A R/S Approach to Trends Breaks Detection

Quantum geometry of correlated many-body states

“…We also need to define the ordering of the operators in Eq. (19). Since the set (k, α) is countable, we associate a unique integer m(k, α) with every element of the set.…”

“…In a classic paper 13 , Walter Kohn had proposed that it is possible to characterize insulators in terms of the structure of the ground state alone. This idea was developed further by several others [14][15][16][17][18][19] , using quantum geometry to describe the structure of the ground state. In particular, the localisation tensor was identified with the integral of the quantum metric over the BZ 15 .…”

“…Thus, this line of work has led to a geometric theory of the insulating state. 19 In all the work discussed above, the quantum distances between two quasi-momenta, the geometric phase associated with three quasi-momenta and the corresponding quantum metric and BC on the BZ is defined in terms of single particle states and used to characterize the quantum geometry of mean-field states. Can these concepts be meaningfully generalised to describe the geometry of correlated states?…”

Molecular design of fullerene‐based ultralow‐k dielectrics

“…An overview of the experimental and theoretical methods for the determination of the polarisability of finite systems is given in [13]. The treatment of extended systems has been reformulated in the past decade with the result that the information about the polarisation is not in the electronic density but in the phases of the wavefunctions [14][15][16]. The present work is concentrated on structures that can approximately be considered in the Clausius-Mossotti limit of localised polarisable units with non-overlapping charge densities.…”