arXiv subjects

Tian-Yi Wang

Publications and source records attributed to Tian-Yi Wang.

14 recordsLinked to original sources

arXiv2026

Quantifying Quantum Computational Advantage on a Processor of Ultracold Atoms

Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate connection with a random matrix ensemble, it is proposed to be classically intractable to sample the driven thermalized many-body states of a Bose-Hubbard system, and further extract multi-point correlations from the output-strings for characterizing quantum systems. Here, leveraging dedicated precise manipulations and atom-number-resolved detection through a quantum gas microscope with bichromatic superlattices, we perform sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of $10^{19}$ and outpacing the most powerful supercomputer in terms of sampling rate by three orders of magnitude. The volume law scaling of the \Renyi entanglement entropy in the thermalized phase is observed, which hinders efficient classical simulation for large systems. We employ the Bayesian tests to verify that our prepared systems operate in the driven thermalized phase. Multi-point correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases, where classical computations such as tensor network fails to give accurate and faithful predictions within a reasonable time cost. Our work demonstrates the sampling of a interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many-body systems.

cond-mat.quant-gas↗

arXiv2026

Global three-dimensional subsonic Euler flows past an axisymmetric obstacle with large vorticity

In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic Euler flow exists provided that the upstream density exceeds a critical threshold. The non-degeneracy of the axial velocity is rigorously established by combining the strong maximum principle with a refined continuity argument. The asymptotic behavior of the flow is obtained from uniform integral estimates for the difference between the flow and the upstream state. In addition, this result accommodates flows with large vorticity under a structural condition, thereby differing from previous results in the two-dimensional case.

math.AP↗

arXiv2025

Well-Posedness of Contact Discontinuity Solutions and Vanishing Pressure Limit for the Aw-Rascle Traffic Flow Model

This paper investigates the well-posedness of contact discontinuity solutions and the vanishing pressure limit for the Aw-Rascle traffic flow model with general pressure functions. The well-posedness problem is formulated as a free boundary problem, where initial discontinuities propagate along linearly degenerate characteristics. To address vacuum degeneracy, a condition at density jump points is introduced, ensuring a uniform lower bound for density. The Lagrangian coordinate transformation is applied to fix the contact discontinuity.The well-posedness of contact discontinuity solutions is established, showing that compressive initial data leads to finite-time blow-up of the velocity gradient, while rarefactive initial data ensures global existence. For the vanishing pressure limit, uniform estimates of velocity gradients and density are derived via level set argument. The contact discontinuity solutions of the Aw-Rascle system are shown to converge to those of the pressureless Euler equations, with matched convergence rates for characteristic triangles and discontinuity lines. Furthermore, under the conditions of pressure, enhanced regularity in non-discontinuous regions yields convergence of blow-up times.

math.AP↗

arXiv2023

Observation of microscopic confinement dynamics by a tunable topological $θ$-angle

The topological $θ$-angle is central to the understanding of a plethora of phenomena in condensed matter and high-energy physics such as the strong CP problem, dynamical quantum topological phase transitions, and the confinement--deconfinement transition. Difficulties arise when probing the effects of the topological $θ$-angle using classical methods, in particular through the appearance of a sign problem in numerical simulations. Quantum simulators offer a powerful alternate venue for realizing the $θ$-angle, which has hitherto remained an outstanding challenge due to the difficulty of introducing a dynamical electric field in the experiment. Here, we report on the experimental realization of a tunable topological $θ$-angle in a Bose--Hubbard gauge-theory quantum simulator, implemented through a tilted superlattice potential that induces an effective background electric field. We demonstrate the rich physics due to this angle by the direct observation of the confinement--deconfinement transition of $(1+1)$-dimensional quantum electrodynamics. Using an atomic-precision quantum gas microscope, we distinguish between the confined and deconfined phases by monitoring the real-time evolution of particle--antiparticle pairs, which exhibit constrained (ballistic) propagation for a finite (vanishing) deviation of the $θ$-angle from $π$. Our work provides a major step forward in the realization of topological terms on modern quantum simulators, and the exploration of rich physics they have been theorized to entail.

cond-mat.quant-gas↗

arXiv2023

On the convergence rates of multi-dimensional subsonic irrotational flows in unbounded domains

This paper is concerned with the convergence rates of subsonic flows for airfoil problem and infinite long largely-open nozzle problem, which is an improvement of [7,11,15,20]. The maximum principle is applied to estimate the potential function, by choosing the proper compared functions. Then, by the weighted Schauder estimates, the convergence rates of velocity at the far field are shown as $|x|^{-n+1}$. Furthermore, we construct the examples to show the optimality of our convergence rates and the expansion of the incompressible airfoil flow at infinity, indicating the higher convergence rates $|x|^{-n}$.

math.AP↗

arXiv2023

Isothermal Limit of Entropy Solutions of the Euler Equations for Isentropic Gas Dynamics

We are concerned with the isothermal limit of entropy solutions in $L^\infty$, containing the vacuum states, of the Euler equations for isentropic gas dynamics. We prove that the entropy solutions in $L^\infty$ of the isentropic Euler equations converge strongly to the corresponding entropy solutions of the isothermal Euler equations, when the adiabatic exponent $γ\rightarrow 1$. This is achieved by combining careful entropy analysis and refined kinetic formulation with compensated compactness argument to obtain the required uniform estimates for the limit. The entropy analysis involves careful estimates for the relation between the corresponding entropy pairs for the isentropic and isothermal Euler equations when the adiabatic exponent $γ\to 1$. The kinetic formulation for the entropy solutions of the isentropic Euler equations with the uniformly bounded initial data is refined, so that the total variation of the dissipation measures in the formulation is locally uniformly bounded with respect to $γ>1$. The explicit asymptotic analysis of the Riemann solutions containing the vacuum states is also presented.

math.AP↗

arXiv2020

Low Mach Number Limit and Far Field Convergence Rates of Potential Flows in Multi-Dimensional Nozzles With an Obstacle Inside

This paper considers the low Mach number limit and far field convergence rates of steady Euler flows with external forces in three-dimensional infinitely long nozzles with an obstacle inside. First, the well-posedness theory for both incompressible and compressible subsonic flows with external forces in multidimensional nozzle with an obstacle inside are established by several uniform estimates. The uniformly subsonic compressible flows tend to the incompressible flows as quadratic order of Mach number as the compressibility parameter goes to zero. Furthermore, we also give the convergence rates of both incompressible flow and compressible flow at far fields as the boundary of nozzle goes to flat even when the forces do not admit convergence rate at far fields. The convergence rates obtained for the flows at far fields clearly describe the effects of the external force.

math.AP↗

arXiv2020

Singularity formation for radially symmetric expanding wave of Compressible Euler Equations

In this paper, for compressible Euler equations in multiple space dimensions, we prove the break-down of classical solutions with a large class of initial data by tracking the propagation of radially symmetric expanding wave including compression. The singularity formation is corresponding to the finite time shock formation. We also provide some new global sup-norm estimates on velocity and density functions for classical solutions. The results in this paper have no restriction on the size of solutions, hence are large data results.

math.AP↗

arXiv2019

Steady Euler Flows with Large Vorticity and Characteristic Discontinuities in Arbitrary Infinitely Long Nozzles

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles. We first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity, or the Bernoulli and entropy functions, at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets/entropy waves by nonlinear arguments. This is the first result on the global existence of solutions of the multidimensional steady compressible full Euler equations with free boundaries, which are not necessarily small perturbations of piecewise constant background solutions. The subsonic-sonic limit of the solutions is also shown. Finally, through the incompressible limit, we establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets. The methods and techniques developed here will be useful for solving other problems involving similar difficulties.

math.AP↗

arXiv2019

Low Mach Number Limit of Multidimensional Steady Flows on the Airfoil Problem

In this paper, we justify the low Mach number limit of the steady irrotational Euler flows for the airfoil problem, which is the first result for the low Mach number limit of the steady Euler flows in an exterior domain. The uniform estimates on the compressibility parameter $\varepsilon$, which is singular for the flows, are established via a variational approach based on the compressible-incompressible difference functions. The limit is on the Hölder space and is unique. Moreover, the convergence rate is of order $\varepsilon^2$. It is noticeable that, due to the feature of the airfoil problem, the extra force dominates the asymptotic decay rate of the compressible flow to the infinity. And the effect of extra force vanishes in the limiting process from compressible flows to the incompressible ones, as the Mach number goes to zero.

math.AP↗

arXiv2019

Low Mach Number Limit of Steady Euler Flows in Multi-Dimensional Nozzles

In this paper, we consider the steady irrotational Euler flows in multidimensional nozzles. The first rigorous proof on the existence and uniqueness of the incompressible flow is provided. Then, we justify the corresponding low Mach number limit, which is the first result of the low Mach number limit on the steady Euler flows. We establish several uniform estimates, which does not depend on the Mach number, to validate the convergence of the compressible flow with extra force to the corresponding incompressible flow, which is free from the extra force effect, as the Mach number goes to zero. The limit is on the Holder space and is unique. Moreover, the convergence rate is of order $\varepsilon^2$, which is higher than the ones in the previous results on the low Mach number limit for the unsteady flow.

math.AP↗

arXiv2016

Diffusive Wave in the Low Mach Limit for Compressible Navier-Stokes Equations

The low Mach limit for 1D non-isentropic compressible Navier-Stokes flow, whose density and temperature have different asymptotic states at infinity, is rigorously justified. The problems are considered on both well-prepared and ill-prepared data. For the well-prepared data, the solutions of compressible Navier-Stokes equations are shown to converge to a nonlinear diffusion wave solution globally in time as Mach number goes to zero when the difference between the states at $\pm\infty$ is suitably small. In particular, the velocity of diffusion wave is only driven by the variation of temperature. It is further shown that the solution of compressible Navier-Stokes system also has the same property when Mach number is small, which has never been observed before. The convergence rates on both Mach number and time are also obtained for the well-prepared data. For the ill-prepared data, the limit relies on the uniform estimates including weighted time derivatives and an extended convergence lemma. And the difference between the states at $\pm\infty$ can be arbitrary large in this case.

math.AP↗

arXiv2016

Incompressible Limit of Solutions of Multidimensional Steady Compressible Euler Equations

A compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass conservation and the vorticity. Another observation is that the incompressibility of the limit for the homentropic Euler flow is directly from the continuity equation, while the incompresibility of the limit for the full Euler flow is from a combination of all the Euler equations. As direct applications of the compactness framework, we establish two incompressible limit theorems for multidimensional steady Euler flows through infinitely long nozzles, which lead to two new existence theorems for the corresponding problems for multidimensional steady incompressible Euler equations.

math.AP↗

arXiv2015

Subsonic-sonic Limit of Approximate Solutions to Multidimensional Steady Euler Equations

A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional irrotational case do not directly apply for the steady full Euler equations in higher dimensions. The new compactness framework we develop applies for both non-homentropic and rotational flows. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass balance and the vorticity, along with the Bernoulli law and the entropy relation, through a more delicate analysis on the phase space. As direct applications, we establish two existence theorems for multidimensional subsonic-sonic full Euler flows through infinitely long nozzles.

math.AP↗