Few-particle Green's functions for strongly correlated systems on infinite lattices

We show how few-particle Green's functions can be calculated efficiently for models with nearest-neighbor hopping, for infinite lattices in any dimension. As an example, for one dimensional spinless fermions with both nearest-neighbor and second nearest-neighbor interactions, we investigate the ground states for up to 5 fermions. This allows us not only to find the stability region of various bound complexes, but also to infer the phase diagram at small but finite concentrations.Comment: 4 pages with 4 figures + 7 pages with 2 figures of suppl. materia

Phase transitions and quantum effects in anharmonic crystals

The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some temperature are given in the form of simple inequalities involving the interaction strength and the parameters describing a single oscillator. The main characteristic feature of the theory is that both mentioned phenomena are described in one and the same setting, in which thermodynamic phases of the model appear as probability measures on path spaces. Then the possibility of a phase transition to occur is related to the existence of multiple phases at the same values of the relevant parameters. Other definitions of phase transitions, based on the non-differentiability of the free energy density and on the appearance of ordering, are also discussed

Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip

Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a subsystem of discrete states coupled to an external environment characterized by a continuum of states, into which they generally decay. It is shown that, by flipping the discrete-continuum coupling from an Hermitian to a non-Hermitian interaction, thus resulting in a non unitary dynamics, time reversal of the subsystem of discrete states can be achieved, while the continuum of states is not reversed. Exact time reversal requires frequency degeneracy of the discrete states, or large frequency mismatch among the discrete states as compared to the strength of indirect coupling mediated by the continuum. Interestingly, periodic and frequent switch of the discrete-continuum coupling results in a frozen dynamics of the subsystem of discrete states.Comment: 9 pages, 4 figure