Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces

Understand

Statistical mechanics of 1D multivalent Coulomb gas may be mapped onto non-Hermitian quantum mechanics.

• We use this example to develop instanton calculus on Riemann surfaces.
• Borrowing from the formalism developed in the context of Seiberg-Witten duality, we treat momentum and coordinate as complex variables.
• Constant energy manifolds are given by Riemann surfaces of genus $g\geq 1$.