Related Experiment Video
Updated: Mar 2, 2026
11:22
Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
Published on: January 30, 2018
10.7K
Kramers problem for a dimer: Effect of noise correlations.
1Institute of Mathematical Sciences, 4th Cross Road, CIT Campus, Taramani, Chennai 600113, India.
Physical Review. E
|May 17, 2017
Summary
Correlated noise in a dimer system alters dynamics, affecting first passage times and relaxation behaviors. This study reveals unique system responses under varying noise correlations and coupling strengths.
Area of Science:
- Statistical Mechanics
- Chemical Physics
- Polymer Dynamics
Background:
- The Kramers problem describes escape from a potential well.
- Correlated noise processes can significantly alter system dynamics compared to independent noise.
- Understanding these effects is crucial for modeling complex systems like polymers.
Purpose of the Study:
- To investigate the Kramers problem for a dimer in a bistable potential with correlated noise.
- To analyze the impact of noise correlation and inter-particle coupling on system dynamics.
- To explore the system's behavior in strong coupling and extreme anticorrelation limits.
Main Methods:
- Studied the Kramers problem for a dimer in a piecewise linear potential.
- Incorporated correlated noise processes.
- Analyzed the strong coupling limit using adiabatic elimination.
- Investigated the distribution of first passage times.
Main Results:
- Correlated noise redistributes thermal power, causing deviations from independent noise dynamics.
- First passage time distributions exhibit exponentially decaying tails dependent on correlation and coupling.
- In the low noise intensity regime, relaxation and mean escape times are comparable.
- Higher noise levels lead to slower relaxation relative to escape times.
- Perfect anticorrelation results in deterministic behavior and trapping in potential minima.
Conclusions:
- Noise correlation is a critical factor influencing the dynamics of bistable systems.
- The findings have implications for understanding polymer dynamics in complex potentials.
- The study highlights the importance of considering noise correlations in physical models.
Related Concept Videos
01:10Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
2.8K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
2.8K
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
1.6K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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...
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...
1.6K
01:162D NMR: Overview of Homonuclear Correlation Techniques
726
Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
COSY90 is the standard two-dimensional (2D) COSY experiment that...
COSY90 is the standard two-dimensional (2D) COSY experiment that...
726
01:182D NMR: Overview of Heteronuclear Correlation Techniques
841
Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
841
01:13¹H NMR: Complex Splitting
2.0K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
2.0K
01:062D NMR: Homonuclear Correlation Spectroscopy (COSY)
2.0K
Homonuclear correlation spectroscopy, or COSY, is a 2-dimensional NMR technique that provides information about coupled protons. Typically, the geminal and vicinal coupling are observed. For example, consider the COSY spectrum of ethyl acetate, where its 1D proton NMR spectrum is plotted along the vertical and horizontal axes with their corresponding chemical shift scale. Three spots on the diagonal corresponding to the three peaks in the 1D proton spectrum are called diagonal peaks. The COSY...
2.0K