A realization fo the q-harmonic oscillator

Kang Cheng .

mu1 t i p l i e d bya f u n c t i o n o f x', z and T . Here we have de f ined -r = (tr't r ) / n f o r l a t e r convenience. He then c a r r i e r s o u t c a l c u l a t i o n s as T + O ( o r n +a). H i s method has r e c e n t l y been a p p l i e d f o r e v a l u a t i n g t h e propag a t o r o f t ime-dependent fo rced harmonic occ i 1 l a t o r 5 . J n the p resen t work the sane method has been genera l i zed f u r t h e r t o c a l c u l a t e t h e propaga to r o f time-dependent harmonic o s c i l l a t o r w i t h cons tan t damping. I n Sec t ion 2, we a r e a b l e t o t rans fo rm o u r p a t h i n t e g r a l i n t o a f u n c t i o n o f x', x and T. t h e Gaussian i n t e g r a l (1.2) mul t i p l i e d by

Emmanuel G. Floratos, Theodore N. Tomaras

Miaomiao Zhao, Wei-Wei Yang, Hong‐Gang Luo +1 more

When non-magnetic impurity immerses in Fermi sea, a regular modulation of charge density around impurity will appear and such phenomena is called Friedel oscillation (FO). Although both Luttinger liquid and Landau Fermi liquid show such characteristic oscillation, FO in generic non-Fermi liquid (NFL) phase is still largely unknown. Here, we show that FO indeed exists in NFL state of an exactly solvable model, i.e. the Hatsugai-Kohmoto model which has been intensively explored in recent years. Combining T-matrix approximation and linear-response-theory, an interesting picture emerges, if two interaction-induced quasi-particles bands in NFL are partially occupied, FO in this situation is determined by a novel structure in momentum space, i.e. the 'average Fermi surface' (average over two quasi-particle Fermi surface), which highlights the inter-band particle-hole excitation. We hope our study here provides a counterintuitive example in which FO with Fermi surface coexists with NFL quasi-particle, and it may be useful to detect hidden 'average Fermi surface' structure in other correlated electron systems.

Emmanuel G. Floratos

Banhi Chatterjee, Jan Skolimowski, Krzysztof Byczuk

We study the interference patterns in the Friedel oscillations (FO) due to the scattering off either two or multiple impurities and scattering off extended inhomogeneities both in the non-interacting and two-dimensional lattice systems of interacting fermions. Correlations are accounted for by using an approximate method based on the real-space dynamical mean-field theory. We find that the interference maxima and minima change systematically as we vary the relative distance between the two impurities. At the same time, the interaction increase does not shift the position of interference fringes but only reduces their intensities. A comparison with the single impurity studies clearly shows complex patterns in FO induced by the additional scattering potentials. In the case of an extended step potential the system becomes more homogeneous when the interaction increases. FO and interference patterns are not present in the Mott insulating phase in the single and the many impurity models. Our theoretical study provides promising initial insights and motivate a further realistic modeling to investigate the role of interstitial defects, embedded impurities, ad-atoms on the surfaces, and surface irregularities in materials with different degrees of electronic correlation. For a complete description we also present analytical and numerical results of FO for non-interacting particles moving in a two and three dimensional continuous spaces. In the diluted impurity limit we derive results for FO due to scattering off many impurities, which are generalization of the original Friedel formula.