arXiv subjects

Jie Shen

Publications and source records attributed to Jie Shen.

At least 91 records · Page 5Linked to original sources

arXiv2024

SAV-based entropy-dissipative schemes for a class of kinetic equations

We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first and second order schemes are constructed. Since the positivity of the solution is closely related to entropy, we also propose positivity-preserving versions of these schemes to ensure robustness, which include a scheme specially designed for the Boltzmann equation and a more general scheme using Lagrange multipliers. The accuracy and provable entropy-dissipation properties of the proposed schemes are validated for both the Boltzmann equation and the Landau equation through extensive numerical examples.

math.NA↗

arXiv2024

Microwave-assisted unidirectional superconductivity in Al-InAs nanowire-Al junctions under magnetic fields

Under certain symmetry-breaking conditions, a superconducting system exhibits asymmetric critical currents, dubbed the ``superconducting diode effect". Recently, systems with the ideal superconducting diode efficiency or unidirectional superconductivity have received considerable interest. In this work, we report the study of Al-InAs nanowire-Al Josephson junctions under microwave irradiation and magnetic fields. We observe an enhancement of superconducting diode effect under microwave driving, featured by a horizontal offset of the zero-voltage step in the voltage-current characteristic that increases with microwave power. Devices reach the unidirectional superconductivity regime at sufficiently high driving amplitudes. The offset changes sign with the reversal of the magnetic field direction. Meanwhile, the offset magnitude exhibits a roughly linear response to the microwave power in dBm when both the power and the magnetic field are large. The signatures observed are reminiscent of a recent theoretical proposal using the resistively shunted junction (RSJ) model. However, the experimental results are not fully explained by the RSJ model, indicating a new mechanism for unidirectional superconductivity that is possibly related to non-equilibrium dynamics or dissipation in periodically driven superconducting systems.

cond-mat.mes-hall↗

arXiv2024

Versatile Method of Engineering the Band Alignment and the Electron Wavefunction Hybridization of Hybrid Quantum Devices

With the development of quantum technology, hybrid devices that combine superconductors (S) and semiconductors (Sm) have attracted great attention due to the possibility of engineering structures that benefit from the integration of the properties of both materials. However, until now, none of the experiments have reported good control of band alignment at the interface, which determines the strength of S-Sm coupling and the proximitized superconducting gap. Here, we fabricate hybrid devices in a generic way with argon milling to modify the interface while maintaining its high quality. First, after the milling the atomically connected S-Sm interfaces appear, resulting in a large induced gap, as well as the ballistic transport revealed by the multiple Andreev reflections and quantized above-gap conductance plateaus. Second, by comparing transport measurement with Schrödinger-Poisson (SP) calculations, we demonstrate that argon milling is capable of varying the band bending strength in the semiconducting wire as the electrons tend to accumulate on the etched surface for longer milling time. Finally, we perform nonlocal measurements on advanced devices to demonstrate the coexistence and tunability of crossed Andreev reflection (CAR) and elastic co-tunneling (ECT) -- key ingredients for building the prototype setup for realization of Kitaev chain and quantum entanglement probing. Such a versatile method, compatible with the standard fabrication process and accompanied by the well-controlled modification of the interface, will definitely boost the creation of more sophisticated hybrid devices for exploring physics in solid-state systems.

cond-mat.mes-hall↗

arXiv2024

Higher-Order Energy-Decreasing Exponential Time Differencing Runge-Kutta methods for Gradient Flows

In this paper, we develop a general framework for constructing higher-order, unconditionally energy-stable exponential time differencing Runge-Kutta methods applicable to a range of gradient flows. Specifically, we identify conditions sufficient for ETDRK schemes to maintain the original energy dissipation. Our analysis reveals that commonly used third-order and fourth-order ETDRK schemes fail to meet these conditions. To address this, we introduce new third-order ETDRK schemes, designed with appropriate stabilization, which satisfy these conditions and thus guarantee the unconditional energy decaying property. We conduct extensive numerical experiments with these new schemes to verify their accuracy, stability, behavior under large time steps, long-term evolution, and adaptive time stepping strategy across various gradient flows. This study is the first to examine the unconditional energy stability of high-order ETDRK methods, and we are optimistic that our framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable.

math.NA↗

arXiv2024

Structure preserving schemes for a class of Wasserstein gradient flows

We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass, positivity and to be uniquely solvable. In addition, they also ensure energy dissipation in many typical scenarios. Through extensive numerical experiments, we demonstrate the schemes' robustness, accuracy and efficiency.

math.NA↗

arXiv2024

A new flow dynamic approach for Wasserstein gradient flows

We develop in this paper a new regularized flow dynamic approach to construct efficient numerical schemes for Wasserstein gradient flows in Lagrangian coordinates. Instead of approximating the Wasserstein distance which needs to solve constrained minimization problems, we reformulate the problem using the Benamou-Brenier's flow dynamic approach, leading to algorithms which only need to solve unconstrained minimization problem in $L^2$ distance. Our schemes automatically inherit some essential properties of Wasserstein gradient systems such as positivity-preserving, mass conservative and energy dissipation. We present ample numerical simulations of Porous-Medium equations, Keller-Segel equations and Aggregation equations to validate the accuracy and stability of the proposed schemes. Compared to numerical schemes in Eulerian coordinates, our new schemes can capture sharp interfaces for various Wasserstein gradient flows using relatively smaller number of unknowns.

math.NA↗

arXiv2024

Inverse-current quantum electro-oscillations in a charge-density wave insulator

Quantum magneto-oscillations have long been a vital subject in condensed matter physics, with ubiquitous quantum phenomena and diverse underlying physical mechanisms. Here, we demonstrate the intrinsic and reproducible DC-current-driven quantum electro-oscillations with a periodicity in the inverse of the current (1/I), in quasi-one-dimensional charge-density-wave (CDW) insulators (TaSe$_4$)$_2$I and TaS$_3$ nanowires. Such oscillations manifest in the nearly infinite Fröhlich conductivity region where the undamped CDW flow forms in a finite electric current, and finally disappear after the oscillation index n reaches 1. A systematic investigation on the effect of temperature and magnetic field establishes that the observed electro-oscillations are a coherent quantum phenomenon. We discuss the possibilities of the physical mechanisms, including the formation of sliding-driven inherent Floquet sidebands. Our results introduce a new member in the family of quantum oscillations, and shed light on plausible avenues to explore novel physics and potential applications of coherent density-wave condensates.

cond-mat.mes-hall↗

arXiv2024

A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on rectangular domains and its applications

It is well known since 1960s that by exploring the tensor product structure of the discrete Laplacian on Cartesian meshes, one can develop a simple direct Poisson solver with an $\mathcal O(N^{\frac{d+1}d})$ complexity in d-dimension, where N is the number of the total unknowns. The GPU acceleration of numerically solving PDEs has been explored successfully around fifteen years ago and become more and more popular in the past decade, driven by significant advancement in both hardware and software technologies, especially in the recent few years. We present in this paper a simple but extremely fast MATLAB implementation on a modern GPU, which can be easily reproduced, for solving 3D Poisson type equations using a spectral-element method. In particular, it costs less than one second on a Nvidia A100 for solving a Poisson equation with one billion degree of freedoms. We also present applications of this fast solver to solve a linear (time-independent) Schrödinger equation and a nonlinear (time-dependent) Cahn-Hilliard equation.

math.NA↗

arXiv2024

Ta2Pd3Te5 topological thermometer

In recent decades, there has been a persistent pursuit of applications for surface/edge states in topological systems, driven by their dissipationless transport effects. However, there have been limited tangible breakthroughs in this field. This work demonstrates the remarkable properties of the topological insulator Ta2Pd3Te5, as a thermometer. This material exhibits a power-law correlation in temperature-dependent resistance at low temperatures, stemming from its Luttinger liquid behavior of edge states, while exhibiting semiconductor behavior at high temperatures. The power-law behavior effectively addresses the issue of infinite resistance in semiconductor thermometers at ultra-low temperatures, thereby playing a crucial role in enabling efficient thermometry in refrigerators supporting millikelvin temperatures or below. By employing chemical doping, adjusting thickness, and controlling gate voltage, its power-law behavior and semiconductor behavior can be effectively modulated. This enables efficient thermometry spanning from millikelvin temperatures to room temperature, and allows for precise local temperature measurement. Furthermore, this thermometer exhibits excellent temperature sensitivity and resolution, and can be fine-tuned to show small magnetoresistance. In summary, the Ta2Pd3Te5 thermometer, also referred to as a topological thermometer, exhibits outstanding performance and significant potential for measuring a wider range of temperatures compared to conventional low-temperature thermometers.

cond-mat.mtrl-sci↗

arXiv2024

Charge-4e and charge-6e flux quantization and higher charge superconductivity in kagome superconductor ring devices

The flux quantization is a key indication of electron pairing in superconductors. For example, the well-known h/2e flux quantization is considered strong evidence for the existence of the charge-2e, two-electron Cooper pairs. Here we report evidence for multi-charge flux quantization in mesoscopic ring devices fabricated using the transition-metal kagome superconductor CsV3Sb5. We perform systematic magneto-transport measurements and observe unprecedented quantization of magnetic flux in units of h/4e and h/6e in magnetoresistance oscillations. Specifically, at low temperatures, magnetoresistance oscillations with period h/2e are detected, as expected from the flux quantization for charge-2e superconductivity. We find that the h/2e oscillations are suppressed and replaced by resistance oscillations with h/4e periodicity when temperature is increased. Increasing the temperature further suppresses the h/4e oscillations and robust resistance oscillations with h/6e periodicity emerge as evidence for charge-6e flux quantization. Our observations provide the first experimental evidence for the existence of multi-charge flux quanta and emergent quantum matter exhibiting higher-charge superconductivity in the strongly fluctuating region above the charge-2e Cooper pair condensate, revealing new insights into the intertwined and vestigial electronic order in kagome superconductors.

cond-mat.supr-con↗

arXiv2024

Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene

Graphene-based, high quality two-dimensional electronic systems have emerged as a highly tunable platform for studying superconductivity. Specifically, superconductivity has been observed in both electron-doped and hole-doped twisted graphene moire systems, whereas in crystalline graphene systems, superconductivity has so far only been observed in hole-doped rhombohedral trilayer and hole-doped Bernal bilayer graphene (BBG). Recently, enhanced superconductivity has been demonstrated in BBG due to the proximity with a monolayer WSe2. Here, we report the observation of superconductivity and a series of flavor-symmetry-breaking phases in both electron- and hole-doped BBG/WSe2 device by electrostatic doping. The strength of the observed superconductivity is tunable by applied vertical electric fields. The maximum Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for the electron- and hole-doped superconductivity is about 210 mK and 400 mK, respectively. Superconductivities emerge only when applied electric fields drive BBG electron or hole wavefunctions toward the WSe2 layer, underscoring the importance of the WSe2 layer in the observed superconductivity. We find the hole-doped superconductivity violates the Pauli paramagnetic limit, consistent with an Ising-like superconductor. In contrast, the electron-doped superconductivity obeys the Pauli limit, even though the proximity induced Ising spin-orbit coupling is also notable in the conduction band. Our findings highlight the rich physics associated with the conduction band in BBG, paving the way for further studies into the superconducting mechanisms of crystalline graphene and the development of novel superconductor devices based on BBG.

cond-mat.supr-con↗

arXiv2024

Unique solvability and error analysis of the Lagrange multiplier approach for gradient flows

The unique solvability and error analysis of the original Lagrange multiplier approach proposed in [8] for gradient flows is studied in this paper. We identify a necessary and sufficient condition that must be satisfied for the nonlinear algebraic equation arising from the original Lagrange multiplier approach to admit a unique solution in the neighborhood of its exact solution, and propose a modified Lagrange multiplier approach so that the computation can continue even if the aforementioned condition is not satisfied. Using Cahn-Hilliard equation as an example, we prove rigorously the unique solvability and establish optimal error estimates of a second-order Lagrange multiplier scheme assuming this condition and that the time step is sufficient small. We also present numerical results to demonstrate that the modified Lagrange multiplier approach is much more robust and can use much larger time step than the original Lagrange multiplier approach.

math.NA↗

arXiv2024

On a new class of BDF and IMEX schemes for parabolic type equations

When applying the classical multistep schemes for solving differential equations, one often faces the dilemma that smaller time steps are needed with higher-order schemes, making it impractical to use high-order schemes for stiff problems. We construct in this paper a new class of BDF and implicit-explicit (IMEX) schemes for parabolic type equations based on the Taylor expansions at time $t^{n+β}$ with $β> 1$ being a tunable parameter. These new schemes, with a suitable $β$, allow larger time steps at higher-order for stiff problems than that is allowed with a usual higher-order scheme. For parabolic type equations, we identify an explicit uniform multiplier for the new second- to fourth-order schemes, and conduct rigorously stability and error analysis by using the energy argument. We also present ample numerical examples to validate our findings.

math.NA↗

arXiv2024

A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator Ta$_2$Pd$_3$Te$_5$

The interplay between topology and interaction always plays an important role in condensed matter physics and induces many exotic quantum phases, while rare transition metal layered material (TMLM) has been proved to possess both. Here we report a TMLM Ta$_2$Pd$_3$Te$_5$ has the two-dimensional second-order topology (also a quadrupole topological insulator) with correlated edge states - Luttinger liquid. It is ascribed to the unconventional nature of the mismatch between charge- and atomic- centers induced by a remarkable double-band inversion. This one-dimensional protected edge state preserves the Luttinger liquid behavior with robustness and universality in scale from micro- to macro- size, leading to a significant anisotropic electrical transport through two-dimensional sides of bulk materials. Moreover, the bulk gap can be modulated by the thickness, resulting in an extensive-range phase diagram for Luttinger liquid. These provide an attractive model to study the interaction and quantum phases in correlated topological systems.

cond-mat.mes-hall↗

arXiv2024

On a class of higher-order length preserving and energy decreasing IMEX schemes for the Landau-Lifshitz equation

We construct new higher-order implicit-explicit (IMEX) schemes using the generalized scalar auxiliary variable (GSAV) approach for the Landau-Lifshitz equation. These schemes are linear, length preserving and only require solving one elliptic equation with constant coefficients at each time step. We show that numerical solutions of these schemes are uniformly bounded without any restriction on the time step size, and establish rigorous error estimates in $l^{\infty}(0,T;H^1(Ω)) \bigcap l^{2}(0,T;H^2(Ω))$ of orders 1 to 5 in a unified framework.

math.NA↗

arXiv2024

A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system

For time-dependent PDEs, the numerical schemes can be rendered bound-preserving without losing conservation and accuracy, by a post processing procedure of solving a constrained minimization in each time step. Such a constrained optimization can be formulated as a nonsmooth convex minimization, which can be efficiently solved by first order optimization methods, if using the optimal algorithm parameters. By analyzing the asymptotic linear convergence rate of the generalized Douglas-Rachford splitting method, optimal algorithm parameters can be approximately expressed as a simple function of the number of out-of-bounds cells. We demonstrate the efficiency of this simple choice of algorithm parameters by applying such a limiter to cell averages of a discontinuous Galerkin scheme solving phase field equations for 3D demanding problems. Numerical tests on a sophisticated 3D Cahn-Hilliard-Navier-Stokes system indicate that the limiter is high order accurate, very efficient, and well-suited for large-scale simulations. For each time step, it takes at most $20$ iterations for the Douglas-Rachford splitting to enforce bounds and conservation up to the round-off error, for which the computational cost is at most $80N$ with $N$ being the total number of cells.

math.NA↗

arXiv2024

On the interplay of liquid-like and stress-driven dynamics in a metallic glass former observed by temperature scanning XPCS

Modern detector technology and highly brilliant fourth-generation synchrotrons allow to improve the temporal resolution in time-resolved diffraction studies. Profiting from this, we applied temperature scanning X-ray photon correlation spectroscopy (XPCS) to probe the dynamics of a Pt-based metallic glass former in the glass, glass transition region, and supercooled liquid, covering up to six orders of magnitude in time scales. Our data demonstrates that the structural alpha-relaxation process is still observable in the glass, although it is partially masked by a faster source of decorrelation observed at atomic scale. We present an approach that interprets these findings as the superposition of heterogeneous liquid-like and stress-driven ballistic-like atomic motions. This work not only extends the dynamical range probed by standard isothermal XPCS, but also clarifies the fate of the alpha-relaxation across the glass transition and provides a new perception on the anomalous, compressed temporal decay of the density-density correlation functions observed in metallic glasses and many out-of-equilibrium soft materials.

cond-mat.mtrl-sci↗

arXiv2024

Attribute-Efficient PAC Learning of Low-Degree Polynomial Threshold Functions with Nasty Noise

The concept class of low-degree polynomial threshold functions (PTFs) plays a fundamental role in machine learning. In this paper, we study PAC learning of $K$-sparse degree-$d$ PTFs on $\mathbb{R}^n$, where any such concept depends only on $K$ out of $n$ attributes of the input. Our main contribution is a new algorithm that runs in time $({nd}/ε)^{O(d)}$ and under the Gaussian marginal distribution, PAC learns the class up to error rate $ε$ with $O(\frac{K^{4d}}{ε^{2d}} \cdot \log^{5d} n)$ samples even when an $η\leq O(ε^d)$ fraction of them are corrupted by the nasty noise of Bshouty et al. (2002), possibly the strongest corruption model. Prior to this work, attribute-efficient robust algorithms are established only for the special case of sparse homogeneous halfspaces. Our key ingredients are: 1) a structural result that translates the attribute sparsity to a sparsity pattern of the Chow vector under the basis of Hermite polynomials, and 2) a novel attribute-efficient robust Chow vector estimation algorithm which uses exclusively a restricted Frobenius norm to either certify a good approximation or to validate a sparsity-induced degree-$2d$ polynomial as a filter to detect corrupted samples.

cs.DS↗