Stochastic symplectic ice

Dual wavefunction of the symplectic ice

The wavefunction of the free-fermion six-vertex model was found to give a natural realization of the Tokuyama combinatorial formula for the Schur polynomials by Bump-Brubaker-Friedberg. Recently, we studied the correspondence between the dual version of the wavefunction and the Schur polynomials, which gave rise to another combinatorial formula. In this paper, we extend the analysis to the reflecting boundary condition, and show the exact correspondence between the dual wavefunction and the symplectic Schur functions. This gives a dual version of the integrable model realization of the symplec…

Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions

We introduce generalizations of type $C$ and $B$ ice models which were recently introduced by Ivanov and Brubaker-Bump-Chinta-Gunnells, and study in detail the partition functions of the models by using the quantum inverse scattering method. We compute the explicit forms of the wavefunctions and their duals by using the Izergin-Korepin technique, which can be applied to both models. For type $C$ ice, we show the wavefunctions are expressed using generalizations of the symplectic Schur functions. This gives a generalization of the correspondence by Ivanov. For type $B$ ice, we prove that the ex…

Symplectic Noise & The Classical Analog of the Lindblad Generator

We introduce the concepts of Poisson brackets for classical noise, and of canonically conjugate Wiener processes (symplectic noise). Phase space diffusions driven by these processes are considered and the general form of a stochastic process preserving the full (system and noise) Poisson structure is obtained. We show that, once the classical stochastic model is required to preserve the joint system and noise Poisson bracket, it has much in common with quantum markovian models.

随机离散哈密顿变分积分器

Stochastic Discrete Hamiltonian Variational Integrators

本文提出了一种随机哈密顿系统的结构保持数值方法，通过构造随机离散哈密顿量来近似II型随机生成函数，统一了多种已有积分器并提出新的结构保持数值方案，所得积分器具有辛性、保持李群对称的守恒量，并包含随机辛龙格-库塔方法作为特例。

湍流闭合的辛理论：隐藏的储层动力学、内生随机输运与Kraichnan双级串

A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades

该研究提出辛几何闭合（SGC），基于多层随机模型几何约化构建，保留二维湍流双级串所需几何与哈密顿结构，重现Kraichnan理论算子架构，为几何约束的稳定数据驱动闭合提供基础。

Exact Mapping Noisy van der Pol Type Oscillator onto Quasi-symplectic Dynamics

We find exact mappings for a class of limit cycle systems with noise onto quasi-symplectic dynamics, including a van der Pol type oscillator. A dual role potential function is obtained as a component of the quasi-symplectic dynamics. Based on a stochastic interpretation different from the traditional Ito's and Stratonovich's, we show the corresponding steady state distribution is the familiar Boltzmann-Gibbs type for arbitrary noise strength. The result provides a new angle for understanding processes without detailed balance and can be verified by experiments.