechanically using the Schrödinger equation. The Volkov wavefunction is derived, and the first-Born S-matrix element is computed to evaluate the scattering process. The results show that the DCS decreases with increasing screening parameters, with linear polarization yielding higher values than circular or elliptical polarization. Specifically, at an initial momentum of 8 MeV and a final momentum of 9 MeV, the DCS for elliptical polarization is notably higher. The DCS also varies with potential strength and well width, showing a peak at 0.14 Å for potential well width. The findings suggest that linear polarization is most effective for scattering studies under varying potential strengths. It is recommended to focus on linear polarization for enhanced scattering efficiency and to carefully adjust screening parameters and potential well widths for optimal results.

Extracellular Matrix as a Target in Melanoma Therapy: From Hypothesis to Clinical Trials.

Melanoma is a malignant, highly metastatic neoplasm showing increasing morbidity and mortality. Tumor invasion and angiogenesis are based on remodeling of the extracellular matrix (ECM). Selective inhibition of functional components of cell-ECM interaction, such as hyaluronic acid (HA), matrix metalloproteinases (MMPs), and integrins, may inhibit tumor progression and enhance the efficacy of combination treatment with immune checkpoint inhibitors (ICIs), chemotherapy, or immunotherapy. In this review, we combine the results of different approaches targeting extracellular matrix elements in melanoma in preclinical and clinical studies. The identified limitations of many approaches, including side effects, low selectivity, and toxicity, indicate the need for further studies to optimize therapy. Nevertheless, significant progress in expanding our understanding of tumor biology and the development of targeted therapies holds great promise for the early approaches developed several decades ago to inhibit metastasis through ECM targeting.

Electric-field-induced polarization anisotropy of interband photoluminescence in GaAs

Near-infrared photoluminescence spectra of the n-doped gallium arsenide epilayer under heating lateral electric field conditions are studied. The field dependences of hot electron and hole temperatures are determined from photoluminescence spectra and from solving the power balance equation using current–voltage characteristic. Polarization anisotropy of the photoluminescence radiation arising due to the anisotropy of hot electron distribution function and angular dependence of the interband optical matrix element in the momentum space is observed and investigated. The obtained experimental data are in satisfactory agreement with the theoretical model.

Effects of Two Decellularization Protocols on the Mechanical Behavior and Structural Properties of the Human Urethra.

This study evaluates the effects of two decellularization protocols, enzyme-detergent (ED) and detergent-detergent (DD), on the structural and biomechanical properties of human urethral tissue. Urethral samples from 18 individuals were divided into ED (n = 7) and DD (n = 11) groups, with native samples (n = 3) serving as controls. Histological and ultrastructural analyses confirmed that both protocols effectively removed cellular content while preserving essential extracellular matrix (ECM) elements, such as collagen and elastic fibers. Immunohistochemical staining for collagen IV and fibronectin revealed no significant differences between decellularized and native tissues, indicating intact ECM structure. Biomechanical testing demonstrated that DD-treated tissues had significantly lower Cauchy stress (1494.8 ± 518.4 kPa) when compared to native tissues (2439.7 ± 578.7 kPa, p = 0.013), while ED-treated tissues were similar to both groups. Both decellularized groups exhibited reduced stretch at failure and elastic modulus compared to native tissues. Cytotoxicity assays using adipose-derived stem cells demonstrated no signs of toxicity in either protocol. Overall, both ED and DD protocols effectively preserved the urethral ECM structure and mechanical properties, making them suitable for potential use in tissue-engineered grafts and for biobanking purposes. Further research is needed to refine and optimize decellularization methods to improve scaffold recellularization and ensure clinical safety and efficacy.

Euclidean wormholes in holographic RG flows

We describe a one-parameter family of Euclidean wormhole solutions with the topology of a compact hyperbolic space times an interval in Einstein gravity minimally coupled to a massless scalar field in AdSd+1 commonly referred to as Einstein-dilaton gravity. These solutions are locally described by the same metric and dilaton profile as the single-boundary Janus domain wall solutions in the same theory which are usually studied in the context of holographic RG flows. The wormholes compute the averaged product of partition functions of CFTs on either boundary deformed by different marginal couplings to the scalar operator dual to the dilaton. We observe that the renormalised volumes of these wormholes increase monotonically with the difference in the marginal couplings on the boundary thereby showing that the pair of CFTs on the boundaries get increasingly decorrelated as the difference in the marginal couplings increases. We use the partition functions of the three-dimensional wormhole solutions to determine the variance of the OPE data of local operators between the marginally deformed 2d CFTs and quantify how the variance decays with the difference in marginal couplings. In addition, a family of wormholes sourced by a thin shell of dust determine how the variance of the matrix elements of the dual line defect decays with the difference in marginal couplings. Applying the GKPW dictionary to wormholes, we compute averages of integrated dilaton correlators treating the wormhole amplitude as a functional of the dilaton sources. We observe that the crossed two-point correlators with a dilaton insertion on either boundary decay monotonically with the difference in marginal couplings consistent with the observation that the CFTs increasingly decorrelate as the difference in marginal couplings grows.