相关论文: Det-Det Correlations for Quantum Maps: Dual Pair a…

The trace of an arbitrary product of quantum operators with the density operator is rendered as a multiple phase space integral of the product of their Weyl symbols with the Wigner function. Interspersing the factors with various evolution…

Operator scrambling is a crucial ingredient of quantum chaos. Specifically, in the quantum chaotic system, a simple operator can become increasingly complicated under unitary time evolution. This can be diagnosed by various measures such as…

The Renormalization Group equation describing the evolution of the metric of the nonlinear sigma model poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. In this article we…

In the realm of computer vision and graphics, accurately establishing correspondences between geometric 3D shapes is pivotal for applications like object tracking, registration, texture transfer, and statistical shape analysis. Moving…

Piecewise $\alpha$-stable Ornstein-Uhlenbeck (OU) processes arising in queue networks usually do not have an explicit dissipation, which makes the related numerical methods such as Euler-Maruyama (EM) scheme more difficult to analyze. We…

In this article, we study the scrambling dynamics in supersymmetric quantum mechanical systems. The eigenstate representation of such supersymmetric systems allows us to present an explicit form of the $2N$-point out-of-time-order…

We study large charge sectors in the $O(N)$ model in $6-\epsilon $ dimensions. For $4<d<6$, in perturbation theory, the quartic $O(N)$ theory has a UV stable fixed point at large $N$. It was recently argued that this fixed point can be…

We construct on-shell ${\mathcal{N}}=2$ nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ by holomorphically embedding the models in the hyper-K\"{a}hler nonlinear sigma model on the cotangent bundle of the Grassmann manifold $T^\ast…

We study unitary random matrix ensembles of the form $Z_{n,N}^{-1} |\det M|^{2\alpha} e^{-N \Tr V(M)}dM$, where $\alpha>-1/2$ and $V$ is such that the limiting mean eigenvalue density for $n,N\to\infty$ and $n/N\to 1$ vanishes quadratically…

We develop the ODE/IM correspondence for the higher-order Mathieu equation arising from the quantum Seiberg-Witten curve of the pure $SU(r+1)$ ${\cal N}=2$ supersymmetric Yang-Mills theory. From the subdominant solutions, we construct the…

We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the…

The renormalized trajectory (RT) is determined from two different Monte Carlo renormalization group techniques with $\delta$-function block spin transformation in the multi-dimensional coupling parameter space of the two-dimensional…

The presence of symmetries can lead to nontrivial dynamics of operator entanglement in open quantum many-body systems, which characterizes the cost of an matrix product density operator (MPDO) representation of the density matrix in the…

The surface code is a promising platform for a quantum memory, but its threshold under coherent errors remains incompletely understood. We study maximum-likelihood decoding of the square-lattice surface code in the presence of single-qubit…

This paper shows that the semi-dual formulation of the optimal transport problem has a degenerate saddle-point structure, and that its numerical solution is equivalent to solving a constrained optimization problem. We derive necessary and…

$O(n) \times O(m)$ symmetric Landau-Ginzburg models in $d=3$ dimension possess a rich structure of the renormalization group and its understanding offers a theoretical prediction of the phase diagram in frustrated spin models with…

This work develops an operator-theoretic and dynamical framework inspired by the Riemann--von Mangoldt formula, chaotic dynamics, and random-matrix models for the Riemann zeta function, without attempting to prove the Riemann Hypothesis.…

The uniform quadratic optimizatin problem (UQ) is a nonconvex quadratic constrained quadratic programming (QCQP) sharing the same Hessian matrix. Based on the second-order cone programming (SOCP) relaxation, we establish a new sufficient…

We extend our earlier work on the massive $O(N)$ nonlinear sigma model to other observables. We derive expressions at leading order in the large $N$ expansion at all orders in the loop expansion for the decay constant, vacuum expectation…

An extended formulation of out-of-time-ordered correlators (OTOCs), which quantify noncommutative operator growth and information scrambling in quantum many-body systems, is developed for turbulence dynamics as a representative of…