Semi-classical bound on Lyapunov exponent and acoustic Hawking radiation in $c=1$ matrix model
Semi-classical bound on Lyapunov exponent and acoustic Hawking radiation in $c=1$ matrix model
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$c=1$ 矩阵模型中李亚普诺夫指数和声学霍金辐射的半经典界
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发表时间：
2018
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通讯作者：
T. Morita
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作者：
T. Morita
经典粒子在反谐振势中的运动表现出对初始条件的指数敏感性，并且李雅普诺夫指数λ_L由势的形状唯一地确定。因此，如果我们天真地应用Lyapunov指数的界$lambda_L le 2pi T/hbar$，它就预言了这个系统中温度界(最低温度)的存在。我们考虑了逆谐振势(c=1矩阵模型)中的非相对论自由费米子，证明了温度最低的热辐射是由与Hawking辐射相似的量子力学引起的。这种辐射与玻色子非临界弦理论中费米海通过隧道的不稳定性有关，也与将$N$费米子视为费米流体的声霍金辐射有关。因此，逆谐振势可视为具有最低温度的热浴，且温度界可能是饱和的。
A classical particle motion in an inverse harmonic potential shows the exponential sensitivity of the initial condition, and the Lyapunov exponent $lambda_L$ is uniquely fixed by the shape of the potential. Hence, if we naively apply the bound on the Lyapunov exponent $lambda_L le 2pi T/ hbar$, it predicts the existence of the bound on temperature (the lowest temperature) in this system. We consider $N$ non-relativistic free fermions in the inverse harmonic potential ($c=1$ matrix model), and show that thermal radiation with the lowest temperature is induced quantum mechanically similar to the Hawking radiation. This radiation is related to the instability of the fermi sea through the tunneling in the bosonic non-critical string theory, and it is also related to acoustic Hawking radiation by regarding the $N$ fermions as a fermi fluid. Thus the inverse harmonic potential may be regarded as a thermal bath with the lowest temperature and the temperature bound may be saturated.