TCL6 and Beyond: Late-Time Resummations, Asymptotic Inflation and Time Limit

• URL: http://arxiv.org/abs/2406.11088v2
• Date: Wed, 29 Jan 2025 03:06:53 GMT
• Title: TCL6 and Beyond: Late-Time Resummations, Asymptotic Inflation and Time Limit
• Authors: Lance Lampert, Srikar Gadamsetty, Shantanu Chaudhary, Yiting Pei, Jiahao Chen, Elyana Crowder, Dragomir Davidović,
• Abstract summary: This article examines late-time resummations of perturbative master equations. We find inflation in quantum dynamics generators when environmental correlations decay algebraically with time.
• Score: 1.7620619500719317
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• Abstract: This article examines late-time resummations of perturbative master equations, and finds asymptotic inflation in quantum dynamics generators when environmental correlations decay algebraically with time. We utilize the time-convolutionless master equation (TCL), which we compute perturbatively as TCL2$n$, where 2$n$ is the order in the expansion in time-ordered cumulants. We introduce Hadamarded time-ordered cumulants and classify them by their late-time growth. In the unbiased spin boson model (SBM), we find a maximum order of the expansion $n_{\text{max}}=\lceil s+1\rceil $ above which the dynamics has {\it no} Markovian limit, resulting in the precision limit of the reduced states of $O(\lambda^{2\lceil s\rceil})$. $s$ is the exponent in the power law of the spectral density versus frequency at zero frequency and $\lambda$ is the dimensionless weak-coupling constant. We perform resummation of the leading cumulants in TCL2$n$, resulting in a new master equation with renormalized Bohr frequencies (rTCL). The frequency shifts include the imaginary decoherence rates and nonlocal spectral overlaps (F\"orsters resonances). The inflation rate in the unbiased SBM is temperature independent and equal to the decoherence rate $\nu_2$, leading to the time limit for the validity of master equations of $t_L\approx (s+1)/\nu_2$. rTCL can be regularized by analytic continuation, resulting in a highly accurate Markovian approximation respecting the precision limit. Only if the environmental correlations decay exponentially with time, the resummation generator have a Markovian limit below a threshold $\lambda$, in both biased and unbiased SBM.

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