#### Title

On The Stochastic Behavior of Brownian Particles in Potential Wells, as Observed with Optical Traps

#### Date of Award

2008

#### Level of Access Assigned by Author

Open-Access Thesis

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics

#### Advisor

R. Dean Astumian

#### Second Committee Member

James P. McClymer

#### Third Committee Member

Jayendran C. Rasaiah

#### Abstract

When the random fluctuations of a system are viewed as energetic fluctuations, many of the unique qualities of the system become irrelevant to the fundamental behavior. Consequently, many stochastic processes are fundamentally identical and are treated mathematically as such. For this reason the study of colloidal particles in aqueous solution has been invaluable to investigations of biologically relevant stochastic processes. This work addresses the motion of a Brownian particle, in a potential well, whose random fluctuations are described by a Gaussian-Markov random variable. By performing optical trapping experiments on micron sized, non-interacting, latex spheres in aqueous solution we have shown that at equilibrium, fluctuations in a forward sense are as likely to occur as fluctuations in the reverse sense. One relationship we have investigated relates the conditional probability of a transition occurring during a specific elapsed time and its spatial inverse to the equilibrium probabilities of the initial and final states a and b, P(b,∆t|a, 0)/P(a,∆t|b, 0) = e−∆U/kBT . We have shown this relationship holds for times both short and long compared to the average time to transition from a to b. A second relationship we have investigated, which may be explained by microscopic reversibility alone, equates the average time for a “direct” transition from a to b to the average time for a “direct” transition from b to a. We refer to these as last-touch-first-touchtimes (LTFTT), or the average time that elapses between the last touching of the initial position and the first touching of the final position. Experimental limitations prevented direct measurement of LTFTTs, however, we did observe an equality between last-observed-first-observed times (LOFOT). Using a discretized Langevin equation to simulate our system we recovered the equality between LTFTTs and obtained numerical results for LTFTTs.

#### Recommended Citation

Brody, Ross Paul, "On The Stochastic Behavior of Brownian Particles in Potential Wells, as Observed with Optical Traps" (2008). *Electronic Theses and Dissertations*. 266.

https://digitalcommons.library.umaine.edu/etd/266