Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScaling crossovers in activated escape of nonequilibrium systems: a resonantly driven oscillator
287
0
0.0
(
0
)
Authors
Oleg Kogan
Ask ChatGPT about the research
No Arabic abstract
The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears. Recently such behavior was observed and some of the earlier predicted exponents were found in experiments on several types of systems described by a model of a modulated oscillator. Here we establish the range where different scaling behavior is displayed and show how the crossover between different types of scaling occurs. The analysis is done for a nonlinear oscillator with two coexisting stable states of forced vibrations. Our numerical calculations, based on the the instanton method allow the mapping of the entire parameter range of bi-stability. We find the regions where the scaling exponents are 1 or 3/2, depending on the damping. The exponent 3/2 is found to extend much further from the bifurcation then were it would be expected to hold as a result of an over-damped soft mode. We also uncover a new scaling behavior with exponent of $approx$ 1.3 which extends, numerically, beyond the close vicinity of the bifurcation point.
rate research
Read More
We discuss the scaling of characteristic lengths in diffusion limited aggregation (DLA) clusters in light of recent developments using conformal maps. We are led to the conjecture that the apparently anomalous scaling of lengths is due to one slow crossover. This is supported by an analytical argument for the scaling of the penetration depth of newly arrived random walkers, and by numerical evidence on the Laurent coefficients which uniquely determine each cluster. We find a single crossover exponent of -0.3 for all the characteristic lengths in DLA. This gives a hint about the structure of the renormalization group for this problem.
Using path-integral methods, a formula is deduced for the noise-induced escape rate from an attracting fixed point across an unstable fixed point in one-dimensional maps. The calculation starts from the trace formula for the eigenvalues of the Frobenius-Perron operator ruling the time evolution of the probability density in noisy maps. The escape rate is determined from the loop formed by two heteroclinic orbits connecting back and forth the two fixed points of the one-dimensional map extended to a two-dimensional symplectic map. The escape rate is obtained with the expression of the prefactor to Arrhenius-vant Hoff exponential factor.
In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide class of microscopic stochastic models where they are satisfied. The description however does not refer in any way to an underlying microscopic dynamics: the only input required are transport coefficients as functions of thermodynamic variables, which are experimentally accessible. The basic postulates are local equilibrium which allows a hydrodynamic description of the evolution, the Einstein relation among the transport coefficients, and a variational principle defining the out of equilibrium free energy. Associated to the variational principle there is a Hamilton-Jacobi equation satisfied by the free energy, very useful for concrete calculations. Correlations over a macroscopic scale are, in our scheme, a generic property of nonequilibrium states. Correlation functions of any order can be calculated from the free energy functional which is generically a non local functional of thermodynamic variables. Special attention is given to the notion of equilibrium state from the standpoint of nonequilibrium.
The energy dissipation rate in a nonequilibirum reaction system can be determined by the reaction rates in the underlying reaction network. By developing a coarse-graining process in state space and a corresponding renormalization procedure for reaction rates, we find that energy dissipation rate has an inverse power-law dependence on the number of microscopic states in a coarse-grained state. The dissipation scaling law requires self-similarity of the underlying network, and the scaling exponent depends on the network structure and the flux correlation. Implications of this inverse dissipation scaling law for active flow systems such as microtubule-kinesin mixture are discussed.
Laser technology has developed and accelerated photo-induced nonequilibrium physics from both scientific and engineering viewpoints. The Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is a forefront of quantum physics of light-matter interaction, but limited to ideal dissipationless systems. For the Floquet engineering extended to a variety of materials, it is vital to understand the quantum states emerging in a balance of the periodic drive and energy dissipation. Here we derive the general description for nonequilibrium steady states (NESS) in periodically driven dissipative systems by focusing on the systems under high-frequency drive and time-independent Lindblad-type dissipation with the detailed balance condition. Our formula correctly describes the time-average, fluctuation, and symmetry property of the NESS, and can be computed efficiently in numerical calculations. Our approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems such as atoms and molecules, mesoscopic systems, and condensed matter.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
