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The exploration of the Berry phase in classical mechanics has opened new frontiers in understanding the dynamics of physical systems, analogous to quantum mechanics. Here, we show controlled accumulation of the Berry phase in a two-level elastic bit, which is a classical counterpart to qubits, achieved by manipulating coupled granules with external drivers. Employing the Bloch sphere representation, the paper demonstrates the manipulation of elastic bit states and the realization of quantum-analog logic gates. A key achievement is the calculation of the Berry phase for various system states, revealing insights into the system’s topological nature. Unique to this study is the use of external parameters to explore topological transitions, contrasting with traditional approaches focusing on internal system modifications. By linking the classical and quantum worlds through the Berry phase of an elastic bit, this work extends the potential applications of topological concepts in designing new materials and computational models.
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Combing a double helix
Combing hair involves brushing away the topological tangles in a collective curl, defined as a bundle of interacting elastic filaments. Using a combination of experiment and computation, we study this problem that naturally links topology, geometry and mechanics. Observations show that the dominant interactions in hair are those of a two-body nature, corresponding to a braided homochiral double helix. This minimal model allows us to study the detangling of an elastic double helix driven by a single stiff tine that moves along it and leaves two untangled filaments in its wake. Our results quantify how the mechanics of detangling correlates with the dynamics of a topological quantity, the link density, that propagates ahead of the tine and flows out the free end as a link current. This in turn provides a measure of the maximum characteristic length of a single combing stroke in the many-body problem on a head of hair, producing an optimal combing strategy that balances trade-offs between comfort, efficiency and speed of combing in hair curls of varying geometrical and topological complexity.
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- Award ID(s):
- 1830901
- PAR ID:
- 10356322
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 18
- Issue:
- 14
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 2767 to 2775
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/d1sm01533h
