Luca Guido Molinari

Bio: Luca Guido Molinari is an academic researcher from University of Milan. The author has contributed to research in topics: Weyl tensor & Ricci curvature. The author has an hindex of 26, co-authored 117 publications receiving 2034 citations. Previous affiliations of Luca Guido Molinari include Istituto Nazionale di Fisica Nucleare.

Scaling properties of band random matrices.

Abstract: It is shown on the basis of numerical data that the normalized localization length of eigenvectors of band random matrices follows a scaling law. The scaling parameter is ${\mathit{b}}^{2}$/N, where b measures the bandwidth and N is the size of the matrix.

Cosmological perfect-fluids in f(R) gravity

Abstract: We show that an n-dimensional generalized Robertson–Walker (GRW) space-time with divergence-free conformal curvature tensor exhibits a perfect fluid stress–energy tensor for any f(R) gravity model....

Double excitations in finite systems

Abstract: Time-dependent density-functional theory (TDDFT) is widely used in the study of linear response properties of finite systems However, there are difficulties in properly describing excited states, which have double- and higher-excitation characters, which are particularly important in molecules with an open-shell ground state These states would be described if the exact TDDFT kernel were used; however, within the adiabatic approximation to the exchange-correlation (xc) kernel, the calculated excitation energies have a strict single-excitation character and are fewer than the real ones A frequency-dependent xc kernel could create extra poles in the response function, which would describe states with a multiple-excitation character We introduce a frequency-dependent xc kernel, which can reproduce, within TDDFT, double excitations in finite systems In order to achieve this, we use the Bethe–Salpeter equation with a dynamically screened Coulomb interaction W(ω), which can describe these excitations, and f

Generalized Robertson-Walker spacetimes — A survey

Abstract: Generalized Robertson–Walker spacetimes extend the notion of Robertson–Walker spacetimes, by allowing for spatial non-homogeneity. A survey is presented, with main focus on Chen's characterization ...

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Random Matrix Theories in Quantum Physics: Common Concepts

Abstract: We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.

Progress in Time-Dependent Density-Functional Theory

Abstract: The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Beginning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT have grown, so too has our understanding of the strengths and weakness...