Spin 1/2 as propagation on a lattice with symmetries modulo gauge transformations

基于SAT模对称性的共证书学习

Co-Certificate Learning with SAT Modulo Symmetries

本文提出共证书学习扩展SMS框架，用于生成满足共NP性质的图，并改进Kochen-Specker向量系统下界，方法更快且扩展性更优。

Invariant current approach to wave propagation in locally symmetric structures

A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schrödinger equation. The local symmetries of the potential are encoded into corresponding local basis vectors in terms of symmetry-induced two-point invariant currents which map the basis amplitudes between symmetry-related points. A universal wavefunction structure in locally symmetric potentials is revealed, independently of the physical boundary conditions, by using special local bases which are adapted to the existing local symmet…

Symmetries and transport in site-dependently driven quantum lattices

We explore the quantum dynamics of particles in a spatiotemporally driven lattice. A powerful numerical scheme is developed, which provides us with the Floquet modes and thus enables a stroboscopic propagation of arbitrary initial states. A detailed symmetry analysis represents the cornerstone for an intricate manipulation of the Floquet spectrum. Specifically, we show how exact crossings can be converted into avoided ones, while the width of these resulting avoided crossings can be engineered by adjusting parameters of the local driving. Asymptotic currents are shown to be controllable over a…

Invariant currents and scattering off locally symmetric potential landscapes

We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of spatially invariant nonlocal currents, emerging when the corresponding generalized potential exhibits symmetries in arbitrary spatial domains. These invariants characterize the wave propagation and provide a spatial mapping of the wave function between any symmetry related domains. This generalizes the Bloch and parity theorems for broken reflection and translat…

耗散马约拉纳链——反常与非可逆对称性

Dissipative Majorana Chain---Anomalies and Non-Invertible Symmetries

该研究分析耗散马约拉纳链的对称性与反常，通过算子-态映射建立其Lindbladian的非厄米表述，结合格点玻色化与投影得到伊辛Lindbladian，为开放量子系统的相关扩展提供可控框架。

$XX$ 模型及其同类模型的 $\mathbb{Z}_2$ 规范对偶与自对偶性

$\mathbb{Z}_2$ gauging and self-dualities of the $XX$ model and its cousins

本文通过动量和绕数 $U(1)$ 对称性研究一维 $XX$ 格子模型及其同类模型，基于两个自对偶种子模型建立 $\mathbb{Z}_2$ 规范关系网络，推导出包括 $XX$ 和 Levin-Gu 模型在内的自对偶性，并统一了局部守恒荷映射框架。