Spectral Function Research Articles

Mean field theory for strongly coupled systems: Holographic approach

In this paper, we develop the holographic mean field theory for strongly interacting fermion systems. We investigate various types of the symmetry-breakings and their effect on the spectral function. We found analytic expressions of fermion Green’s functions in the probe-limit for all types of tensor order parameter fields. We classified the spectral shapes and singularity types from the analytic Green’s function. We calculated the fermions spectral function in the full backreacted background and then compared it with the analytic results to show the reliability of analytic results in the probe limit. The fact that all the main features of the spectral features in the current condensed matter physics including gaps of s-,p- waves, nodal rings and nodal shells, the flat band of dimension 1,2,3, can be obtained in the absence of the lattice as consequences of the order and symmetry breaking pattern, is a pleaseant surprise.

Modal identification from turbulence response based on improved frequency domain decomposition

Turbulence excitation is an unavoidable form of excitation in flutter flight tests, and it is also a necessary and effective excitation method in high-speed flights, dives, other high-risk test, and high-frequency modal information mining. However, because the turbulence excitation signals are unmeasurable in the time domain, although the turbulence response contains rich and valuable flutter test information, the randomness and low quality of the data often cause difficulties in modal analysis. Therefore, an improved frequency domain decomposition algorithm for turbulence response processing is proposed in this paper. First, due to the irrelevancy of the atmospheric excitation, the power spectral density function matrix of the multi-channel turbulence response is subjected to singular value decomposition. There is a mathematical relationship between the maximum singular value curve and the system frequency response function. Second, the modal assurance criteria are used to calculate the maximum singular value of a single-degree-of-freedom system. Finally, an orthogonal polynomial method is applied to fit the maximum singular value curve, and the system identification is performed directly in the frequency domain. The simulated data and a certain type of aircraft flutter flight test data are used to verify the proposed method, and the results confirm the effectiveness and engineering applicability of the method developed in this work.

Research on system spectral response functions’ calibration and data processing methods for computational imaging spectrometers based on filter modulation

To enhance the performance of the optical payload, a novel computational imaging spectrometer using a board-bandpass film-filter line array (IS-BFLA) was developed. Since there is an obvious difference between the IS-BFLA and the one utilizing dispersion, conventional calibration and evaluation methods are not suitable. In this paper, we present a calibration method for the IS-BFLA. The calibration objects are determined by the mathematical model. We develop an automated calibration system and design a set of data processing procedures. Two evaluation methods: self-evaluation of multi-measurement based on Euclidean distance and multi-pixel inter-evaluation based on spectral angle, are developed to evaluate the precision and accuracy of the calibration. Furthermore, comparing the calibration value with the design value and spectral reconstruction are also utilized. The accuracy of spectral reconstruction: R2 is greater than 0.99, which determines the feasibility of the calibrated data. We hope that the work in this paper will assist in subsequent related studies.

Influence of atmospheric wind on the propagation of radio waves

Background. It is necessary to study the influence of the physical characteristics of the atmosphere, in particular, wind on atmospheric turbulence and, consequently, on the characteristics of the radio signal it is shown. Aim. The dependence of the time-spectral function of the radio signal energy flux on the wind speed in the troposphere in the antenna plane is found. Methods. A method of transition from the Cartesian coordinate system in the antenna plane to the polar coordinate system of wave numbers has been developed. Based on this method the relationship between the Fourier spectral function of the correlation moment and the representation of the Bessel function is found. For the Fourier spectral function of the correlation moment, the previously obtained solution of the differential equation for the fluctuations of the eikonal amplitude of electromagnetic wave in a turbulent atmosphere at the front of the electromagnetic wave at the coordinate of the receiving antenna is used. Using the inverse Fourier transform the relationship between the time-spectral function of the radio signal energy flux and the time-correlation function of this flux is found. Results. Based on the study of the time-correlation function of the radio signal energy flow its relationship with the two-point correlation moment characterizing the fluctuations of the eikonal amplitude of the radio signal is found. To analyze the effect of wind, a turbulence model was used, reflecting the inertial turbulence interval, in which the energy flow from larger turbulent vortices to smaller vortices is determined by the viscous dissipation of the smallest vortices. Conclusion. Numerical calculations have shown that such a wind in the antenna plane blows away turbulent vortices in this plane, bettering the quality of the received radio signal.

Darboux transformation-based LPNN generating novel localized wave solutions

Darboux transformation method is one of the most essential and important methods for solving localized wave solutions of integrable systems. In this work, we introduce the core idea of Darboux transformation of integrable systems into the Lax pairs informed neural networks (LPNNs), which we proposed earlier. By fully utilizing the data-driven solutions, spectral parameter and spectral function obtained from LPNNs, we present the novel Darboux transformation-based LPNN (DT-LPNN). The notable feature of DT-LPNN lies in its ability to solve data-driven localized wave solutions and spectral problems with high precision, and it also can employ Darboux transformation formulas of integrable systems and non-trivial seed solutions to discover novel localized wave solutions that were previously unobserved and unreported. The numerical results indicate that, by utilizing the single-soliton solutions as the non-trivial seed solutions, we obtain novel localized wave solutions for the Kraenkel–Manna–Merle (KMM) system by employing DT-LPNN, in which solution u changes from original bright single-soliton on zero background wave to new dark single-soliton dynamic behavior on a variable non-zero background wave. Moreover, by treating the two-soliton solutions as the non-trivial seed solutions, DT-LPNN generates novel localized wave solutions for the KMM system that exhibit completely different dynamic behaviors from prior two-soliton solutions. DT-LPNN combines the Darboux transformation theory of integrable systems with deep neural networks, offering a new approach for generating novel localized wave solutions using non-trivial seed solutions.

Non-polynomial interactions as a path towards a non-renormalizable UV-completion

We propose a new class of single-field scalar quantum field theories with non-polynomial interactions leading to a two-point Green's function that can be naturally continued beyond the naive cutoff scale. This provides a new prospect for self-completing theories in the UV-domain. In our approach, the formal power series for the scalar potential has a vanishing radius of convergence and is defined through Borel resummation. We discuss concrete examples, among others with a spectral function that vanishes at large momenta, potentially leading to an asymptotically free theory. Finally, we give an outlook on future research, with a view towards possible applications to inflation and gravity.

Classical and quantum computing of shear viscosity for (2+1)D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for (2+1)-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density ηs is consistent with a well-known holographic result 14π at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=12. We also find the ratio of the spectral function and frequency ρxy(ω)ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond jmax=12 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including jmax truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

Considerations on measurement of bidirectional transmittance distribution function of thick samples over a wide range of viewing zenith angles

Abstract We delve into theoretical and experimental considerations for determining the spectral bidirectional transmittance distribution function (BTDF) of thick samples across a broad viewing zenith angle range. Nominally, BTDF is defined as the ratio of transmitted radiance to incident irradiance measured from the same plane. However, when employing thick samples for BTDF measurements, the viewing plane of the transmitted beam may shift from the front to the rear surface of the sample, altering the measurement geometry compared to using the sample front surface as the reference plane. Consequently, the viewing zenith angle from the sample rear surface increases relative to the sample front surface, and the sample-to-detector-aperture distance decreases by an amount corresponding to the sample thickness. We introduce a method for determining the BTDF of thick samples, considering the transformation of practical measurement results to a scenario where the measurements are conducted at a very large distance from the sample. To validate the method, we utilize a BTDF facility equipped with two instruments that significantly differ in their sample-to-detector-aperture distances. We evaluate the impact of a 2 mm sample thickness on the BTDF by assessing the ratio of transmitted and incident radiant fluxes as a function of viewing zenith angle relative to the sample rear surface. The evaluation is conducted in the wavelength range from 550 nm to 1450 nm in 300 nm steps, and in the viewing zenith angle range from −70° to 70° in 5° steps. Measurements are performed in-plane at an incident zenith angle of 0°. It is concluded that consistent determination of BTDF of a thick sample is possible by converting the experimental parameters of the real measurements at relatively short distances from the sample to correspond to those that would be obtained from measurements at very large distances from the sample.

Deuterium spin relaxation of fractionally deuterated ribonuclease H using paired 475 and 950MHz NMR spectrometers.

Deuterium (2H) spin relaxation of 13CH2D methyl groups has been widely applied to investigate picosecond-to-nanosecond conformational dynamics in proteins by solution-state NMR spectroscopy. The B0 dependence of the 2H spin relaxation rates is represented by a linear relationship between the spectral density function at three discrete frequencies J(0), J(ωD) and J(2ωD). In this study, the linear relation between 2H relaxation rates at B0 fields separated by a factor of two and the interpolation of rates at intermediate frequencies are combined for a more robust approach for spectral density mapping. The general usefulness of the approach is demonstrated on a fractionally deuterated (55%) and alternate 13C-12C labeled sample of E. coli RNase H. Deuterium relaxation rate constants (R1, R1ρ, RQ, RAP) were measured for 57 well-resolved 13CH2D moieties in RNase H at 1H frequencies of 475MHz, 500MHz, 900MHz, and 950MHz. The spectral density mapping of the 475/950MHz data combination was performed independently and jointly to validate the expected relationship between data recorded at B0 fields separated by a factor of two. The final analysis was performed by jointly analyzing 475/950MHz rates with 700MHz rates interpolated from 500/900MHz data to yield six J(ωD) values for each methyl peak. The J(ω) profile for each peak was fit to the original (τM, Sf2, τf) or extended model-free function (τM, Sf2, Ss2, τf, τs) to obtain optimized dynamic parameters.

Continuous multiplicative spectral functionals on Hermitian Banach algebras

Continuous multiplicative spectral functionals on Hermitian Banach algebras

Contrastive Investigation of High rise building with distinctive infill wall by Pushover analysis

Pushover analysis is a method that uses simple nonlinear techniques to predict seismic structural deformations. Today, we use masonry infill in reinforced concrete (R/C) frames for architectural, aesthetic or economic reasons. In this project, we need to study the effect of backfill on the damage structure of the reinforced concrete frame. The main purpose of this study is to show that adding walls to the reinforced concrete frame can increase the strength and stiffness of seismic resistant structure loads and increase the feedback for strength and stiffness analysis.These instructions strictly comply with FEMA-356. In this project, we use three types of bricks: red brick, fly ash brick, deep brick and siporex brick. Taking the output of non-linear analysis, we compare layer V/S i) Base Shear, ii) Storey Displacement, iii) Floor Shift Base Shear V/S Attack and Observe Spectrum Acceleration V/S spectral function . We also use ETABS 2017 software to study the effects of bare shear walls.. Key Words: Pushover Examination, Brick infill, FEMA-356, Displacement, Float, Shear Divider, ETAB-2017

Local and Nonlocal Electronic Correlations at the Metal-Insulator Transition in the Two-Dimensional Hubbard Model.

Elucidating the physics of the single-orbital Hubbard model in its intermediate-coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent nonperturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.

Functional changes in sleep-related arousal after ketamine administration in individuals with treatment-resistant depression

The glutamatergic modulator ketamine is associated with changes in sleep, depression, and suicidal ideation (SI). This study sought to evaluate differences in arousal-related sleep metrics between 36 individuals with treatment-resistant major depression (TRD) and 25 healthy volunteers (HVs). It also sought to determine whether ketamine normalizes arousal in individuals with TRD and whether ketamine’s effects on arousal mediate its antidepressant and anti-SI effects. This was a secondary analysis of a biomarker-focused, randomized, double-blind, crossover trial of ketamine (0.5 mg/kg) compared to saline placebo. Polysomnography (PSG) studies were conducted one day before and one day after ketamine/placebo infusions. Sleep arousal was measured using spectral power functions over time including alpha (quiet wakefulness), beta (alert wakefulness), and delta (deep sleep) power, as well as macroarchitecture variables, including wakefulness after sleep onset (WASO), total sleep time (TST), rapid eye movement (REM) latency, and Post-Sleep Onset Sleep Efficiency (PSOSE). At baseline, diagnostic differences in sleep macroarchitecture included lower TST (p = 0.006) and shorter REM latency (p = 0.04) in the TRD versus HV group. Ketamine’s temporal dynamic effects (relative to placebo) in TRD included increased delta power earlier in the night and increased alpha and delta power later in the night. However, there were no significant diagnostic differences in temporal patterns of alpha, beta, or delta power, no ketamine effects on sleep macroarchitecture arousal metrics, and no mediation effects of sleep variables on ketamine’s antidepressant or anti-SI effects. These results highlight the role of sleep-related variables as part of the systemic neurobiological changes initiated after ketamine administration. Clinical Trials Identifier: NCT00088699.

Probing the Mott insulating behavior of Ba2MgReO6 with DFT+DMFT

We investigate the interplay of spin-orbit coupling, electronic correlations, and lattice distortions in the 5d1 double perovskite Ba2MgReO6. Combining density-functional theory (DFT) and dynamical mean-field theory (DMFT), we establish the Mott insulating character of Ba2MgReO6 in both its cubic and tetragonal paramagnetic phases. Despite substantial spin-orbit coupling, its impact on the formation of the insulating state is minimal, consistent with theoretical expectations for d1 systems. We further characterize the electronic properties of the cubic and tetragonal phases by analyzing spectral functions and local occupations in terms of multipole moments centered on the Re sites. Our results confirm the presence of ferroically ordered z2 quadrupoles in addition to the antiferroic x2−y2-type order. We compare two equivalent but complementary descriptions in terms of either effective Re-t2g frontier orbitals or more localized atomiclike Re-d and O-p orbitals. The former maps directly on a physically intuitive picture in terms of nominal d1 Re cations, while the latter explicitly demonstrates the role of hybridization with the ligands in the spin-orbit splitting and the formation of the charge quadrupoles around the Re sites. Finally, we compare our DFT+DMFT results with a previous DFT+U study of the tetragonal paramagnetic state. We find good qualitative agreement for the dominant charge quadrupoles, but also notable differences in the corresponding spectral functions, underscoring the need for more comparative studies between these two methods. Published by the American Physical Society 2024

Probing molecular spectral functions and unconventional pairing using Raman spectroscopy

An impurity interacting with an ultracold Fermi gas can form either a polaron state or a dressed molecular state, the molaron, in which the impurity forms a bound state with one gas particle. This molaron state features rich physics, including a negative effective mass around unitarity and a first-order transition to the polaron state. However, these features have remained so far experimentally inaccessible. In this work we show theoretically how the molaron state can be directly prepared experimentally even in its excited states using Raman spectroscopy techniques. Initializing the system in the ultrastrong coupling limit, where the binding energy of the molaron is much larger than the Fermi energy, our protocol maps out the momentum-dependent spectral function of the molecule. Using a diagrammatic approach we furthermore show that the molecular spectral function serves as a direct precursor of the elusive Fulde-Ferell-Larkin-Ovchinnikov phase, which is realized for a finite density of fermionic impurity particles. Our results pave the way to a systematic understanding of how composite particles form in quantum many-body environments and provide a basis to develop new schemes for the observation of exotic phases of quantum many-body systems. Published by the American Physical Society 2024

Correlation and Spectral Density Functions in Mode-Stirred Reverberation – III. Measurements

Correlation and Spectral Density Functions in Mode-Stirred Reverberation – III. Measurements

Correlation and Spectral Density Functions in Mode-Stirred Reverberation – I. Theory

Correlation and Spectral Density Functions in Mode-Stirred Reverberation – I. Theory

Correlation and Spectral Density Functions in Mode-Stirred Reverberation – II. Spectral Moments, Sampling, Noise, EMI, and Understirring

Correlation and Spectral Density Functions in Mode-Stirred Reverberation – II. Spectral Moments, Sampling, Noise, EMI, and Understirring

Dissipative systems fractionally coupled to a bath.

Quantum diffusion is a major topic in condensed-matter physics, and the Caldeira-Leggett model has been one of the most successful approaches to study this phenomenon. Here, we generalize this model by coupling the bath to the system through a Liouville fractional derivative. The Liouville fractional Langevin equation is then derived in the classical regime, without imposing a non-Ohmic macroscopic spectral function for the bath. By investigating the short- and long-time behavior of the mean squared displacement, we show that this model is able to describe a large variety of anomalous diffusion. Indeed, we find ballistic, sub-ballistic, and super-ballistic behavior for short times, whereas for long times, we find saturation and sub- and super-diffusion.

Manifolds whose Weyl spectral asymptotics have small but not tiny remainders

A compact, n -dimensional Riemannian manifold M has Weyl spectral asymptotics with remainder E_{M}(R) ; i.e., the spectral counting function satisfies \mathcal{N}(\Delta_{M},R)=C(M)R^{n}+ E_{M}(R) , with E_{M}(R)=o(R^{n}) . Generally, one actually has E_{M}(R)=O(R^{n-1}) , and one seeks geometrical conditions under which stronger estimates hold on the remainder and also conditions limiting how extra small the remainder can be. Here, we produce n -dimensional manifolds whose Weyl remainders are o(R^{n-1}) but not O(R^{n-1-\alpha}) for any \alpha>0 .