arXiv subjects

Jianghui Yu

Publications and source records attributed to Jianghui Yu.

3 recordsLinked to original sources

arXiv2026

Higher-Order Corrections to Scrambling Dynamics in Brownian Spin SYK Models

We investigate operator growth in a Brownian spin Sachdev--Ye--Kitaev (SYK) model with random all-to-all interactions, focusing on the full operator-size distribution. For Hamiltonians containing interactions of order two up to $L$, we derive a closed master equation for the Pauli-string expansion coefficients and recast their dynamics into a generating-function formulation suitable for the large-$N$ limit. This approach allows us to diagonalize the leading-order evolution operator explicitly and obtain exact solutions for arbitrary initial operator distributions, including the effects of decoherence. Going beyond leading order, we develop a systematic $1/N$ expansion that captures higher-order corrections to the operator-size dynamics and the late-time behavior. Our results demonstrate that higher-order effects play a crucial role in operator scrambling and that the full operator-size distribution provides a more refined probe of quantum chaos in Brownian and open quantum systems.

quant-ph↗

arXiv2025

Graph-Theoretic Analysis of $n$-Replica Time Evolution in the Brownian Gaussian Unitary Ensemble

In this paper, we investigate the $n$-replica time evolution operator $\mathcal{U}_n(t)\equiv e^{\mathcal{L}_nt} $ for the Brownian Gaussian Unitary Ensemble (BGUE) using a graph-theoretic approach. We examine the moments of the generating operator $\mathcal{L}_n$, which governs the Euclidean time evolution within an auxiliary $D^{2n}$-dimensional Hilbert space, where $D$ represents the dimension of the Hilbert space for the original system. Explicit representations for the cases of $n = 2$ and $n = 3$ are derived, emphasizing the role of graph categorization in simplifying calculations. Furthermore, we present a general approach to streamline the calculation of time evolution for arbitrary $n$, supported by a detailed example of $n = 4$. Our results demonstrate that the $n$-replica framework not only facilitates the evaluation of various observables but also provides valuable insights into the relationship between Brownian disordered systems and quantum information theory.

quant-ph↗

arXiv2021

Baby universes, ensemble averages and factorizations with matters

We investigate 2D topological gravity theories with matter fields turned on. We compute correlators of boundary creation operators with extra matter insertions. We provide a systematic procedure to determine a set of $\alpha$-states on which the correlation functions of the different boundary operators factorize. Our results suggest that the boundary dual is an ensemble average of theories with different numbers of replicas of a seed matter contribution that is represented by excitations on top of the gravity sector. The construction of the $\alpha$-states and the subsequent computations in the Hilbert space point of view are most conveniently done when the bulk couplings of the matter fields are expanded in a basis of vortices, which can be thought of as a 1-dimensional analogue of the SD-branes. We further demonstrate the existence of null states and the conditions imposed by reflection positivity. Moreover, in the CGS model with only disk and cylinder topologies, we map the baby universe creation and annihilation operators to the coupling constants in the one time SYK model, which allows us to match the wormhole and half-wormhole contributions in the CGS model explicitly to those identified in the SYK model. This explicitly realizes Coleman's initial idea. Some details of the computations in a variety of concrete models are presented.

hep-th↗