BMN模型在相变中的传播复杂度
BMN Spread Complexity Across Phase Transitions
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中文总结 AI 辅助
该研究探究有限温度和化学势下带U(1)荷的质量形变BMN矩阵模型中量子态的传播复杂度演化，分析不同温度相的动力学行为，推导中间温度下Lanczos系数的次阶修正，补充相关技术推导的附录。
中文摘要 AI 辅助
我们研究了有限温度β⁻¹和化学势ν下，配备涌现U(1)整体荷的质量形变BMN矩阵模型中量子态的动力学行为与传播复杂度。聚焦强耦合 regime（μ≫1），我们通过带电热场双态（cTFD态）建模动力学，并追踪传播复杂度在三种不同热力学相中的演化：在低温有能隙相（βμ≫1），离散质量束缚态主导，捕获波包色散，产生非混沌的早期振荡增长；在高温连续相（βμ≪1），热激发压倒质量隙，驱动向连续平流场的转变，该场表现出最大混沌 scrambling，其Krylov李雅普诺夫指数λ_K=π/β达到普适界；在中间温度 regime（βμ~1，βν~1），质量束缚态与连续热背景的相互作用对Lanczos系数产生次阶修正b_n~(π/β)n+γ√n，该修正决定了完全混沌热化前的连续次指数交叉。关于KMS边界条件、巨正则谱矩、留数分析及Krylov空间中时间反演对称性破缺的技术推导，在四个专门附录中详细阐述。
英文摘要
We investigate the dynamical behavior and spread complexity of quantum states within the mass-deformed BMN matrix model equipped with an emergent $U(1)$ global charge at finite temperature $β^{-1}$ and chemical potential $ν$. Focusing on the strong-coupling regime ($μ\gg 1$), we model the dynamics via a charged Thermofield Double (cTFD) state and trace the evolution of spread complexity across three distinct thermodynamic regimes. In the low-temperature gapped phase ($βμ\gg 1$), discrete mass-gap bound states dominate, trapping wavepacket dispersion and producing non-chaotic, oscillatory early-time growth. Conversely, in the high-temperature continuum phase ($βμ\ll 1$), thermal excitations overwhelm the mass gap, driving a transition to a continuous advection field that exhibits maximal chaotic scrambling with a Krylov Lyapunov exponent $λ_K = π/ β$ that saturates the universal bound. In the intermediate temperature regime ($βμ\sim 1, βν\sim 1$), the interplay between mass-gap bound states and the continuous thermal background induces a sub-leading correction to the Lanczos coefficients $b_n \sim \fracπβ n + γ\sqrt{n}$, governing a continuous sub-exponential crossover before full chaotic thermalization. Technical derivations regarding KMS boundary conditions, grand canonical spectral moments, residue analysis, and time-reversal symmetry breaking in Krylov space are detailed in four dedicated appendices.
发表机构
- Indian Institute of Technology Roorkee（印度理工学院罗尔基分校）
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