Applications in Theoretical Physics
Module code: PA7112
Module co-ordinator: Dr Sergei Nayakshin
- Revision of classical mechanics.
- Applications: electron specific heat, equation of state of neutron star, black-body radiation.
- Phase space and its uses: the partition function. The Ergodic Hypothesis.
- Development of virial theorem and equation of state of interacting particle system.
- Need for numerical results
- Molecular Dynamics: Solving the equations of motion
- Monte Carlo methods: random variables have uses!
- Data analysis: Reverse Monte Carlo
Quantum finance and social science:
- Tools of analysis in finance/economics and physics
- Potential functions in social science
- Lagrangians and Principle of least action in social science
- Momentum conservation in finance? Hamiltonians in finance? Can the Hamiltonian be conserved?
- Fokker-Planck PDE in finance. Examples: trading models and volatility estimations
- Option pricing theory with the Backward Kolmogorov PDE: wealth approach versus stochastic approach
- Semi-classical approach: Bohmian mechanics : basics and interpretation of quantum potential
- Characteristics of the Newton-Bohm path; Quantum potential and Fisher information; applications to non-arbitrage theory
- Universal Brownian motion (stochastic mechanic counterpart of Hamilton-Jacobi equations); applications to option pricing
- Classical and quantum probability; probability interference and decision making paradoxes
- Quantum versus classical description of systems. Use of Dirac notation for states, operators and expectation values.
- Quantum counting: introducing annihilation, creation and number operators, and the need for non-abelian variables
- Dynamics via the Hamiltonian and the Heisenberg equation of motion.
- Interaction via quantum trading: A simple, universal model of fluctuations.
- Some simple toy models in finance and population dynamics
- Constructing Hamiltonians for more realistic models of many actor systems.
- 30 one-hour lectures
- Exam, three hours (70%)
- Coursework (30%)