Search

Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally believed to be a critical phenomenon and fragile to random perturbations. In this work, we propose a set of generic principles based on the power-law decay of the eigenstates which allow us to distinguish a fractal phase from a genuine multifractal phase. We demonstrate the above principles in a 1d tight-binding model with inhomogeneous nearest-neighbor hopping that can be mapped to the standard quantum harmonic oscillator via energy-coordinate duality. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions which are in agreement with numerical simulations., Comment: 4.25 pages, 3 figures, 106 references + 3 pages in Appendices

Regularized estimation of quantitative ultrasound (QUS) parameters, such as attenuation and backscatter coefficients, has gained research interest. Recently, the alternating direction method of multipliers (ADMM) has been applied successfully to estimate these parameters, by utilizing L2 and L1 norms for attenuation and backscatter coefficient regularization, respectively. While this method improves upon previous approaches, it does not fully leverage the prior knowledge of minimum physically feasible parameter values, sometimes yielding values outside the realistic range. This work addresses this limitation by incorporating minimum QUS parameter values as constraints to enhance ADMM estimation. The proposed method is validated using experimental phantom data., Comment: accepted in ISBI 2025

Typically, metallic systems localized under strong disorder exhibit a transition to finite conduction as kinetic terms increase. In this work, we reveal the opposite effect--increasing kinetic terms leads to an unexpected suppression of conductivity, enhancing localization of the system, and even lead to re-entrant delocalization transitions. Specifically, we add a nearest-neighbor hopping with amplitude $\kappa$ to the Rosenzweig-Porter (RP) model with fractal on-site disorder and surprisingly see that, as $\kappa$ grows, the system initially tends to localization from the fractal phase, but then re-enters the ergodic phase. We build an analytical framework to explain this re-entrant behavior, supported by exact diagonalization results. The interplay between the spatially local $\kappa$ term, insensitive to fractal disorder, and the energy-local RP coupling, sensitive to fine-level spacing structure, drives the observed re-entrant behavior. This mechanism offers a novel pathway to re-entrant localization phenomena in many-body quantum systems., Comment: 7 pages, 4 figures

To mitigate the BBU instability and improve characteristics of accelerated bunches in Dielectric Wakefield Accelerator one can be used the isotropic plasma filling of the transport channel. Here we present the results of analytical and numerical studies of the dynamics of accelerated electron/positron and drive electron bunches under wake acceleration in a plasma DWA (PDWA) with a vacuum channel. The wake field is excited by an electron bunch in a quartz dielectric tube inserted into a cylindrical metal waveguide. The inner region of the dielectric tube is filled with plasma with a vacuum channel along the waveguide axis. At the numerical simulations the energy and spatial characteristics, efficiency, emittance, and energy spread for accelerated positron and electron bunches is studied for different radii of the vacuum channel. The transverse instability of the drive bunch in PDWA is studied analytically and numerically. The analytical studies have discovered the presence of one surface and one bulk eigenwaves, which are absent in corresponding dielectric-loaded waveguide without plasma filling. The main contribution to amplitude of transverse wakefield, responsible for stabilization of transverse motion of bunches, brings the bulk plasma eigenwave. The comparative analysis of the data resulting from analytical studies and the ones obtained by numerical simulation has demonstrated qualitative agreement between the results., Comment: 33 pages, 13 fugures, AAC2024 Worhshop, will be submitted to Nuclear Instruments and Methods in Physics Research

Homodyned K-distribution (HK-distribution) parameter estimation in quantitative ultrasound (QUS) has been recently addressed using Bayesian Neural Networks (BNNs). BNNs have been shown to significantly reduce computational time in speckle statistics-based QUS without compromising accuracy and precision. Additionally, they provide estimates of feature uncertainty, which can guide the clinician's trust in the reported feature value. The total predictive uncertainty in Bayesian modeling can be decomposed into epistemic (uncertainty over the model parameters) and aleatoric (uncertainty inherent in the data) components. By decomposing the predictive uncertainty, we can gain insights into the factors contributing to the total uncertainty. In this study, we propose a method to compute epistemic and aleatoric uncertainties for HK-distribution parameters ($\alpha$ and $k$) estimated by a BNN, in both simulation and experimental data. In addition, we investigate the relationship between the prediction error and both uncertainties, shedding light on the interplay between these uncertainties and HK parameters errors., Comment: 4 pages, 2 figures

We report on the induction of magnetization in Rydberg systems by means of the inverse Faraday effect, and propose the appearance of the effect in two such systems, Rydberg atoms proper and shallow dopants in semiconductors. Rydberg atoms are characterized by a large orbital radius. This large radius gives such excited states a large angular moment, which when driven with circularly polarized light, translates to a large effective magnetic field. We calculate this effect to generate effective magnetic fields of $O(10\,\text{mT})\times\left( \frac{\omega}{1\,\text{THz}} \right)^{-1} \left( \frac{I}{10\,{W\,cm}^{-2}} \right)$ in Rydberg states of Rb and Cs for a $1\,\text{THz}$ beam of intensity $10\,\text{W}\,\text{cm}^{-2}$. The magnitude of the effective magnetic field scales with the principal quantum number as $n^4$. Additionally, THz spectroscopy of phosphorus doped silicon reveals a large cross-section for excitation of shallow dopants to Rydberg-like states, which even for small $n$ can be driven similarly with circularly polarized light to produce even larger magnetization, with ${B}_{\text{eff}}$ which we estimate as $O(1\,\text{mT})$ for Si:P with the same beam parameters.

We investigate the effect of pressure on the carbon dioxide (CO$_{2}$) hydrate-water interfacial free energy along its dissociation line using advanced computer simulation techniques. In previous works, we have determined the interfacial energy of the hydrate at $400 \,\text{bar}$ using the TIP4P/ice and TraPPE molecular models for water and CO$_{2}$, respectively, in combination with two different extensions of the Mold Integration technique [J. Chem. Phys. 141, 134709 (2014)]. Results obtained from computer simulation, $29(2)$ and $30(2)\,\text{mJ/m}^{2}$, are found to be in excellent agreement with the only two measurements that exist in the literature, $28(6)\,\text{mJ/m}^{2}$ determined by Uchida et al. [J. Phys. Chem. B 106, 8202 (2002)] and $30(3)\,\text{mJ/m}^{2}$ by Anderson et al. [J. Phys. Chem. B 107, 3507 (2002)]. Since the experiments do not allow to obtain the variation of the interfacial energy along the dissociation line of the hydrate, we extend our previous studies to quantify the effect of pressure on the interfacial energy at different pressures. Our results suggest that there exists a correlation between the interfacial free energy values and the pressure, i.e., it decreases with the pressure between $100$ and $1000\,\text{bar}$. We expect that the combination of reliable molecular models and advanced simulation techniques could help to improve our knowledge of the thermodynamic parameters that control the interfacial free energy of hydrates from a molecular perspective., Comment: 7 pages, 4 figures

In this paper, the solubility of carbon dioxide (CO$_{2}$) in water along the isobar of 400 bar is determined by computer simulations using the well-known TIP4P/Ice force field for water and TraPPE model for CO$_{2}$. In particular, the solubility of CO$_{2}$ in water when in contact with the CO$_{2}$ liquid phase, and the solubility of CO$_{2}$ in water when in contact with the hydrate have been determined. The solubility of CO$_{2}$ in a liquid-liquid system decreases as temperature increases. The solubility of CO$_{2}$ in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the dissociation temperature of the hydrate at 400 bar ($T_{3}$). We compare the predictions with the $T_{3}$ obtained using the direct coexistence technique in a previous work. The results of both methods agree and we suggest 290(2)K as the value of $T_{3}$ for this system using the same cutoff distance for dispersive interactions. We also propose a novel and alternative route to evaluate the change in chemical potential for the formation of hydrate along the isobar. The new approach is based on the use of the solubility curve of CO$_{2}$ when the aqueous solution is in contact with the hydrate phase. It considers rigorously the non-ideality of the aqueous solution of CO$_{2}$, providing reliable values for driving force for nucleation of hydrates in good agreement with other thermodynamic routes used. It is shown that the driving force for hydrate nucleation at 400 bar is larger for the methane hydrate than for the carbon dioxide hydrate when compared at the same supercooling. We have also analyzed and discussed the effect of the cutoff distance of the dispersive interactions and the occupancy of CO$_{2}$ on the driving force for nucleation of the hydrate., Comment: 25 pages, 19 figures

Averaged local bond order parameters based on spherical harmonics, also known as Lechner and Dellago order parameters, are routinely used to determine crystal structures in molecular simulations. Among different options, the combination of the $\overline{q}_{4}$ and $\overline{q}_{6}$ parameters is one of the best choices in the literature since allows one to distinguish, not only between solid- and liquid-like particles but also between different crystallographic phases, including cubic and hexagonal phases. Recently, Algaba et al. [J. Colloid Interface Sci. 623, 354, (2022)] have used the Lechner and Dellago order parameters to distinguish hydrate- and liquid-like water molecules in the context of determining the carbon dioxide hydrate-water interfacial free energy. According to the results, the preferred combination previously mentioned is not the best option to differentiate between hydrate- and liquid-like water molecules. In this work, we revisit and extend the use of these parameters to deal with systems in which clathrate hydrates phases coexist with liquid phases of water. We consider carbon dioxide, methane, tetrahydrofuran, nitrogen, and hydrogen hydrates that exhibit sI and sII crystallographic structures. We find that the $\overline{q}_{3}$ and $\overline{q}_{12}$ combination is the best option possible between a large number of possible different pairs to distinguish between hydrate- and liquid-like water molecules in all cases., Comment: 18 pages, 8 figures

In this work, we have calculated self-diffusion and shear viscosity, two of the most important transport properties, of the spherical square-well (SW) fluid interacting with potential range $\lambda = 1.5 \, \sigma$. To this end, we have used a combination of molecular dynamics simulation and the continuous version of the square-well (CSW) intermolecular potential recently proposed by Zer\'on et al. [Mol. Phys. 116, 3355 (2018)]. In addition to that, we have also determined a number of equilibrium properties, including internal energy, compressibility factor, radial distribution function, and coordination number. All properties are evaluated in a wide range of temperatures and densities, including subcritical and supercritical thermodynamic conditions. Results obtained in this work show an excellent agreement with available data reported in the literature and demonstrate that the CSW intermolecular potential can be used in molecular dynamics simulations to emulate SW transport properties with confidence., Comment: 9 pages, 10 figures, 8 tables included in supplementary material

Focusing on Bethe-ansatz integrable models, robust to both time-reversal symmetry breaking and disorder, we consider the Russian Doll Model (RDM) for finite system sizes and energy levels. Suggested as a time-reversal-symmetry breaking deformation of Richardson's model, the well-known and simplest model of superconductivity, RDM revealed an unusual cyclic renormalization group (RG) over the system size $N$, where the energy levels repeat themselves, shifted by one after a finite period in $\ln N$, supplemented by a hierarchy of superconducting condensates, with the superconducting gaps following the so-called Efimov (exponential) scaling. The equidistant single-particle spectrum of RDM made the above Efimov scaling and cyclic RG to be asymptotically exact in the wideband limit of the diagonal potential. Here, we generalize this observation in various respects. We find that, beyond the wideband limit, when the entire spectrum is considered, the periodicity of the spectrum is not constant, but appears to be energy-dependent. Moreover, we resolve the apparent paradox of shift in the spectrum by a single level after the RG period, despite the disappearance of a finite fraction of energy levels. We also analyze the effects of disorder in the diagonal potential on the above periodicity and show that it survives only for high energies beyond the energy interval of the disorder amplitude. Our analytic analysis is supported with exact diagonalization., Comment: 15 pages, 3 figures, 34 references

The prominent role of electron-electron interactions in two-dimensional (2D) materials versus three-dimensional (3D) ones is at the origin of the great variety of fermionic correlated states reported in the literature. In this respect, artificial van der Waals heterostructures comprising single layers of highly correlated insulators allow one to explore the effect of the subtle interlayer interaction in the way electrons correlate. In this work, we study the temperature dependence of the electronic properties of a van der Waals heterostructure composed of a single-layer Mott insulator lying on a metallic substrate by performing quasi-particle interference (QPI) maps. We show the emergence of a Fermi contour in the 2D Mott insulator at temperatures below 11K, which we attribute to the delocalization of the Mott electrons associated with the formation of a quantum coherent Kondo lattice. This Kondo lattice introduces a new periodicity in the system, so that the resulting Fermi surface encompasses both the substrate conduction electrons and the now delocalized correlated electrons from the 2D Mott insulator. Density Functional Theory calculations allow us to pinpoint the scattering vectors responsible for the experimentally observed quasi-particle interference maps, thus providing a complete picture of the delocalization of highly correlated electrons in a 2D Mott insulator., Comment: 15 pages, 4 figures

This study delves into the intriguing properties of 1H/1T-TaS$_2$ van der Waals heterostructure, focusing on the transparency of the 1H layer to the Charge Density Wave of the underlying 1T layer. Despite the sizable interlayer separation and metallic nature of the 1H layer, positive bias voltages result in a pronounced superposition of the 1T charge density wave structure on the 1H layer. The conventional explanation relying on tunneling effects proves insufficient. Through a comprehensive investigation combining lowtemperature scanning tunneling microscopy, scanning tunneling spectroscopy, non-contact atomic force microscopy, and firstprinciples calculations, we propose an alternative interpretation. The transparency effect arises from a weak yet substantial electronic coupling between the 1H and 1T layers, challenging prior understanding of the system. Our results highlight the critical role played by interlayer electronic interactions in van der Waals heterostructures to determine the final ground states of the systems.

Quantitative ultrasound (QUS) analyzes the ultrasound backscattered data to find the properties of scatterers that correlate with the tissue microstructure. Statistics of the envelope of the backscattered radiofrequency (RF) data can be utilized to estimate several QUS parameters. Different distributions have been proposed to model envelope data. The homodyned K-distribution (HK distribution) is one of the most comprehensive distributions that can model ultrasound backscattered envelope data under diverse scattering conditions (varying scatterer number density and coherent scattering). The scatterer clustering parameter (alpha) and the ratio of the coherent to diffuse scattering power (k) are the parameters of this distribution that have been used extensively for tissue characterization in diagnostic ultrasound. The estimation of these two parameters (which we refer to as HK parameters) is done using optimization algorithms in which statistical features such as the envelope point-wise signalto-noise ratio (SNR), skewness, kurtosis, and the log-based moments have been utilized as input to such algorithms. The optimization methods minimize the difference between features and their theoretical value from the HK model. We propose that the true value of these statistical features is a hyperplane that covers a small portion of the feature space. In this paper, we follow two approaches to reduce the effect of sample features' error. We propose a model projection neural network based on denoising autoencoders to project the noisy features into this space based on this assumption. We also investigate if the noise distribution can be learned by the deep estimators. We compare the proposed methods with conventional methods using simulations, an experimental phantom, and data from an in vivo animal model of hepatic steatosis. A demo code are available online at http://code.sonography.ai

In various chaotic quantum many-body systems, the ground states show non-trivial athermal behavior despite the bulk states exhibiting thermalization. Such athermal states play a crucial role in quantum information theory and its applications. Moreover, any generic quantum many-body system in the Krylov basis is represented by a tridiagonal Lanczos Hamiltonian, which is analogous to the matrices from the $\beta$ ensemble, a well-studied random matrix model with level repulsion tunable via the parameter $\beta$. Motivated by this, here we focus on the localization properties of the ground and anti-ground states of the $\beta$ ensemble. Both analytically and numerically, we show that both the edge states demonstrate non-ergodic (fractal) properties for $\beta\sim\mathcal{O}(1)$ while the typical bulk states are ergodic. Surprisingly, the fractal dimension of the edge states remain three time smaller than that of the bulk states irrespective of the global phase of the $\beta$ ensemble. In addition to the fractal dimensions, we also consider the distribution of the localization centers of the spectral edge states, their mutual separation, as well as the spatial and correlation properties of the first excited states., Comment: 4 figures in main text, 2 figures in appendix

In this work, we investigate the localization properties of a paradigmatic model, coupled to a monitoring environment and possessing a many-body localized (MBL) phase. We focus on the post-selected no-click limit with quench random rates, i.e., random gains and losses. In this limit, the system is modeled by adding an imaginary random potential, rendering non-Hermiticity in the system. Numerically, we provide an evidence that the system is localized for any finite amount of disorder. To analytically understand our results, we extend the quantum random energy model (QREM) to the non-Hermitian scenario. The Hermitian QREM has been used previously as a benchmark model for MBL. The QREM exhibits a size-dependent MBL transition, where the critical value scales as $W_c\sim \sqrt{L} \ln{L}$ with system size and presenting many-body mobility edges. We reveal that the non-Hermitian QREM with random gain-loss offers a significantly stronger form of localization, evident in the nature of the many-body mobility edges and the value for the transition, which scales as $W_c\sim \ln^{1/2}{L}$ with the system size., Comment: 11 pages, 4 figures, 94 references

Motivated by a series of recent works, an interest in multifractal phases has risen as they are believed to be present in the Many-Body Localized (MBL) phase and are of high demand in quantum annealing and machine learning. Inspired by the success of the RosenzweigPorter (RP) model with Gaussian-distributed hopping elements, several RP-like ensembles with the fat-tailed distributed hopping terms have been proposed, with claims that they host the desired multifractal phase. In the present work, we develop a general (graphical) approach allowing a self-consistent analytical calculation of fractal dimensions for a generic RP model and investigate what features of the RP Hamiltonians can be responsible for the multifractal phase emergence. We conclude that the only feature contributing to a genuine multifractality is the on-site energies' distribution, meaning that no random matrix model with a statistically homogeneous distribution of diagonal disorder and uncorrelated off-diagonal terms can host a multifractal phase.

In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction $\beta$ of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in {a certain range of parameters} $(d,\beta)$ at infinitely large uniformly distributed disorder. The critical curve separating extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood., Comment: 12 pages, 5 figures, 86 references + 8 pages, 9 figures in Appendices

Models with correlated disorders are rather common in physics. In some of them, like the Aubry-Andr\'e (AA) model, the localization phase diagram can be found from the (self)duality with respect to the Fourier transform. In the others, like the all-to-all translation-invariant Rosenzweig-Porter (TI RP) ensemble or the Hilbert-space structure of the many-body localization, one needs to develop more sophisticated and usually phenomenological methods to find the localization transition. In addition, such models contain not only localization but also the ergodicity-breaking transition, giving way to the non-ergodic extended phase of states with non-trivial fractal dimensions $D_q$. In this work, we suggest a method to calculate both the above transitions and a lower bound to the fractal dimensions $D_2$ and $D_\infty$, relevant for physical observables. In order to verify this method, we apply it to the class of long-range (self-)dual models, interpolating between AA and TI RP ones via both power-law dependences of on-site disorder correlations and hopping terms, and, thus, being out of the validity range of the previously developed methods. We show that the interplay of the correlated disorder and the power-law decaying hopping terms leads to the emergence of the two types of fractal phases in an entire range of parameters, even without having any quasiperiodicity of the AA potential. The analytical results of the above method are in full agreement with the extensive numerical calculations., Comment: 4.5 pages, 3 figures, 85 references + 5 pages, 1 figure in Appendices

Quasiperiodic systems in one dimension can host non-ergodic states, e.g. localized in position or momentum. Periodic quenches within localized phases yield Floquet eigenstates of the same nature, i.e. spatially localized or ballistic. However, periodic quenches across these two non-ergodic phases were thought to produce ergodic diffusive-like states even for non-interacting particles. We show that this expectation is not met at the thermodynamic limit where the system always attains a non-ergodic state. We find that ergodicity may be recovered by scaling the Floquet quenching period with system size and determine the corresponding scaling function. Our results suggest that while the fraction of spatially localized or ballistic states depends on the model's details, all Floquet eigenstates belong to one of these non-ergodic categories. Our findings demonstrate that quasiperiodicity hinders ergodicity and thermalization, even in driven systems where these phenomena are commonly expected.

Quantum transport and localization are fundamental concepts in condensed matter physics. It is commonly believed that in one-dimensional systems, the existence of mobility edges is highly dependent on disorder. Recently, there has been a debate over the existence of an exact mobility edge in a modulated mosaic model without quenched disorder, the so-called mosaic Wannier-Stark lattice. Here, we experimentally implement such disorder-free mosaic photonic lattices using a silicon photonics platform. By creating a synthetic electric field, we could observe energy-dependent coexistence of both extended and localized states in a finite number of waveguides. The Wannier-Stark ladder emerges when the resulting potential is strong enough, and can be directly probed by exciting different spatial modes of the lattice. Our studies provide the experimental proof of coexisting sets of strongly localized and conducting (though weakly localized) states in finite-sized mosaic Wannier-Stark lattices, which hold the potential to encode high-dimensional quantum resources with compact and robust structures.

The mobility edge (ME) is a crucial concept in understanding localization physics, marking the critical transition between extended and localized states in the energy spectrum. Anderson localization scaling theory predicts the absence of ME in lower dimensional systems. Hence, the search for exact MEs, particularly for single particles in lower dimensions, has recently garnered significant interest in both theoretical and experimental studies, resulting in notable progress. However, several open questions remain, including the possibility of a single system exhibiting multiple MEs and the continual existence of extended states, even within the strong disorder domain. Here, we provide experimental evidence to address these questions by utilizing a quasiperiodic mosaic lattice with meticulously designed nanophotonic circuits. Our observations demonstrate the coexistence of both extended and localized states in lattices with broken duality symmetry and varying modulation periods. By single site injection and scanning the disorder level, we could approximately probe the ME of the modulated lattice. These results corroborate recent theoretical predictions, introduce a new avenue for investigating ME physics, and offer inspiration for further exploration of ME physics in the quantum regime using hybrid integrated photonic devices.

We consider the properties of the random regular graph with node degree $d$ perturbed by chemical potentials $\mu_k$ for a number of short $k$-cycles. We analyze both numerically and analytically the phase diagram of the model in the $(\mu_k,d)$ plane. The critical curve separating the homogeneous and clusterized phases is found and it is demonstrated that the clusterized phase itself generically is separated as the function of $d$ into the phase with ideal clusters and phase with coupled ones when the continuous spectrum gets formed. The eigenstate spatial structure of the model is investigated and it is found that there are localized scar-like states in the delocalized part of the spectrum, that are related to the topologically equivalent nodes in the graph. We also reconsider the localization of the states in the non-perturbative band formed by eigenvalue instantons and find the semi-Poisson level spacing distribution. The Anderson transition for the case of combined ($k$-cycle) structural and diagonal (Anderson) disorders is investigated. It is found that the critical diagonal disorder gets reduced sharply at the clusterization phase transition, but does it unevenly in non-perturbative and mid-spectrum bands, due to the scars, present in the latter. The applications of our findings to $2$d quantum gravity are discussed., Comment: 27 pages, 9 figures, 87 references + 4 pages, 4 figures in Appendices

Rosenzweig-Porter (RP) model has garnered much attention in the last decade, as it is a simple analytically tractable model showing both ergodic--nonergodic extended and Anderson localization transitions. Thus, it is a good toy model to understand the Hilbert-space structure of many body localization phenomenon. In our study, we present analytical evidence, supported by exact numerical computations, that demonstrates the controllable tuning of the phase diagram in the RP model by employing on-site potentials with a non-trivial fractal dimension instead of the conventional random disorder. We demonstrate that doing so extends the fractal phase and creates unusual dependence of fractal dimensions of the eigenfunctions. Furthermore, we study the fate of level statistics in such a system and analyze the return probability of a wave packet localized at a single site to provide a dynamical test-bed for our theory., Comment: 5 pages, 5 figures, 65 references + 3 pages, 2 figures in Appendices

Unlike the well-known Mott's argument that extended and localized states should not coexist at the same energy in a generic random potential, we provide an example of a nearest-neighbor tight-binding disordered model which carries both localized and extended states without forming the mobility edge (ME). Unexpectedly, this example appears to be given by a well-studied $\beta$-ensemble with independently distributed random diagonal potential and inhomogeneous kinetic hopping terms. In order to analytically tackle the problem, we locally map the above model to the 1D Anderson model with matrix-size- and position-dependent hopping and confirm the coexistence of localized and extended states, which is shown to be robust to the perturbations of both potential and kinetic terms due to the separation of the above states in space. In addition, the mapping shows that the extended states are non-ergodic and allows to analytically estimate their fractal dimensions., Comment: 4.5 pages, 4 figures, 60 references + 3.5 pages, 5 figures in Appendices

Quantitative ultrasound (QUS) aims to find properties of scatterers which are related to the tissue microstructure. Among different QUS parameters, scatterer number density has been found to be a reliable biomarker for detecting different abnormalities. The homodyned K-distribution (HK-distribution) is a model for the probability density function of the ultrasound echo amplitude that can model different scattering scenarios but requires a large number of samples to be estimated reliably. Parametric images of HK-distribution parameters can be formed by dividing the envelope data into small overlapping patches and estimating parameters within the patches independently. This approach imposes two limiting constraints, the HK-distribution parameters are assumed to be constant within each patch, and each patch requires enough independent samples. In order to mitigate those problems, we employ a deep learning approach to estimate parametric images of scatterer number density (related to HK-distribution shape parameter) without patching. Furthermore, an uncertainty map of the network's prediction is quantified to provide insight about the confidence of the network about the estimated HK parameter values., Comment: Accepted in SPIE 2023

The power-law random banded matrix (PLRBM) is a paradigmatic ensemble to study the Anderson localization transition (AT). In $d$-dimension the PLRBM are random matrices with algebraic decaying off-diagonal elements $H_{\vec{n}\vec{m}}\sim 1/|\vec{n}-\vec{m}|^\alpha$, having AT at $\alpha=d$. In this work, we investigate the fate of the PLRBM to non-Hermiticity. We consider the case where the random on-site diagonal potential takes complex values, mimicking an open system, subject to random gain-loss terms. We provide an analytical understanding of the model by generalizing the Anderson-Levitov resonance counting technique to the non-Hermitian case. This generalization identifies two competing mechanisms due to non-Hermiticity: one favoring localization and the other delocalization. The competition between the two gives rise to AT at $d/2\le \alpha\le d$. The value of the critical $\alpha$ depends on the strength of the on-site potential, reminiscent of Hermitian disordered short-range models in $d>2$. Within the localized phase, the wave functions are algebraically localized with an exponent $\alpha$ even for $\alpha

Quantitative ultrasound (QUS) allows estimating the intrinsic tissue properties. Speckle statistics are the QUS parameters that describe the first order statistics of ultrasound (US) envelope data. The parameters of Homodyned K-distribution (HK-distribution) are the speckle statistics that can model the envelope data in diverse scattering conditions. However, they require a large amount of data to be estimated reliably. Consequently, finding out the intrinsic uncertainty of the estimated parameters can help us to have a better understanding of the estimated parameters. In this paper, we propose a Bayesian Neural Network (BNN) to estimate the parameters of HK-distribution and quantify the uncertainty of the estimator., Comment: Submitted to IEEE International Symposium on Biomedical Imaging (ISBI) 2023