Module 3 · Beyond Particle Physics
Statistical Physics & Quantum Mechanics
The Dirac Medal also recognises theoretical physics outside the unification programme: statistical mechanics, complex systems, condensed-matter physics, wave turbulence, and the foundations of quantum mechanics. The four lectures in this module showcase that range — including a four-part retrospective by E. C. G. Sudarshan, one of the architects of post-war quantum theory.
Giorgio Parisi — Off-Equilibrium Behaviour
Giorgio Parisi (Dirac Medal 1999) is best known for the replica-symmetry-breaking solution of the Sherrington–Kirkpatrick spin-glass model (1979–1980), which revealed an infinite hierarchy of metastable states in disordered systems and gave rise to a new theoretical vocabulary now applied across physics, biology, optimisation, and machine learning. He shared the 2021 Nobel Prize in Physics for the same body of work.
Giorgio Parisi — Off-Equilibrium Behaviour, Part 1
Replica symmetry breaking, the Parisi ansatz, and the ultrametric organisation of states in spin glasses — with the modern dynamical interpretation in terms of the fluctuation-dissipation theorem.
Giorgio Parisi — Off-Equilibrium Behaviour, Part 2
Aging, slow relaxation, and effective temperatures in glassy systems; connections to constraint-satisfaction problems and message-passing algorithms in computer science.
Vladimir Zakharov — Weak Turbulence
Vladimir Zakharov (Dirac Medal 2003) developed the modern theory of weak turbulence — the statistical mechanics of nonlinear waves with energy cascading through resonant triads or quartets. The Zakharov spectra are exact stationary non-equilibrium solutions of the wave-kinetic equation, analogous to the Kolmogorov 1941 spectrum for hydrodynamic turbulence. Applications run from capillary–gravity waves on the ocean surface to plasma turbulence and Bose condensates.
Vladimir Zakharov — Weak Turbulence, Part 1
The wave-kinetic equation for weakly nonlinear random waves, the Zakharov transformation, and the explicit power-law spectra it produces.
Vladimir Zakharov — Weak Turbulence, Part 2
Applications: ocean-wave forecasting, magnetohydrodynamic turbulence in the solar wind, and the recent rigorous derivation of wave-kinetic equations from nonlinear Schrödinger systems.
Roberto Car — Quantum Mechanics in a Glass of Water
Roberto Car (Dirac Medal 2009, with Michele Parrinello) invented Car–Parrinello molecular dynamicsin 1985 — a unified scheme that solves the electronic Schrödinger equation (within DFT) simultaneously with classical Newtonian motion of the nuclei. The method made first-principles simulations of liquids, glasses, and biomolecules computationally feasible. Car’s lecture, “Quantum mechanics in a glass of water,” tracks the technique from its origins to modern machine-learning potentials.
Roberto Car — Quantum Mechanics in a Glass of Water, Part 1
The Car–Parrinello Lagrangian, fictitious electronic dynamics, and how propagating wavefunctions on the Born–Oppenheimer surface lets you do ab-initio MD at QM accuracy.
Roberto Car — Quantum Mechanics in a Glass of Water, Part 2
Application to liquid water: hydrogen-bond network dynamics, autoionisation, proton transfer, and the move toward neural-network interatomic potentials trained on CPMD data.
E. C. G. Sudarshan — Half a Century of Physics (4 parts)
E. C. G. Sudarshan (1931–2018; Dirac Medal 2010) made foundational contributions across half a century of theoretical physics. With Marshak he proposed the V−A theory of weak interactions (1957) — the basis of the modern Standard Model description of charged-current weak processes. He developed the Sudarshan–Glauber P-representationof quantum optics. He worked on the quantum Zeno effect and the open systems formalism for quantum decoherence. This 4-part retrospective covers all of it.
E. C. G. Sudarshan — Half a Century of Physics, Part 1
Early work in Madras and Rochester; the V−A weak-interaction theory with Robert Marshak (1957) — six months before Feynman–Gell-Mann — and how the two papers came to share credit.
E. C. G. Sudarshan — Half a Century of Physics, Part 2
Quantum optics: the Sudarshan–Glauber P-representation as the universal phase-space representation of quantum optical states, and its consequences for non-classical light.
E. C. G. Sudarshan — Half a Century of Physics, Part 3
Open quantum systems: the GKLS (Gorini–Kossakowski–Lindblad–Sudarshan) form of the quantum master equation and the structure of completely-positive dynamical maps.
E. C. G. Sudarshan — Half a Century of Physics, Part 4
The quantum Zeno effect, tachyons, and reflections on the foundations of quantum mechanics — a century-spanning view from someone who watched most of it from the inside.