Fingerprints of classical memory in quantum hysteresis

Francesco Caravelli

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arXiv · 2601.20287

Fingerprints of classical memory in quantum hysteresis

Francesco Caravelli

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Abstract

We present a simple framework for classical and quantum ``memory'' in which the Hamiltonian at time $t$ depends on past values of a control Hamiltonian through a causal kernel. This structure naturally describes finite-bandwidth or filtered control channels and provides a clean way to distinguish between memory in the control and genuine non-Markovian dynamics of the state. We focus on models where $H(t)=H_0+\int_{-\infty}^{t}K(t-s)\,H_1(s)\,ds$, and illustrate the framework on single-qubit examples such as $H(t)=\sigma_z+\Phi(t)\sigma_x$ with $\Phi(t)=\int_{-\infty}^{t}K(t-s)\,u(s)\,ds$. We derive basic properties of such dynamics, discuss conditions for unitarity, give an equivalent time-local description for exponential kernels, and show explicitly how hysteresis arises in the response of a driven qubit.

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Francesco Caravelli. 2026-01-28. Fingerprints of classical memory in quantum hysteresis. https://arxiv.org/abs/2601.20287

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