We study theoretically the coherent and correlated motion of many fermions inside an infinite square well potential. We will look at electrons and $^{3}\mathrm{He}$ atoms, which behave very differently not only because of their masses, but also because of their different interaction potential. Also, the level of theory and the role of approximations in the solution of the time-dependent Schr\"odinger equation will be discussed.We study theoretically the coherent and correlated motion of many fermions inside an infinite square well potential. We will look at electrons and $^{3}\mathrm{He}$ atoms, which behave very differently not only because of their masses, but also because of their different interaction potential. Also, the level of theory and the role of approximations in the solution of the time-dependent Schr\"odinger equation will be discussed.

Physical Review AFeb 17, 200630 citations

Correlated fermions on a lattice in high dimensions

E. M�ller-Hartmann

The European Physical Journal BDec 1, 1989650 citations

Cover Picture: ZAMM 4/2009

The cover page of 2009 shows high-resolution interference “quantum carpet” patterns for the momentum wave function of an interacting Bose-Einstein condensate (BEC). As time progresses (from back to front), the many-body mean field interaction of the BEC first leads to a broadening of the wave function, but then also to a time-varying interference structure by inducing site-dependent nonlinear phase shifts when the BEC is confined in a spatially periodic potential. Imaging the wave function in momentum space for different times leads to a pattern that one reminds of a carefully woven carpet and is hence termed “quantum carpet”. Quantum carpets beautifully demonstrate the surprisingly high matter wave coherence of particle-particle interactions in the zero-temperature limit.The cover page of 2009 shows high-resolution interference “quantum carpet” patterns for the momentum wave function of an interacting Bose-Einstein condensate (BEC). As time progresses (from back to front), the many-body mean field interaction of the BEC first leads to a broadening of the wave function, but then also to a time-varying interference structure by inducing site-dependent nonlinear phase shifts when the BEC is confined in a spatially periodic potential. Imaging the wave function in momentum space for different times leads to a pattern that one reminds of a carefully woven carpet and is hence termed “quantum carpet”. Quantum carpets beautifully demonstrate the surprisingly high matter wave coherence of particle-particle interactions in the zero-temperature limit.

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikApr 6, 20090 citations

Dynamical Properties of Strongly Correlated Fermionic Systems

Stephan Haas

Jan 1, 19951 citation

We study theoretically the coherent and correlated motion of many fermions inside an infinite square well potential. We will look at electrons and

^{3}\mathrm{He}

atoms, which behave very differently not only because of their masses, but also because of their different interaction potential. Also, the level of theory and the role of approximations in the solution of the time-dependent Schr\"odinger equation will be discussed.