Monday, January 28 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |
09:00 - 10:00 |
Gero Friesecke: The strong interaction limit of DFT: what's known, what's new, what's open (REVIEW) ↓ I will survey main results (both at the rigorous and the nonrigorous level) and open questions on the strongly correlated limit of DFT, including:
- the connection between Hohenberg-Kohn-Lieb-Levy constrained-search and minimization of the interaction energy over |Ψ|2 (alias Kantorovich optimal transport)
- the SCE (alias Monge) ansatz in the Kantorovich problem: where it works, where it fails
- the new quasi-Monge ansatz [1] which - unlike the SCE ansatz - always yields the minimum Kantorovich cost, but whose data complexity scales linearly instead of exponentially with the number of particles/marginals
- asymptotic and semi-empirical exchange-correlation functionals related to the strictly correlated limit
- representability challenges.
[1] G.Friesecke, D.Vögler, Breaking the curse of dimension in multi-marginal Kantorovich optimal transport on finite state spaces, SIAM J. Math. Analysis Vol. 50 No. 4, 3996-4019, 2018 (TCPL 201) |
10:00 - 10:30 |
Coffee Break (TCPL Foyer) |
10:30 - 11:30 |
Michael Seidl: The strictly correlated electron functional in chemistry and physics (REVIEW) (TCPL 201) |
11:30 - 12:00 |
Aurora Pribram-Jones: Strong interaction and thermal effects for finite-temperature density functional theory ↓ The strictly correlated electron approach to density functional theory, first proposed by Seidl and coworkers [1-4], offers a unique perspective on finite-temperature density functional theory and one of its application areas, simulations in the warm dense matter regime. In this region of phase space, many of the assumptions of traditional Kohn-Sham density functional theory no longer hold, requiring exchange-correlation free energy approximations that include explicit temperature dependence and better handling of complicated ionization processes. Formal analysis of the strong interaction limit for thermal ensembles will be demonstrated using the asymmetric Hubbard model, accompanied by discussions of the finite-temperature uniform gas and the competition between strong interaction and temperature in complicated physical systems.
[1] M. Seidl, Phys. Rev. A 60, 4387 (1999).
[2] M. Seidl, J. P. Perdew, and M. Levy, Phys. Rev. A 59, 51 (1999).
[3] M. Seidl, P. Gori-Giorgi, and A. Savin, Phys. Rev. A 75, 042511 (2007).
[4] P. Gori-Giorgi, G. Vignale, and M. Seidl, J. Chem. Theory Comput. 5, 743 (2009). (TCPL 201) |
12:00 - 13:30 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus. (Corbett Hall Lounge (CH 2110)) |
14:00 - 14:20 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL 201) |
14:20 - 15:20 |
Eric Cances: A mathematical introduction to Density Functional Theory and Kohn-Sham models (REVIEW) (TCPL 201) |
15:20 - 15:45 |
Coffee Break (TCPL Foyer) |
15:45 - 16:15 |
Jonas Lampart: The role of interactions in the Runge-Gross Theorem ↓ Time-dependent density functional theory relies on a one-to-one correspondence between external potentials in the N-particle Schrodinger equation and the one-particle densities they generate. Runge and Gross argued that this correspondence holds (up to a time-dependent constant in the potential) for sufficiently "nice" external potentials. I will discuss a mathematical setting for this argument and explain when it can be made fully rigorous. The interaction potentials play an important role for this and I will discuss the problems that arise in the presence of singular interactions, like the Coulomb potential. This is joint work with S. Fournais, M. Lewin, and T. Ostergaard Sorensen. (TCPL 201) |
16:15 - 16:30 |
Sara Giarrusso: Strong-interaction limit of an adiabatic connection in Hartree-Fock theory ↓ The talk will focus on the leading term in the strong-interaction limit of the adiabatic connection that has as weak-interaction expansion the Møller-Plesset perturbation theory. Such term can be fully determined from a functional of the Hartree-Fock density. We analyse this functional and highlight similarities and differences with the strong-interaction limit of the density-fixed adiabatic connection case of Kohn-Sham density functional theory. (TCPL 201) |
16:30 - 16:45 |
Juri Grossi: Functional derivative of the Zero Point Energy Functional from the Strong Coupling Limit of Density Functional Theory ↓ We compute explicitly the functional derivative of the subleading term in the strong coupling limit expansion of the generalized Hohenberg-Kohn functional for the special case of two electrons in one dimension, analyzing its features. (TCPL 201) |
16:45 - 17:00 |
Louis Garrigue: Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem ↓ The Hohenberg-Kohn theorem is one of the cornerstones of Density functional theory, and it relies on a unique continuation property, a mathematical tool which is in general used to prove uniqueness of Cauchy problems. We present a recent result on unique continuation which can treat potentials in many-body magnetic Schrödinger operator, and apply it to show the Hohenberg-Kohn theorem in presence of a fixed magnetic field. (TCPL 201) |
17:00 - 17:15 |
Laestadius Andre: Hohenberg-Kohn-like theorems for current densities ↓ We here discuss Hohenberg-Kohn-like theorems for systems with magnetic fields where different current densities are used together with the particle density. The situation is much more complicated than the case of no magnetic field, a fact that we further explore. (TCPL 201) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |