Fingerprints of classical memory in quantum hysteresis
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908793267290112 |
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| author | Caravelli, Francesco |
| author_facet | Caravelli, Francesco |
| contents | 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 $H(t)=σ_z+Φ(t)σ_x$ with $Φ(t)=\int_{-\infty}^{t}K(t-s)\,u(s)\,ds$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20287 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fingerprints of classical memory in quantum hysteresis Caravelli, Francesco Quantum Physics Other Condensed Matter 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 $H(t)=σ_z+Φ(t)σ_x$ with $Φ(t)=\int_{-\infty}^{t}K(t-s)\,u(s)\,ds$. 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. |
| title | Fingerprints of classical memory in quantum hysteresis |
| topic | Quantum Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2601.20287 |