Getfert, Sebastian: Escape processes far from thermal equilibrium : path integrals and force spectroscopy. 2009
Inhalt
- List of Symbols
- List of Figures
- General introduction and concepts
- Single-molecule force spectroscopy: Theory and evaluation of experimental data
- Principle and theory of single-molecule force spectroscopy
- Introduction
- Single-molecule force spectroscopy with the AFM
- Atomic force microscope
- Force spectroscopy
- Force distance curves
- Force spectroscopy with other techniques
- Theoretical modeling of bond rupture
- Evaluation of single-molecule force spectroscopy experiments
- Parameter estimation: Properties of the maximum likelihood estimator
- Maximum likelihood estimator
- Asymptotic properties
- Cramér-Rao bound
- Parameter inference: Main steps for the practical application
- Application to Bell's model
- Extension of Bell's model
- Discussion
- Incompatibilities between experiment and theory
- Escape rates of overdamped Brownian particles far from thermal equilibrium
- A unified approach to the approximation of escape rates
- Introduction
- General formulation of the problem
- Theoretical framework
- A new path integral approach to the escape problem
- Renewal approach
- Approximation of the first passage time density
- Behavior of the optimizing paths in vicinity of the stable and unstable orbit
- Asymptotics of the integrand
- Expansion around asymptotic paths
- Main steps for a practical application
- Adiabatically slowly modulated potentials
- Examples
- Piecewise parabolic potential: General case with time-dependent coefficients
- The piecewise parabolic potential: Periodic tilting
- The piecewise parabolic potential: Moderately fast driving
- The cubic potential
- Time-dependent temperatures
- Suppression of thermally activated escape by heating
- Model
- Dynamics
- Case 1: Equilibrium condition
- Case 2: Effective escape rate
- Temperature modulations
- Model potential
- Transition rate
- The quasi-stationary distribution
- Non-equilibrium stabilization by heating
- Discussion
- Summary and outlook
- Appendices
- Supplements to chapter 4
- Asymptotic distribution of the maximum likelihood estimate
- Statistical uncertainties for Bell's model
- Optimal bin-width for histograms
- Supplements to chapter 6
- Limit of the integral (6.71)
- Series expansion of the first passage time density for a piecewise linear potential
- Escape rate for an adiabatically slowly driven, piecewise parabolic potential
- Escape rate from a piecewise parabolic potential: Rectangular pulse
- Bibliography
- Acknowledgments