AI 中文总结
本文利用$\boldsymbol{\tilde{PT}}$对称将奇粘滞性的难测量特性转化为测量原理，构建含非线性惯性项的奇纳维-斯托克斯方程，通过$\boldsymbol{\tilde{PT}}$相变等实现奇粘滞性的高灵敏度测量，为奇输运系数测量提供多类方案。
AI 中文摘要
奇粘滞性是时间反演对称性破缺流体的粘滞响应中无耗散的部分，因不做功而极难精确测量。本文表明，非厄米光学中熟知的宇称-时间（$\boldsymbol{\tilde{PT}}$）对称可将这种难以捉摸的特性转化为测量原理。包含非线性惯性项的奇纳维-斯托克斯方程具有$\boldsymbol{\tilde{PT}}$对称性，源于拉格朗日量，且线性化为奇粘滞性扮演普朗克常数角色的薛定谔方程；位涡满足广义厄特尔守恒律。被困在奇粘滞液体中的探针实现一对由奇摩擦耦合的振子，提供平衡损耗与增益会引发双重$\boldsymbol{\tilde{PT}}$相变，其例外点与拉比边带以平方根增强的灵敏度定位奇粘滞性。量子化后谱为福克-达尔文形式，耗散对展现出将线性加热与指数加热分隔的李奥维尔例外点。这些结果为经典与量子流体中奇输运系数的测量提供了力学、随机与光谱学方案。
英文摘要
Odd viscosity, the nondissipative part of the viscous response of a time-reversal-broken fluid, is notoriously difficult to measure precisely because it does no work. Here we show that parity-time ($\mathscr{PT}$) symmetry, familiar from non-Hermitian optics, converts this elusiveness into a measurement principle. The odd Navier-Stokes equations, that include the nonlinear inertial terms, are $\mathscr{PT}$-symmetric, follow from a Lagrangian, and linearize to a Schrödinger equation in which the odd viscosity plays the role of Planck's constant; potential vorticity obeys a generalized Ertel conservation law. A probe trapped in an odd liquid realizes a pair of oscillators coupled by odd friction, and supplying balanced loss and gain drives a twofold $\mathscr{PT}$ transition whose exceptional point and Rabi sidebands locate the odd viscosity with square-root-enhanced sensitivity. Upon quantization the spectrum is of Fock-Darwin form, and the dissipative pair exhibits a Liouvillian exceptional point separating linear from exponential heating. These results furnish mechanical, stochastic, and spectroscopic protocols for measuring odd transport coefficients in classical and quantum fluids.
