Applications in Theoretical Physics

Module code: PA7112

Module co-ordinator: Dr Sergei Nayakshin

Topics 

Statistical mechanics:

  • 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.

Computer Simulations:

  • 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.

Learning

  • 30 one-hour lectures

Assessment

  • Exam, three hours (70%)
  • Coursework (30%)