Symmetries and local transformations of translationally invariant Matrix Product States

一种具有平方反比相互作用的新型平移不变超对称链：配分函数、热力学与临界性

A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality

本文提出一类具有平方反比长程相互作用的平移不变su(m|n)超对称自旋链，确立其玻色子-费米子对偶性，并借助相关多体动力学模型给出任意m、n和自旋数下的闭合配分函数；进而分析热力学Schottky峰与临界行为，证明仅m=0,1,2链可临界并计算相应中心荷。

与例外$X_m$多项式相关的任意D维有理扩展形状不变势

Rationally extended shape invariant potentials in arbitrary D-dimensions associated with exceptional $X_m$ polynomials

利用点正则变换（PCT）方法，得到了任意D维空间的有理扩展形状不变势。这些精确可解势的束缚态解可以用X_mLaguerre或X_mJacobi例外正交多项式表示。这些势与通常的势是等谱的，并具有几何形状不变性。

牛顿力学中的动力学相关对称性

Dynamics-dependent symmetries in Newtonian mechanics

我们展示了两个对称性的一维牛顿力学，其中一个解决方案是建立从另一个解决方案的历史，通过一般的非线性和复杂的潜在的依赖于时间的变换。一种对称性将动能和势能的平方根缠绕在一起，并将同一动力学问题的解联系起来（势能是不变函数）。另一种对称性连接了不同动力学问题的解（势是一个标量函数）。利用Noethers定理检验了相应守恒量的存在性，并证明了不变势对称性与能量守恒有关。在哈密顿-雅可比图中，不变势变换提供了点力学中依赖场对称性的一个例子。结果表明，这种变换不是薛定谔方程的对称性。

最低朗道能级中的试探波函数、分子态和振转光谱：玻色子和费米子的普遍描述

Trial wave functions, molecular states, and ro-vibrational spectra in the lowest Landau level: A universal description for bosons and fermions

通过引入一类适当的非线性不变试探波函数，我们证明了在有限系统中最低朗道能级（LLL）的强关联反映了与通过粒子局域化形成的分子的旋转和振动相关的内禀点群对称性的出现.这种分子描述是通用的，对玻色子和费米子都有效，对LLL光谱的yraast和激发态都有效，对低角动量和高角动量都有效。这种物理图像与贾斯特罗型试探函数所对应的“量子流体”图像有着根本的不同。

Quantum reference frame transformations as symmetries and the paradox of the third particle

In a quantum world, reference frames are ultimately quantum systems too -- but what does it mean to "jump into the perspective of a quantum particle"? In this work, we show that quantum reference frame (QRF) transformations appear naturally as symmetries of simple physical systems. This allows us to rederive and generalize known QRF transformations within an alternative, operationally transparent framework, and to shed new light on their structure and interpretation. We give an explicit description of the observables that are measurable by agents constrained by such quantum symmetries, and app…

Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems

We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian, and as such connect energy eigenstates from different total quasimomentum sectors. We consider quantum-chaotic and interacting integrable points of the Hamiltonian, and focus on average energies at the center of the spectrum. In the quantum-chaotic model, we find that there is eigenstate thermalization; specifically, the matrix elements are Gaussian distributed with a variance that is a smooth function of $ω=E_α-E_β$ ({$E_α$} are the eigenenergies) and scales as $1/D$ ($D…

发生时间可观测量：扩展到其他对称性

Time of ocurrence observables: expanding to other symmetries

本文将正算子值测度的时间测量构造方法推广到因果庞加莱变换，以构造协变时间可观测量。