Bulk-Edge Correspondence for Two-Dimensional Topological Insulators
- G. M. Graf, M. Porta
- Physics
- 25 July 2012
Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle…
Mean–Field Evolution of Fermionic Systems
- Niels Benedikter, M. Porta, B. Schlein
- Physics, Mathematics
- 13 May 2013
The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems.…
Effective Evolution Equations from Quantum Dynamics
- Niels Benedikter, M. Porta, B. Schlein
- Physics
- 9 February 2015
In these notes we review the material presented at the summer school on "Mathematical Physics, Analysis and Stochastics" held at the University of Heidelberg in July 2014. We consider the…
Lattice quantum electrodynamics for graphene
- A. Giuliani, V. Mastropietro, M. Porta
- Physics
- 24 July 2011
From the Hartree Dynamics to the Vlasov Equation
- Niels Benedikter, M. Porta, C. Saffirio, B. Schlein
- Mathematics
- 14 February 2015
We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards…
Mean‐Field Evolution of Fermionic Mixed States
- Niels Benedikter, V. Jaksic, M. Porta, C. Saffirio, B. Schlein
- Mathematics
- 4 November 2014
In this paper we study the dynamics of fermionic mixed states in the mean‐field regime. We consider initial states that are close to quasi‐free states and prove that, under suitable assumptions on…
Mean Field Evolution of Fermions with Coulomb Interaction
- M. Porta, Simone Rademacher, C. Saffirio, B. Schlein
- Physics
- 18 August 2016
We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges…
Mean-field dynamics of fermions with relativistic dispersion
- Niels Benedikter, M. Porta, B. Schlein
- Physics
- 25 November 2013
We extend the derivation of the time-dependent Hartree-Fock equation recently obtained by Benedikter et al. [“Mean-field evolution of fermionic systems,” Commun. Math. Phys. (to be published)] to…
Universality of Conductivity in Interacting Graphene
- A. Giuliani, V. Mastropietro, M. Porta
- Physics
- 11 January 2011
The Hubbard model on the honeycomb lattice describes charge carriers in graphene with short range interactions. While the interaction modifies several physical quantities, like the value of the Fermi…
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