The notion of a physical object overcoming an energetic barrier driven by random thermal fluctuations is ubiquitous in the physical sciences. For example, the barrier is known as the activation energy in chemical kinetics.
We work in an overdamped, stochastic-markovian setting and develop path integral formalisms working in the weak noise limit. The calculations get initiated from a Langevin equation: a deterministic, Newtonian equation that gets augmented by a stochastic noise term to perturb the particle trajectory to a `random walk’.
The Langevin equation is equivalent to a Fokker-Planck-Smoluchowski equation and offers no analytic tractability for potentials of order higher than quadratic. Hence, we seek to extract approximate solutions working with path integrals.
We are particularly interested in extending the contemporary theory into the complex domain to analyse the contributions from complex path trajectories to the transition probability.
Moreover, we are deeply interested in an underlying connection between the energy of the system and the Laplace parameter; we postulate that the energy is a scaled Laplace parameter.
- Mathematics BSc University of Leeds
- Mathematics MMath University of Leeds
- Awarded Top 10 Scholarship
- Awarded Leeds Doctoral Scholarship (LDS) Bursary
- Awarded HL Price Prize for my Master's thesis