TY - JOUR
AB - Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation.
AU - Benedikter, Niels P
ID - 7900
IS - 1
JF - Reviews in Mathematical Physics
SN - 0129-055X
TI - Bosonic collective excitations in Fermi gases
VL - 33
ER -
TY - JOUR
AB - We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.
AU - Boccato, Chiara
ID - 7685
IS - 1
JF - Reviews in Mathematical Physics
SN - 0129-055X
TI - The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime
VL - 33
ER -
TY - JOUR
AB - We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.
AU - Seiringer, Robert
ID - 10852
IS - 01
JF - Reviews in Mathematical Physics
KW - Mathematical Physics
KW - Statistical and Nonlinear Physics
SN - 0129-055X
TI - The polaron at strong coupling
VL - 33
ER -
TY - JOUR
AB - We first review the problem of a rigorous justification of Kubo’s formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo’s formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper, we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit.
AU - Henheik, Sven Joscha
AU - Teufel, Stefan
ID - 9285
IS - 01
JF - Reviews in Mathematical Physics
KW - Mathematical Physics
KW - Statistical and Nonlinear Physics
SN - 0129-055X
TI - Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results
VL - 33
ER -