论文标题
超对称阳米尔型模型中的量子混乱：状态，纠缠和光谱形式的方程
Quantum chaos in supersymmetric Yang-Mills-like model: equation of state, entanglement, and spectral form-factors
论文作者
论文摘要
我们详细分析了低能量，低维征本形与光谱的高能混乱之间的急剧过渡，以使用Hamiltonian $ \ hat { \ hat {x} _1^2 \，\ hat {x} _2^2 \ right）\ otimes i + \ hat {x} _1 \ otimesσ_1 + \ hat {x} _2 _2 _2 _2 _2 _2 _2 \ otimies timesσ_3$，它模仿了banks-fisschler-susssssssssssssssssss stan forder stan forder（空间压缩的$ \ MATHCAL {N} = 1 $ SUPER-YANG-MILLS理论。我们猜想这种过渡可能类似于BFSS模型中$ d0 $ - brane和$ m $ - 理论制度之间的过渡，并发现它不会导致状态热力学方程式中的不规则性。我们证明了我们的超对称模型的实时光谱形式因子表现出``坡道''行为典型的量子混乱行为。我们还考虑了$ \ hat {h} _s $的特征态的纠缠熵和降低的密度矩阵的频谱，考虑到了自由度的一个子系统。低能特征态的纠缠熵实际上是与能量无关的。正是在随机矩阵型水平的间隔波动的开始时，这种行为迅速变成了能量纠缠的稳定生长。我们证明，降低密度矩阵的光谱也表现出通用的水平间距波动，即使对于超对称模型的基态也是如此。因此，即使是经常间隔的非差异本征态，也包含一些有关高能量下半古典混沌动力学的信息。
We analyze in detail a sharp transition between the low-energy, low-dimensional eigenstates and the high-energy chaotic bulk of the spectrum for a simple supersymmetric quantum-mechanical model with Hamiltonian $\hat{H}_S = \left(\hat{p}_1^2 + \hat{p}_2^2 + \hat{x}_1^2 \, \hat{x}_2^2 \right) \otimes I + \hat{x}_1 \otimes σ_1 + \hat{x}_2 \otimes σ_3$, which mimics the structure of the Banks-Fischler-Susskind-Stanford (BFSS) matrix model, the spatially compactified $\mathcal{N} = 1$ super-Yang-Mills theory. We conjecture that this transition might be similar to the transition between the $D0$-brane and $M$-theory regimes in the BFSS model, and find that it does not lead to irregularities in the thermodynamic equation of state. We demonstrate that real-time spectral form-factor for our supersymmetric model exhibits the ``ramp'' behavior typical for quantum chaos. We also analyze the entanglement entropy and the spectrum of the reduced density matrix of the eigenstates of $\hat{H}_S$, considering one of the bosonic degrees of freedom as a subsystem. The entanglement entropy of low-energy eigenstates appears to be practically energy-independent. Exactly at the onset of random-matrix-type level spacing fluctuations, this behavior rapidly changes into a steady growth of entanglement with energy. We demonstrate that the spectrum of the reduced density matrix also exhibits universal level-spacing fluctuations towards its higher end, even for the ground state of the supersymmetric model. Thus even the regularly spaced, non-chaotic eigenstates contain some information about semi-classical chaotic dynamics at high energies.
