Response function of the second kind in many-body systems

Arnold J. Glick

Enrico Perfetto

We study the two-particle dynamics in one-dimensional (1D) electron systems described by the Tomonaga-Luttinger model. By using bosonization methods we compute analytically two different kinds of two-particle response functions. In the first case the creation of the two particles does not involve any other degree of freedom in the system, and the subsequent propagation is described by a standard two-body Green's function. This is relevant to address, e.g, the behavior of recently observed local pairs in 1D optical lattices. In the second case the creation of the two particles occurs coherently with the decay of a third localized particle. Such a condition is crucial to study the Auger transitions in 1D systems like carbon nanotubes, where two holes are left in the valence band after the decay of a core-hole.

Gianluca Stefanucci, Robert van Leeuwen

Ursula Schröter, Elke Scheer

For systems governed by two kinds of interactions it is shown that these can be built successively into the Green’s functions describing the system’s response. Whereas for the ordinary Green’s function the Dyson equation to solve has the same form in each step, we derive the non-trivial second-step equation for the transfer or coupling function, which on the one hand is closely related to the self-energy and on the other hand of practical relevance in transport calculations. PACS numbers: 02.60.Cb, 02.90.+p, 72.10.Bg 1.

Vedika Khemani

Lukas Junge, François Louis Antoine Visconti

We study the ground state energy of trapped two-dimensional Bose gases with mean-field type interactions that can be attractive. We prove the stability of second kind of the many-body system and the convergence of the ground state energy per particle to that of a non-linear Schrödinger (NLS) energy functional. Notably, we can take any polynomial scaling of the interaction, and even exponential scalings arbitrarily close to the Gross–Pitaevskii regime, which is a drastic improvement on the best-known result for systems with attractive interactions. As a consequence of the stability of second kind we also obtain Bose–Einstein condensation for the many-body ground states for a much improved range of the diluteness parameter.