Gamma‐convergence of gradient flows with applications to Ginzburg‐Landau
- E. Sandier, S. Serfaty
- Mathematics
- 1 December 2004
We present a method to prove convergence of gradient flows of families of energies that Γ‐converge to a limiting energy. It provides lower‐bound criteria to obtain the convergence that correspond to…
Vortices in the Magnetic Ginzburg-Landau Model
- E. Sandier, S. Serfaty
- Physics
- 19 December 2006
With the discovery of type-II superconductivity by Abrikosov, the prediction of vortex lattices, and their experimental observation, quantized vortices have become a central object of study in…
Bogoliubov Spectrum of Interacting Bose Gases
- Mathieu Lewin, P. T. Nam, S. Serfaty, J. P. Solovej
- Physics
- 12 November 2012
We study the large‐N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next…
A deterministic‐control‐based approach motion by curvature
- R. Kohn, S. Serfaty
- Mathematics
- 1 March 2006
The level‐set formulation of motion by mean curvature is a degenerate parabolic equation. We show that its solution can be interpreted as the value function of a deterministic two‐person game. More…
Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals
- N. Rougerie, S. Serfaty
- Physics
- 10 July 2013
We consider a classical system of n charged particles in an external confining potential in any dimension d ≥ 2. The particles interact via pairwise repulsive Coulomb forces and the coupling…
Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
- S. Serfaty
- Mathematics
- 1 September 2011
We are concerned with -convergence of gradient ows, which is a notion meant to ensure that if a family of energy functionals depending of a parameter -converges, then the solutions to the associated…
Large deviation principle for empirical fields of Log and Riesz gases
- Thomas Leblé, S. Serfaty
- Mathematics
- 10 February 2015
We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which…
From the Ginzburg-Landau Model to Vortex Lattice Problems
- E. Sandier, S. Serfaty
- Mathematics, Physics
- 20 November 2010
It is shown that the vortices of minimizer of Ginzburg-Landau, blown-up at a suitable scale, converge to minimizers of W, thus providing a first rigorous hint at the Abrikosov lattices, which is a next order effect compared to the mean-field type results.
Coulomb Gases and Ginzburg - Landau Vortices
- S. Serfaty
- Physics
- 26 March 2014
These are the lecture notes of a "Nachdiplomvorlesung" course taught at ETH Zurich in the Spring of 2013. They appeared in the EMS series Zurich Lectures in Advanced Mathematics.
2D Coulomb Gases and the Renormalized Energy
- E. Sandier, S. Serfaty
- Mathematics
- 17 January 2012
We study the statistical mechanics of classical two-dimensional “Coulomb gases” with general potential and arbitrary β, the inverse of the temperature. Such ensembles also correspond to random matrix…
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