We used a thermally reversible hybrid gel made of billions of physically jam-packed swollen thermally sensitivepoly(N-isopropyl-acrylamide) chemical microgels. Laser light scattering study on a series of such hybrid g...We used a thermally reversible hybrid gel made of billions of physically jam-packed swollen thermally sensitivepoly(N-isopropyl-acrylamide) chemical microgels. Laser light scattering study on a series of such hybrid gels formed atdifferent gelling rates and temperatures revealed that the position-dependence of the scattering speckle pattern(staticnonergodicity) came from large voids formed during the sol-gel transition. With a proper preparation, such a nonergodicitycould be completely removed, indicating that the static nonergodicity generally observed in a gel is not indinsic, but comesfrom the clustering "island" structure formed during the gelation process.展开更多
We study non-equilibrium behaviors of a particle subjected to a high-frequency cutoff noise in terms of generalized Langevin equation, where the spectrum of internal noise is considered to be of the generalized Debye ...We study non-equilibrium behaviors of a particle subjected to a high-frequency cutoff noise in terms of generalized Langevin equation, where the spectrum of internal noise is considered to be of the generalized Debye form. A closed solution is impossible even if the equation is linear, because the Laplace transform of the memory kernel is a multi-value function. We use a numerical method to calculate the velocity correlation function of a force-free particle and the probability of a particle passing over the top of an inverse harmonic potential. We indicate the nonergodicity of the second type, i.e., the auto-correlation function of the velocity approaches to non-stationary at large times. Applied to the barrier passage problem, we find and analyse a resonant phenomenon that the dependence of the cutoff frequency is nonmonotonic when the initial directional velocity of the particle is less than the critical value, the latter is determined by the passing probability equal to 0.5.展开更多
A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed, which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling. This model allo...A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed, which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling. This model allows ballistic diffusion and classical localization simultaneously, in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken. The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium, however, when the system starts from nonthermal conditions, it does not approach the equilibration even though a nonlinear potential is used to bound the particle, this can be confirmed by the zerotb law of thermodynamics. In the dynamics of Brownian localization, due to the memory damping function inducing a constant term, our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum. The coupled oscillator chain with a fixed end boundary acts as a heat bath, which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration, we investigate this problem from the viewpoint of nonergodicity.展开更多
基金The financial support of the NNSF Fund (No. 29974027), the CAS Bai Ren Project, and the Research Grants Council of the Hong Kong Special Administration Region Earmarked Grant (CUHK 4266/00P, 2160135) is gratefully acknowledged.
文摘We used a thermally reversible hybrid gel made of billions of physically jam-packed swollen thermally sensitivepoly(N-isopropyl-acrylamide) chemical microgels. Laser light scattering study on a series of such hybrid gels formed atdifferent gelling rates and temperatures revealed that the position-dependence of the scattering speckle pattern(staticnonergodicity) came from large voids formed during the sol-gel transition. With a proper preparation, such a nonergodicitycould be completely removed, indicating that the static nonergodicity generally observed in a gel is not indinsic, but comesfrom the clustering "island" structure formed during the gelation process.
文摘We study non-equilibrium behaviors of a particle subjected to a high-frequency cutoff noise in terms of generalized Langevin equation, where the spectrum of internal noise is considered to be of the generalized Debye form. A closed solution is impossible even if the equation is linear, because the Laplace transform of the memory kernel is a multi-value function. We use a numerical method to calculate the velocity correlation function of a force-free particle and the probability of a particle passing over the top of an inverse harmonic potential. We indicate the nonergodicity of the second type, i.e., the auto-correlation function of the velocity approaches to non-stationary at large times. Applied to the barrier passage problem, we find and analyse a resonant phenomenon that the dependence of the cutoff frequency is nonmonotonic when the initial directional velocity of the particle is less than the critical value, the latter is determined by the passing probability equal to 0.5.
基金supported by the National Natural Science Foundation of China (Grant No. 11175021)
文摘A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed, which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling. This model allows ballistic diffusion and classical localization simultaneously, in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken. The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium, however, when the system starts from nonthermal conditions, it does not approach the equilibration even though a nonlinear potential is used to bound the particle, this can be confirmed by the zerotb law of thermodynamics. In the dynamics of Brownian localization, due to the memory damping function inducing a constant term, our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum. The coupled oscillator chain with a fixed end boundary acts as a heat bath, which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration, we investigate this problem from the viewpoint of nonergodicity.
