Quantum Butterfly Effect at the Crossroads of Spontaneous Symmetry Breaking
| Autor: | Das, Pranaya Pratik, Ganguli, Biplab |
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| Rok vydání: | 2023 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2304.14272 |
| Popis: | In classical mechanics, spontaneous symmetry breaking of the Hamiltonian can embroil the dynamics of some regular systems into chaos. The classical and quantum pictures are not entirely different in these broken symmetric regions. There exists a correspondence between them, but for a brief time window. However, our numerical observations show that quantum mechanics can emulate the opposite role and forge exponential fluctuations in classically non-chaotic systems within an early-time window by introducing a symmetry-breaking term to the Hamiltonian. In this work, we spontaneously break the existing symmetry in three one-dimensional quantum mechanical models by varying perturbation strength to bring anomaly into the system. With the help of numerical diagnostic tools such as OTOC, Loschmidt echo and spectral form factor(SFF) we detect the anomalies that may sweep into the system with the introduction of the asymmetry. Our primary focus is on the exponential growth of OTOC as it reduces to the Lyapunov exponent in the classical limit. However, these exponential growths of OTOC are not widespread over the entire potential well but are limited only to the eigenstates in the neighbourhood of the broken symmetry. These results suggest that the exponential growth of OTOC, backed by Loschmidt echo and SFF, is due to asymmetry. In other words, OTOC detects the effect of symmetry-breaking, which is often synonymous with the butterfly effect. Comment: 16 pages, 51 figures |
| Databáze: | OpenAIRE |
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