Non-trivial Parameter Research Articles

ML-MCTDH-Aid: An auxiliary package for multilayer multiconfiguration time-dependent Hartree calculations.

The multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) method has garnered significant attention in the realm of theoretical chemistry owing to its powerful ability to perform numerically exact descriptions of multi-dimensional quantum dynamics and exhibit the remarkable performance in simulating the nonadiabatic dynamics of complex systems. Despite the availability of computational packages within the ML-MCTDH framework, executing these calculations seamlessly is not a straightforward task. Typically, substantial efforts are necessitated to configure the correct inputs for ML-MCTDH calculations, which require to correctly define several non-trivial parameters, to reasonably setup the optimal tree expansion of wavefunctions, and to properly select basis function numbers. To address these challenges, we have developed an auxiliary package named ML-MCTDH-Aid, which facilitates the setup of ML-MCTDH calculations using the Heidelberg MCTDH package in a user-friendly manner. This package is primarily tailored to handle the high-dimensional nonadiabatic dynamics governed by the Hamiltonian composed of several electronic states, several vibrational modes and their linear vibronic coupling terms. It automatically generates multiple essential input files, and all the calculations can be performed in an all-in-one black-box easy-to-use manner. To show the utility of the ML-MCTDH-Aid package, we provide a step-by-step tutorial that demonstrates running ML-MCTDH studies on three models. These examples illuminate how the utilization of the ML-MCTDH-Aid package significantly enhances the efficiency and effectiveness of ML-MCTDH calculations. This substantially boosts the accessibility of ML-MCTDH calculations in tackling the high-dimensional quantum dynamics of complex systems.

Exceptional Luttinger liquids from sublattice-dependent interaction

We demonstrate how exceptional points (EPs) naturally occur in the Luttinger liquid (LL) theory describing the low-energy excitations of a microscopic lattice model with sublattice-dependent electron-electron interaction. Upon bosonization, this sublattice dependence directly translates to a nonstandard sine-Gordon-type term responsible for the non-Hermitian matrix structure of the single-particle Green function (GF). As the structure in the lifetime of excitations does not commute with the underlying free Bloch Hamiltonian, non-Hermitian topological properties of the single-particle GF emerge—despite our Hermitian model Hamiltonian. Both finite temperature and a nontrivial Luttinger parameter K≠1 are required for the formation of EPs, and their topological stability in one spatial dimension is guaranteed by the chiral symmetry of our model. In the presence of the aforementioned sine-Gordon term, we resort to leading-order perturbation theory (PT) to compute the single-particle GF. All qualitative findings derived within LL theory are corroborated by comparison to both numerical simulations within the conserving second Born approximation and, for weak interactions and high temperatures, by fermionic plain PT. In certain parameter regimes, quantitative agreement can be reached by a suitable parameter choice in the effective bosonized model. Published by the American Physical Society 2024

Chebyshev Polynomials in the Physics of the One-Dimensional Finite-Size Ising Model: An Alternative View and Some New Results

For studying the finite-size behavior of the Ising model under different boundary conditions, we propose an alternative to the standard transfer matrix technique approach based on Abelès theorem and Chebyshev polynomials. Using it, one can easily reproduce the known results for periodic boundary conditions concerning the Lee–Yang zeros, the exact position-space renormalization-group transformation, etc., and can extend them by deriving new results for antiperiodic boundary conditions. Note that in the latter case, one has a nontrivial order parameter profile, which we also calculate, where the average value of a given spin depends on the distance from the seam with the opposite bond in the system. It is interesting to note that under both boundary conditions, the one-dimensional case exhibits Schottky anomaly.

Unitarity of bespoke amplitudes

We use partial wave unitarity to constrain various bespoke four-point amplitudes. We start by constructing bespoke generalizations of the type-I superstring amplitude, which we show satisfy dual resonance and have suitable high-energy limits. By analyzing the behavior of partial wave coefficients for highly massive states, we strictly rule out all bespoke amplitudes with asymptotically nonlinear Regge trajectories and place constraints on the first few nontrivial parameters in asymptotically linear cases. Finally, we argue that while a large class of unitary bespoke amplitudes fails to satisfy Regge sum rules, there exists a smaller subclass with a vanishing mass gap that is superpolynomially bounded. Published by the American Physical Society 2024

The Improvement of Density Peaks Clustering Algorithm and Its Application to Point Cloud Segmentation of LiDAR.

This work focuses on the improvement of the density peaks clustering (DPC) algorithm and its application to point cloud segmentation in LiDAR. The improvement of DPC focuses on avoiding the manual determination of the cut-off distance and the manual selection of cluster centers. And the clustering process of the improved DPC is automatic without manual intervention. The cut-off distance is avoided by forming a voxel structure and using the number of points in the voxel as the local density of the voxel. The automatic selection of cluster centers is realized by selecting the voxels whose gamma values are greater than the gamma value of the inflection point of the fitted γ curve as cluster centers. Finally, a new merging strategy is introduced to overcome the over-segmentation problem and obtain the final clustering result. To verify the effectiveness of the improved DPC, experiments on point cloud segmentation of LiDAR under different scenes were conducted. The basic DPC, K-means, and DBSCAN were introduced for comparison. The experimental results showed that the improved DPC is effective and its application to point cloud segmentation of LiDAR is successful. Compared with the basic DPC, K-means, the improved DPC has better clustering accuracy. And, compared with DBSCAN, the improved DPC has comparable or slightly better clustering accuracy without nontrivial parameters.

(Invited) Designer 2D Materials and Machine-Learning Assisted Characterization

2D materials offer enormous opportunities to build designer structures with widely tunable properties. The precise atomic engineering and quick characterization approach are critical to advance the application of designer 2D materials. This talk will introduce new optical features of designer 2D materials [1-4] with a focus on atomic substitution in monolayer WS2 [1]. The engineering of 2D materials presents unique opportunities for optoelectronic device and quantum information platform. When designing optoelectronic devices of 2D materials, spectroscopic permittivity of 2D material is a key parameter. While ellipsometry has been used to measure permittivity, it requires simple device structure, non-trivial parameter fitting, and special setup. This talk will also present a new machine-learning assisted approach to measure permittivity of 2D materials embedded in complex device structures without model fitting, which can facilitate a quick, accurate, and in-situ characterization of 2D and other thin film materials [5].

Magnetic field enhanced critical current in Ge–Si nanowire Josephson junctions

Anomalous critical current enhancement was observed with increasing magnetic field in Josephson junctions based on Ge–Si core-shell nanowires. Despite the predicted topological properties of these nanowires, which could potentially lead to non-trivial superconducting order parameter symmetries, our investigation unveils a more generalized, non-topological explanation for the observed critical current enhancement in these devices. Our findings suggest that the enhancement arises from a thermalization process induced by the magnetic field, wherein in-gap quasiparticles are generated. These quasiparticles play a crucial role in enhancing the cooling of the device, thereby lowering the effective temperature and resulting in an increased critical current. Furthermore, we elucidate how this thermalization effect varies with device geometry and measurement configuration.

Quantum tricriticality in a generalized quantum Rabi system

Quantum tricriticality, a unique form of high-order criticality, is expected to exhibit fascinating features including unconventional critical exponents and universal scaling laws. However, a quantum tricritical point (QTCP) is much harder to access, and the corresponding phenomena at tricriticality have rarely been investigated. In this study, we explore a tricritical quantum Rabi model, which incorporates a non-trivial parameter to adjust the coupling ratio between a cavity and a three-level atom. The QTCP emerges at the intersection of first- and second-order superradiant phase transitions according to Landau theory. By using finite-frequency scaling analysis on quantum fluctuations and the average photon number, universal critical exponents differentiate the QTCP from the second-order critical point. Our results indicate that the phase transition at the tricritical point goes beyond the conventional second-order phase transition. Our work explores an interesting direction in the generalization of the well-known Rabi model for the study of higher-order critical points due to its high control and tunability.

Toward a deeper understanding: RetNet viewed through Convolution

The success of Vision Transformer (ViT) has been widely reported on a wide range of image recognition tasks. ViT can learn global dependencies superior to CNN, yet CNN’s inherent locality can substitute for expensive training resources. Recently, the outstanding performance of RetNet in the field of language modeling has garnered attention, surpassing that of the Transformer with explicit local modeling, shifting researchers’ focus toward Transformers in the CV field. This paper investigates the effectiveness of RetNet from a CNN perspective and presents a variant of RetNet tailored to the visual domain. Similar to RetNet we improves ViT’s local modeling by applying a weight mask on the original self-attention matrix. A straightforward way to locally adapt the self-attention matrix can be realized by an Element-wise Learnable Mask (ELM), for which our preliminary results show promising results. However, the Element-wise Learnable Mask not only induces a non-trivial additional parameter overhead but also increases the optimization complexity. To this end, this work proposes a novel Gaussian mixture mask (GMM) in which one mask only has two learnable parameters and it can be conveniently used in any ViT variants whose attention mechanism allows the use of masks. Experimental results on multiple small datasets demonstrate that the effectiveness of our proposed Gaussian mask for boosting ViTs for free (almost zero additional parameter or computation cost). Our code is publicly available at https://github.com/CatworldLee/Gaussian-Mixture-Mask-Attention.

Topological phase diagrams of in-plane field polarized Kitaev magnets

While the existence of a magnetic field induced quantum spin liquid in Kitaev magnets remains under debate, its topological properties often extend to proximal phases where they can lead to unusual behaviors of both fundamental and applied interests. Subjecting a generic nearest-neighbor spin model of Kitaev magnets to a sufficiently strong in-plane magnetic field, we study the resulting polarized phase and the associated magnon excitations. In contrast to the case of an out-of-plane magnetic field where the magnon band topology is enforced by symmetry, we find that it is possible for topologically trivial and nontrivial parameter regimes to coexist under in-plane magnetic fields. We map out the topological phase diagrams of the magnon bands, revealing a rich pattern of variation of the Chern number over the parameter space and the field angle. We further compute the magnon thermal Hall conductivity as a weighted summation of Berry curvatures, and discuss experimental implications of our results to planar thermal Hall effects in Kitaev magnets. Published by the American Physical Society 2024

Dynamical stricture of optical soliton solutions and variational principle of nonlinear Schrödinger equation with Kerr law nonlinearity

The aim of this paper is to discover some new exact solutions for two kinds of nonlinear Schrödinger equation (NLSE), including the (2+1)-dimensional NLSE and the derivative NLSE, through the use of the variational principle method and amplitude ansatz method. We will find the solutions to these equations by selecting a trial function with a single nontrivial variational parameter, and it is continuous at all intervals in three cases from a region of a rectangular box, then using this trial function to obtain the functional integral and the Lagrangian of the system without any loss. After that, we approximate this trial function by quadratic polynomials with two free parameters rather than a piecewise linear ansatz function. Similarly, this trial function will be approximated by the tanh function. Additionally, we accept several new types of soliton solutions, including bright solitons, dark solitons, bright–dark solitary wave solutions, rational dark–bright solutions, and periodic solitary wave solutions. Also, conditions for the stability of the solutions will be proposed. These explanations are of great importance in the fields of applied science and engineering. The results will be shown through different types of graphs, including 2D, 3D, and contour plots.

Tight inapproximability of Nash equilibria in public goods games

We study public goods games, a type of game where every player has to decide whether or not to produce a good which is public, i.e., neighboring players can also benefit from it. Specifically, we consider a setting where the good is indivisible and where the neighborhood structure is represented by a directed graph, with the players being the nodes. Papadimitriou and Peng (2023) recently showed that in this setting computing mixed Nash equilibria is PPAD-hard, and that this remains the case even for ε-well-supported approximate equilibria for some sufficiently small constant ε. In this work, we strengthen this inapproximability result by showing that the problem remains PPAD-hard for any non-trivial approximation parameter ε.

On the Asymptotic of Solutions of Odd-Order Two-Term Differential Equations

This work is devoted to the development of methods for constructing asymptotic formulas as x→∞ of a fundamental system of solutions of linear differential equations generated by a symmetric two-term differential expression of odd order. The coefficients of the differential expression belong to classes of functions that allow oscillation (for example, those that do not satisfy the classical Titchmarsh–Levitan regularity conditions). As a model equation, the fifth-order equation i2p(x)y‴″+p(x)y″‴+q(x)y=λy, along with various behaviors of coefficients p(x),q(x), is investigated. New asymptotic formulas are obtained for the case when the function h(x)=−1+p−1/2(x)∉L1[1,∞) significantly influences the asymptotics of solutions to the equation. The case when the equation contains a nontrivial bifurcation parameter is studied.

Contraction of variational principle and optical soliton solutions for two models of nonlinear Schrödinger equation with polynomial law nonlinearity

<abstract><p>Our study analyzes the two models of the nonlinear Schrödinger equation (NLSE) with polynomial law nonlinearity by powerful and comprehensible techniques, such as the variational principle method and the amplitude ansatz method. We will derive the functional integral and the Lagrangian of these equations, which illustrate the system's dynamic. The solutions of these models will be extracted by selecting the trial ansatz functions based on the Jost linear functions, which are continuous at all intervals. We start with the Jost function that has been approximated by a piecewise linear function with a single nontrivial variational parameter in three cases from a region of a rectangular box, then use this trial function to obtain the functional integral and the Lagrangian of the system without any loss. After that, we approximate this trial function by piecewise linear ansatz function in two cases of the two-box potential, then approximate it by quadratic polynomials with two free parameters rather than a piecewise linear ansatz function, and finally, will be approximated by the tanh function. Also, we utilize the amplitude ansatz method to extract the new solitary wave solutions of the proposed equations that contain bright soliton, dark soliton, bright-dark solitary wave solutions, rational dark-bright solutions, and periodic solitary wave solutions. Furthermore, conditions for the stability of the solutions will be submitted. These answers are crucial in applied science and engineering and will be introduced through various graphs such as 2D, 3D, and contour plots.</p></abstract>

Hamiltonian learning with real-space impurity tomography in topological moiré superconductors

Extracting Hamiltonian parameters from available experimental data is a challenge in quantum materials. In particular, real-space spectroscopy methods such as scanning tunneling spectroscopy allow probing electronic states with atomic resolution, yet even in those instances extracting the effective Hamiltonian is an open challenge. Here we show that impurity states in modulated systems provide a promising approach to extracting non-trivial Hamiltonian parameters of a quantum material. We show that by combining the real-space spectroscopy of different impurity locations in a moiré topological superconductor, modulations of exchange and superconducting parameters can be inferred via machine learning. We demonstrate our strategy with a physically-inspired harmonic expansion combined with a fully-connected neural network that we benchmark against a conventional convolutional architecture. We show that while both approaches allow extracting exchange modulations, only the former approach allows inferring the features of the superconducting order. Our results demonstrate the potential of machine learning methods to extract Hamiltonian parameters by real-space impurity spectroscopy as local probes of a topological state.

Transport of Spin Magnetic Multipole Moments Carried by Bloch Quasiparticles.

Magnetic ordering beyond the standard dipolar order has attracted significant attention in recent years, but it remains an open question how to effectively manipulate such nontrivial order parameters using external perturbations such as electric currents or fields. In particular, it is desirable to have a conceptual tool similar to nonequilibrium spin currents in spintronics to describe the creation and transport of multipole moments. In this context, we present a theory for Cartesian spin magnetic multipole moments of Bloch quasiparticles and their transport based on a general gauge-invariant formula obtained using the wave packet approach. As a concrete example, we point out that the low-energy Hamiltonian of phosphorene subject to a perpendicular electric field has a valley structure that hosts magnetic octupole moments. The magnetic octupole moments can be exhibited by an in-plane electric current and lead to accumulation of staggered spin densities at the corners of a rectangular sample. Our Letter paves the way for systematically seeking and utilizing quasiparticles with higher-order magnetic multipole moments in crystal materials towards the emergence of multipoletronics.

Topological transport properties of highly oriented Bi2Te3 thin film deposited by sputtering

Topological insulators (TIs) are the promising materials for next-generation technology due to their exotic features such as spin momentum locking, conducting surface states, etc. However, the high-quality growth of TIs by sputtering technique, which is one of the foremost industrial requirements, is extremely challenging. Also, the demonstration of simple investigation protocols to characterize topological properties of TIs using electron-transport methods is highly desirable. Here, we report the quantitative investigation of non-trivial parameters employing magnetotransport measurements on a prototypical highly textured Bi2Te3 TI thin film prepared by sputtering. Through the systematic analyses of the temperature and magnetic field dependent resistivity, all topological parameters associated with TIs, such as coherency factor , Berry phase (), mass term (m), the dephasing parameter (p), slope of temperature dependent conductivity correction () and the surface state penetration depth (λ) are estimated by using the modified ‘Hikami–Larkin–Nagaoka’, ‘Lu–Shen’ and ‘Altshuler–Aronov’ models. The obtained values of topological parameters are well comparable to those reported on molecular beam epitaxy grown TIs. The epitaxial growth of Bi2Te3 film using sputtering, and investigation of the non-trivial topological states from its electron-transport behavior are important for their fundamental understanding and technological applications.

Anisotropic Schrödinger black holes with hyperscaling-violation

We investigate novel exact solutions to an Einstein–Maxwell theory non-minimally coupled to a self-interacting dilaton-like scalar. Extending the results of Herrera-Aguilar et al. (Phys. Rev. D 103(12):124025, 2021. arXiv:2012.13412 [hep-th]; arXiv:2110.04445 [hep-th]), we report three families of exact configurations over a non-relativistic Schrödinger background with both, arbitrary dynamical critical exponent z and hyperscaling violating parameter theta in any dimension d. Concretely, we provide field configurations with hyperscaling violation which are locally Schrödinger spaces. Our solutions correspond to three kinds: a zero-temperature background, a naked singularity and, more interestingly, a family of black holes. To the latter, we construct the corresponding Carter–Penrose diagram with a view to understand their causal structure given the non-standard background. We show that a non-trivial hyperscaling violation parameter theta is necessary in order to support a real non-constant dilaton field in the configuration. We explore how the relation between the hyperscaling violation parameter and the critical dynamical exponent determine, in combination with the spacetime dimension, the kinematic aspects of the fields. A further refinement on the physically sensible configurations is obtained from the study of the null energy conditions. We provide a thorough study of the thermodynamics including the quasi-local computation of charges and the verification of the first law. We explore the effects in the thermodynamics from varying the rich parameter space, paying special attention in comparing the qualitative behavior of the thermodynamics of the scalar-free solutions and the ones with a nontrivial dilaton. Lastly, it is found that if the reality condition is loosen up on the scalar, the configuration is prone to acquiring a scalar charge.

Scaling behavior of observables as a model characteristic in multifield inflation

One of the fundamental questions in inflation is how to characterize the structure of different types of models in the field theoretic landscape. Proposals in this direction include attempts to directly characterize the formal structure of the theory by considering complexity measures of the potentials. An alternative intrinsic approach is to focus on the behavior of the observables that result from different models and to ask whether their behavior differs among models. This type of analysis can be applied even to nontrivial multifield theories where a natural measure of the complexity of the model is not obvious and the analytical evaluation of the observables is often impossible. In such cases one may still compute these observables numerically and investigate their behavior. One interesting case is when observables show a scaling behavior, in which case theories can be characterized in terms of their scaling amplitudes and exponents. Generically, models have nontrivial parameter spaces, leading to exponents that are functions of these parameters. In such cases we consider an iterative procedure to determine whether the exponent functions in turn lead to a scaling behavior. We show that modular inflation models can be characterized by families of simple scaling laws and that the scaling exponents that arise in this way in turn show scaling in dependence of the varying energy scales.

On the degradation of forest ecosystems by extreme events: Statistical Model Checking of a hybrid model

In this paper, we study the vulnerability of forest ecosystems perturbed by extreme events, such as those arising from climate change. To investigate the complex interactions between the biological dynamics of the forest and the climatic activity, we construct an original hybrid model, obtained by coupling a continuous reaction–diffusion system, which describes the spatio-temporal dynamics of the forest ecosystem, with a discrete probabilistic process, which models the possible occurrences of extreme events. Properties of ecological interest are considered: invariance of the persistence equilibrium, attraction to the extinction equilibrium and emergence of degraded states. Those properties of the hybrid model are verified through an extension of the Statistical Model Checking framework. We establish the existence of a threshold above which the persistence equilibrium of the forest ecosystem is compromised and give a numerical assessment of this threshold in terms of the probability and intensity of extreme events. We also present non-trivial parameter conditions for which the forest ecosystem converges to a degraded savanna-like state.