# Mean-field evolution of fermionic systems

Séminaire Laurent Schwartz — EDP et applications (2014-2015)

- Volume: 331, Issue: 3, page 1-13
- ISSN: 2266-0607

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topPorta, Marcello. "Mean-field evolution of fermionic systems." Séminaire Laurent Schwartz — EDP et applications 331.3 (2014-2015): 1-13. <http://eudml.org/doc/275807>.

@article{Porta2014-2015,

abstract = {We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent Hartree-Fock equation. Our theorems allow to describe the dynamics of both pure states (zero temperature states) and mixed states (positive temperature states). Our results hold for all times, and give effective estimates on the rate of convergence towards the Hartree-Fock evolution. The results on pure states are based on joint works with N. Benedikter and B. Schlein, [5, 6]; while those on mixed states are based on a joint work with N. Benedikter, V. Jaksic, C. Saffirio and B. Schlein, [7].},

author = {Porta, Marcello},

journal = {Séminaire Laurent Schwartz — EDP et applications},

keywords = {fermionic systems; Hamiltonian; Hilbert space; Hartree dynamics; Schrödinger equation; Hartree-Fock equation; initial data; solution},

language = {eng},

number = {3},

pages = {1-13},

publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},

title = {Mean-field evolution of fermionic systems},

url = {http://eudml.org/doc/275807},

volume = {331},

year = {2014-2015},

}

TY - JOUR

AU - Porta, Marcello

TI - Mean-field evolution of fermionic systems

JO - Séminaire Laurent Schwartz — EDP et applications

PY - 2014-2015

PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique

VL - 331

IS - 3

SP - 1

EP - 13

AB - We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent Hartree-Fock equation. Our theorems allow to describe the dynamics of both pure states (zero temperature states) and mixed states (positive temperature states). Our results hold for all times, and give effective estimates on the rate of convergence towards the Hartree-Fock evolution. The results on pure states are based on joint works with N. Benedikter and B. Schlein, [5, 6]; while those on mixed states are based on a joint work with N. Benedikter, V. Jaksic, C. Saffirio and B. Schlein, [7].

LA - eng

KW - fermionic systems; Hamiltonian; Hilbert space; Hartree dynamics; Schrödinger equation; Hartree-Fock equation; initial data; solution

UR - http://eudml.org/doc/275807

ER -

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