Phase transition from the over-damping to under-damping states is a ubiquitous phenomenon in physical systems. However, what kind of symmetry is broken associated with this phase transition remains unclear. Here, we d...Phase transition from the over-damping to under-damping states is a ubiquitous phenomenon in physical systems. However, what kind of symmetry is broken associated with this phase transition remains unclear. Here, we discover that this phase transition is determined by an anti-parity-time(anti-PT) symmetry hidden in a single damping linear resonator, which is significantly different from the conventional anti-PT-symmetric systems with two or more modes. We show that the breaking of the anti-PT symmetry yields the phase transition from the over-damping to under-damping states, with an exceptional point(EP) corresponding to the critical-damping state. Moreover, we propose an optomechanical scheme to show this anti-PT symmetry breaking by using the optical spring effect in a quadratic optomechanical system. We also suggest an optomechanical sensor with the sensitivity enhanced significantly around the EPs for the anti-PT symmetry breaking. Our work unveils the anti-PT symmetry hidden in damping oscillations and hence opens up new possibilities for exploiting wide anti-PT symmetry applications in single damping linear resonators.展开更多
A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The re...A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The relationship among the resonant response amplitude and frequency, the reflection and transmission coefficients, the gap width, and the damping coefficient is obtained. A quantitative link between the damping coefficient of the theoretical dynamic model（ε） and that devised for the modified potential flow model（μ_p） is established, namely, μ_p=3πεω_n/8 （where ω_n is the natural frequency）. This link clarifies the physical meaning of the damping term introduced into the modified potential flow model. A new explicit approach to determine the damping coefficient for the modified potential model is proposed, without resorting to numerically tuning the damping coefficient by trial and error tests. The effects of the body breadth ratio on the characteristics of the gap resonance are numerically investigated by using both the modified potential flow model and the viscous RNG turbulent model. It is found that the body breadth ratio has a significant nonlinear influence on the resonant wave amplitude and the resonant frequency. With the modified potential flow model with the explicit damping coefficient, reasonable predictions are made in good agreement with the numerical solutions of the viscous fluid model.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12064010,12247105,12175061,11935006,11774086,1217050862,and 11775075)the Natural Science Foundation of Hunan Province(Grant No.2021JJ20036)the Science and Technology Innovation Program of Hunan Province(Grant Nos.2022RC1203,2020RC4047,and 2021RC4029)。
文摘Phase transition from the over-damping to under-damping states is a ubiquitous phenomenon in physical systems. However, what kind of symmetry is broken associated with this phase transition remains unclear. Here, we discover that this phase transition is determined by an anti-parity-time(anti-PT) symmetry hidden in a single damping linear resonator, which is significantly different from the conventional anti-PT-symmetric systems with two or more modes. We show that the breaking of the anti-PT symmetry yields the phase transition from the over-damping to under-damping states, with an exceptional point(EP) corresponding to the critical-damping state. Moreover, we propose an optomechanical scheme to show this anti-PT symmetry breaking by using the optical spring effect in a quadratic optomechanical system. We also suggest an optomechanical sensor with the sensitivity enhanced significantly around the EPs for the anti-PT symmetry breaking. Our work unveils the anti-PT symmetry hidden in damping oscillations and hence opens up new possibilities for exploiting wide anti-PT symmetry applications in single damping linear resonators.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51490673,51479025 and 51279029)
文摘A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The relationship among the resonant response amplitude and frequency, the reflection and transmission coefficients, the gap width, and the damping coefficient is obtained. A quantitative link between the damping coefficient of the theoretical dynamic model（ε） and that devised for the modified potential flow model（μ_p） is established, namely, μ_p=3πεω_n/8 （where ω_n is the natural frequency）. This link clarifies the physical meaning of the damping term introduced into the modified potential flow model. A new explicit approach to determine the damping coefficient for the modified potential model is proposed, without resorting to numerically tuning the damping coefficient by trial and error tests. The effects of the body breadth ratio on the characteristics of the gap resonance are numerically investigated by using both the modified potential flow model and the viscous RNG turbulent model. It is found that the body breadth ratio has a significant nonlinear influence on the resonant wave amplitude and the resonant frequency. With the modified potential flow model with the explicit damping coefficient, reasonable predictions are made in good agreement with the numerical solutions of the viscous fluid model.
