Note on entropy dynamics in the Brownian SYK model

q-局域量子布朗SYK与自旋模型中算子尺寸分布的动力学

Dynamics of operator size distribution in q-local quantum Brownian SYK and spin models

本研究推导了q-局域布朗SYK和自旋模型中算子尺寸分布的精确主方程，给出大N解析解，揭示分布对初始条件的依赖及晚期平均尺寸的普适衰减行为。

长程质心守恒 Brownian SYK 模型中的流体动力学模式与算符扩散

Hydrodynamic modes and operator spreading in a long-range center-of-mass-conserving Brownian SYK model

针对质心守恒且具有 $1/r^η$ 长程相互作用的 Brownian SYK 模型，论文利用 Schwinger-Keldysh 与加倍 Hilbert 空间方法解析刻画输运流体动力学及 OTOC 光锥相图。

Majorana 和 Dirac 费米子的 Brownian SYK 模型的 Frame potential

Frame potential of Brownian SYK model of Majorana and Dirac fermions

本文通过 Keldysh 路径积分研究 Brownian SYK 模型的 Frame potential，发现 $q>2$ 时晚期鞍点正确饱和至 Haar 值，$q=2$ 时仅在 Gaussian 态空间饱和，并解决了 Dirac 费米子的全局 $U(1)$ 对称性问题。

Emergent Replica Conformal Symmetry in Non-Hermitian SYK$_2$ Chains

Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) ${O(2)\times O(2)}$ symmetries, which is broken to ${O(2)}$ by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone …

关于量子布朗运动中非热涨落-耗散关系的注记

Notes on a non-thermal fluctuation-dissipation relation in quantum Brownian motion

本文回顾了Schwinger-Keldysh形式论中幺正性和平稳性如何导出超越热平衡的量子广义涨落-耗散关系，并展示了其在量子布朗运动及广义Langevin方程中的应用。

A note on an absorption problem for a Brownian particle moving in a harmonic potential

An analysis is presented of a Brownian particle moving on the half-line, subject to a restoring force proportional to its displacement and an absorbing boundary at the origin. When the initial displacement is large, the central moments of the time to be absorbed tend to finite constants, as do the position moments when evaluated at the most probable absorption time. These quantities are derived explicitly.

混沌、纠缠与测量：关于量子信息动态的场论视角

Chaos, Entanglement and Measurement: Field-Theoretic Perspectives on Quantum Information Dynamics

本文通过场论方法研究量子信息在多体系统中的动态行为，探讨测量如何影响信息扩散与混乱过程。

Enhanced dynamics of active Brownian particles in periodic obstacle arrays and corrugated channels

We study the motion of an active Brownian particle (ABP) using overdamped Langevin dynamics on a two-dimensional substrate with periodic array of obstacles and in a quasi-one-dimensional corrugated channel comprised of periodically arrayed obstacles. The periodic arrangement of the obstacles enhances the persistent motion of the ABP in comparison to its motion in the free space. Persistent motion increases with the activity of the ABP. We note that the periodic arrangement induces directionality in ABP motion at late time, and it increases with the size of the obstacles. We also note that the …

随机费米子高斯动力学中的算符空间纠缠熵

Operator-Space Entanglement Entropy in Random Fermionic Gaussian Dynamics

该研究通过布朗SYK₂模型研究随机费米子高斯动力学下的算符空间纠缠熵，推导热力学极限下二分OSEE的精确表达式，利用RMT工具分析佩奇曲线，探讨OSEE与非高斯性度量的关联。

Introduction to the theory of stochastic processes and Brownian motion problems

These notes are an introduction to the theory of stochastic processes based on several sources. The presentation mainly follows the books of van Kampen and Wio, except for the introduction, which is taken from the book of Gardiner and the parts devoted to the Langevin equation and the methods for solving Langevin and Fokker-Planck equations, which are based on the book of Risken.

A note on confined diffusion

The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion operator. Unfortunately, the latter depend on space dimensionality and on the particular shape of the domain, and an analytical expression is in most circumstances not available. In this article, it is shown that the series may in some circumstances sum up exactly. Explicit calculations are performed for 2D diffusion restricted to a circular domain and 3D diffusion …