Related Experiment Video
Updated: Jun 14, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Spectral density of fluctuations in fractional bistable Klein-Kramers systems
1Department of Applied Mathematics, School of Science, Xi'an Jiaotong University, Xian 710049, People's Republic of China. kangyanmei2002@yahoo.com.cn
Abstract:
We investigate the stationary spectral density of fractional bistable Klein-Kramers systems. First, we deduce a dissipation-fluctuation relation between the stationary spectral density at thermal equilibrium and the linear response of the system to an applied perturbation. Second, we describe how to obtain the linear dynamic susceptibility from the method of moments, and thus we derive the fluctuating spectral density from the dissipation-fluctuation relation. Finally, we exhibit the structure of this fluctuating spectral distribution and explore the effect of the subdiffusion on it. Compared with the standard bistable Klein-Kramers systems, our observation on the spectral distribution in fractional systems reveals that the subdiffusion weakens the oscillatory components of the intrawell oscillation and the above-barrier motion. This phenomenon should reflect a fact that the particles tend to stand still in separate wells in subdiffusive processes.
Related Concept Videos
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
The de Broglie Wavelength
UV–Vis Spectroscopy: Molecular Electronic Transitions
Deactivation Processes: Jablonski Diagram

