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The Berry phase, a concept of significant interest in quantum and classical mechanics, illuminates the dynamics of physical systems. Our current study explores this phenomenon within a classical granular network, employing an "elastic bit" that serves as a classical counterpart to the quantum bit. This approach establishes a connection between classical and quantum mechanics. By adjusting external forces, we generate an elastic bit within the granular network and map its behavior onto a Bloch sphere, akin to operating quantum logic gates. Varied manipulations of these external drivers yield a spectrum of Berry phases, from trivial (0) to nontrivial (π), unveiling the topological nature of the elastic bit. Crucially, this topological behavior is governed by external manipulations rather than the material or geometric properties of the medium. The nontrivial Berry phases, in particular, highlight energy localization within the granule vibrations, marking a significant insight into system dynamics. This research bridges the gap between the quantum and classical realms and paves the way for designing novel materials with unique properties.
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On the role of geometric phase in the dynamics of elastic waveguides
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of geometric phase, which is an additional phase factor occurring in dynamical systems, holds the same meaning across different fields of application, its use and interpretation can acquire important nuances specific to the system of interest. In recent years, the development of quantum topological materials and its extension to classical mechanical systems have renewed the interest in the concept of geometric phase. This review revisits the concept of geometric phase and discusses, by means of either established or original results, its critical role in the design and dynamic behaviour of elastic waveguides. Concepts of differential geometry and topology are put forward to provide a theoretical understanding of the geometric phase and its connection to the physical properties of the system. Then, the concept of geometric phase is applied to different types of elastic waveguides to explain how either topologically trivial or non-trivial behaviour can emerge based on the geometric features of the waveguide. This article is part of the theme issue ‘Current developments in elastic and acoustic metamaterials science (Part 2)’.
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- Award ID(s):
- 2330957
- PAR ID:
- 10586109
- Publisher / Repository:
- The Royal Society
- Date Published:
- Journal Name:
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 382
- Issue:
- 2279
- ISSN:
- 1364-503X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This study investigates the Berry phase, a key concept in classical and quantum physics, and its manifestation in a classical system. We achieve controlled accumulation of the Berry phase by manipulating the elastic bit (a classical analogue to a quantum bit) in an externally driven, homogeneous, spherical, nonlinear granular network. This is achieved through the classical counterpart of quantum coherent superposition of states. The elastic bit's state vectors are navigated on the Bloch sphere using external drivers' amplitude, phase, and frequency, yielding specific Berry phases. These phases distinguish between trivial and nontrivial topologies of the elastic bit, with the zero Berry phase indicating pure states of the linearized granular system and the nontrivial π phase representing equal superposed states. Other superposed states acquire different Berry phases. Crucially, these phases correlate with the structure's eigenmode vibrations: trivial phases align with distinct, in-phase, or out-of-phase eigenmodes, while nontrivial phases correspond to coupled vibrations where energy is shared among granules, alternating between oscillation and rest. Additionally, we explore Berry's phase generalizations for non-cyclic evolutions. This research paves the way for advanced quantum-inspired sensing and computation applications by utilizing and controlling the Berry phase.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rsta.2023.0357
