Stationary van Hove limit

2005 ◽  
Vol 46 (6) ◽  
pp. 063511 ◽  
Author(s):  
Jan Dereziński ◽  
Rafał Früboes
Keyword(s):  
Van Hove Limit

ON THE WEAK COUPLING LIMIT FOR A FERMI GAS IN A RANDOM POTENTIAL

1993 ◽  
Vol 05 (02) ◽  
pp. 209-298 ◽  
Author(s):  
T. G. HO ◽  
L. J. LANDAU ◽  
A. J. WILKINS
Keyword(s):  
Weak Coupling ◽  
Random Potential ◽  
Perturbation Expansion ◽  
Fermi Gas ◽  
Weak Coupling Limit ◽  
The State ◽  
Asymptotic State ◽  
Initial State ◽  
Translation Invariant ◽  
Van Hove Limit

General conditions are derived for the essential self-adjointness of –∆ + V, where V is a translation-invariant random potential, and for the existence of the perturbation expansion. A sequence of graphs is exhibited violating Dell'Antonio's bound for skeleton graphs. For a translation-invariant and clustering Gaussian random potential V, and a translation-invariant and clustering initial state S of the Fermi gas, uncorrelated with the random potential, the weak coupling limit (Van Hove limit) yields increase of entropy, propagation of chaos, convergence of the state for sufficiently small values of the parameter τ to a gauge-invariant and quasi-free asymptotic state, and the semigroup describing the evolution of the two-point function. The asymptotic system is Bernoulli. Results are obtained not only for the average over the random potential but also with probability one. If the random potential V′ is absolutely continuous with respect to V, and if the state S′ is given by a density matrix in the GNS representation for S, then the weak coupling limit is the same as for V and S.

scholarly journals Van Hove Limit for Infinite Systems

2010 ◽  
Vol 11 (7) ◽  
pp. 1303-1339 ◽  
Author(s):  
David Taj
Keyword(s):  
Infinite Systems ◽  
Van Hove Limit

Fermi gas on a lattice in the van Hove limit

1997 ◽  
Vol 87 (3-4) ◽  
pp. 821-845 ◽  
Author(s):  
T. G. Ho ◽  
L. J. Landau
Keyword(s):  
Fermi Gas ◽  
Van Hove Limit
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