Extreme Decoherence and Quantum Chaos

We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus exceeding the polynomial dependence of systems with fluctuating $k$-body interactions. Our findings suggest the use of quantum chaotic systems as a natural test bed for spontaneous wave function collapse models. We further discuss the implications on the decoherence of AdS/CFT black holes resulting from the unitarity loss associated with energy dephasing.

Figure 1

Extreme decoherence. Comparisson of the decoherence rates associated with fluctuating chaotic systems $D_{\mathrm{GUE}}$ and $k$-body systems $D_{k\text{−}\text{body}}$, with $k=2$ as an example. Inset: The red dots represent the minimum particle number $n$ for which the decoherence rate in a chaotic system surpasses that of a $k$-body system. The condition where $D_{\mathrm{GUE}}>D_{k\text{−}\text{body}}$ is $k\lesssim [n/10+1]$.

Figure 2

Decoherence of a thermofield double state. (a) Purity ${⟨P_t⟩}_{\mathrm{GUE}}$ as a function of $\gamma t$ with different temperatures $\beta$. The numerical average is performed over 1000 realizations of GUE with $n=5$. (b) The decoherence rates for GUE ${\tilde{D}}_{\mathrm{GUE}}/\gamma$ versus the particle (treated as qubits) number $n$ for different temperatures $\beta$. With the increase in the Hilbert space dimension, ${\tilde{D}}_{\mathrm{GUE}}/\gamma$ saturates at $6/{\beta }^2$. (c) The decoherence rates (red solid curve) for GUE ${\tilde{D}}_{\mathrm{GUE}}/\gamma$ as a function of $\beta$ with $n=50$. The asymptotic expressions for ${\tilde{D}}_{\mathrm{GUE}}/\gamma =2^{n+1}$ under $\beta \ll {\beta }_c≔\sqrt{3/2^n}$ (purple dotted-dashed line) and ${\tilde{D}}_{\mathrm{GUE}}/\gamma =6/{\beta }^2$ under $\beta \gg {\beta }_c$ (black dashed line) are also shown.