Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.09871 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911276712591360 |
|---|---|
| author | Matsushima, Kei Yamada, Takayuki |
| author_facet | Matsushima, Kei Yamada, Takayuki |
| contents | This study establishes a non-Bloch band theory for time-modulated discrete mechanical systems. We consider simple mass-spring chains whose stiffness is periodically modulated in time. Using the temporal Floquet theory, the system is characterized by linear algebraic equations in terms of Fourier coefficients. This allows us to employ a standard linear eigenvalue analysis. Unlike non-modulated linear systems, the time modulation makes the coefficient matrix non-Hermitian, which gives rise to, for example, parametric resonance, non-reciprocal wave transmission, and non-Hermitian skin effects. In particular, we study finite-length chains consisting of spatially periodic mass-spring units and show that the standard Bloch band theory is not valid for estimating their eigenvalue distribution. To remedy this, we propose a non-Bloch band theory based on a generalized Brillouin zone. The proposed theory is verified by some numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Bloch band theory for time-modulated discrete mechanical systems Matsushima, Kei Yamada, Takayuki Classical Physics Materials Science Pattern Formation and Solitons This study establishes a non-Bloch band theory for time-modulated discrete mechanical systems. We consider simple mass-spring chains whose stiffness is periodically modulated in time. Using the temporal Floquet theory, the system is characterized by linear algebraic equations in terms of Fourier coefficients. This allows us to employ a standard linear eigenvalue analysis. Unlike non-modulated linear systems, the time modulation makes the coefficient matrix non-Hermitian, which gives rise to, for example, parametric resonance, non-reciprocal wave transmission, and non-Hermitian skin effects. In particular, we study finite-length chains consisting of spatially periodic mass-spring units and show that the standard Bloch band theory is not valid for estimating their eigenvalue distribution. To remedy this, we propose a non-Bloch band theory based on a generalized Brillouin zone. The proposed theory is verified by some numerical experiments. |
| title | Non-Bloch band theory for time-modulated discrete mechanical systems |
| topic | Classical Physics Materials Science Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2407.09871 |