Another comment on Bordley's “higher derivatives of velocity and quantum theory”

Edward R. Floyd

Robert F. Bordley

Irving John Good

Xi Dong, Diandian Wang, Wayne W. Weng +1 more

Abstract We prove the equivalence of two holographic computations of the butterfly velocity in higher-derivative theories with Lagrangian built from arbitrary contractions of curvature tensors. The butterfly velocity characterizes the speed at which local perturbations grow in chaotic many-body systems and can be extracted from the out-of-time-order correlator. This leads to a holographic computation in which the butterfly velocity is determined from a localized shockwave on the horizon of a dual black hole. A second holographic computation uses entanglement wedge reconstruction to define a notion of operator size and determines the butterfly velocity from certain extremal surfaces. By direct computation, we show that these two butterfly velocities match precisely in the aforementioned class of gravitational theories. We also present evidence showing that this equivalence holds in all gravitational theories. Along the way, we prove a number of general results on shockwave spacetimes.

Mendel Sachs

Jincheng Zhang

Quantum liquids, such as liquid helium and ultracold atomic gases, exhibit complex collective behaviors that traditional linear response theory fails to fully capture. In this work, we propose the theoretical framework of Hidden Sound Velocity in Quantum Liquids (HSVQL), hypothesizing the existence of multiple undiscovered collective velocities denoted as v_1, v_2, ..., v_n beyond standard propagation modes. By employing higher-order response theory, specifically analyzing the third-order susceptibility chi^(3) and nonlinear correlation functions, we demonstrate that nonlinear coupling channels reveal these hidden modes. We formulate a comprehensive hydrodynamic and microscopic theory to derive dispersion relations and quasiparticle characteristics, opening a new paradigm for uncovering novel excitations in strongly interacting many-body systems.