Search

Un testo di riferimento per la teoria delle equazioni alla derivate parziali (PDE) e lo (Smirnov 1988b, 1985). Un’ottima introduzione alle PDE in generale, ed in particolare alle PDE di interesse per la fisica, e data da (1998). Molto piu generale e dettagliato e il classico libro di (1949). Per gli esempi e le applicazioni delle serie di Fourier alla soluzione di particolari PDE, vedi (1989).

Kruger some years ago proposed a cluster LiBeBCNOF, now called periodane. His ground-state isomer proposal has recently been refined by Bera et al. using DFT. Here, we take the approach of molecules in such a cluster as starting point. We first study therefore the triangular molecule LiOB by coupled cluster theory (CCSD) and thereby specify accurately its equilibrium geometry in free space. The second fragment we consider is FBeCN, but treated now by restricted Hartree–Fock (RHF) theory. This four-center species is found to be linear, and the bond lengths are obtained from both RHF and CCSD calculations. Finally, we bring these two entities together and find that while LiOB remains largely intact, FBeCN becomes bent by the interaction with LiOB. Hartree–Fock and CCSD theories then predict precisely the same lowest isomer found by Bera et al. solely on the basis of DFT.

Recent ab initio predictions concerning the metal-insulator (MI) transition in rings of the light alkali atoms, Li and Na, are compared and contrasted with experimental facts concerning diluted Rb and Cs alkalis. The main focus here is on the local coordination number as a function of density as these two heavy alkali metallic fluids are taken along the liquid–vapour coexistence curve towards the critical point, which in these cases coincides with the MI transition. Also recorded are the results of experiments in which Cs chains are observed at large interatomic spacing outside semiconducting substrates of InSb and GaAs.

Motivated by current experimental interest in the interaction of H2O with nanographene, we have made a start on modelling the above system by reporting a Hartree-Fock calculation of H2O on coronene. The lowest energy configuration predicted has the H2O molecule perpendicular to the plane of the coronene molecule, with the oxygen atom away from the plane. The geometry of H2O in this adsorbed state is reported. The case of two H2O molecules interacting with anthracene is also considered, and compared with the structure of the free-space H2O dimer.

We evaluate the optical reflectivity for a uniaxially strained graphene single layer between a SiO2 substrate and air. A tight binding model for the band dispersion of graphene is employed. As a function of the strain modulus and direction, graphene may traverse one of several electronic topological transitions, characterized by a change of topology of its Fermi line. This results in features in the conductivity within the optical range, which might be observable experimentally., Comment: High Press. Res., to appear

After a brief summary of early work, involving the present authors, relating to low coordination phases of some alkalis in either dense crystalline states at high pressure (e.g. Li) or low density metallic fluids near criticality (Cs and Rb), contact is made with the very recent density functional study by Pickard and Needs (Phys. Rev. Lett. 102, 146401 (2009)). Whereas these authors predict three- and four-fold coordination numbers for extremely high pressure crystalline phases of Li, we stress here the remarkable behaviour of the heavy alkali metallic fluids Cs and Rb along the liquid-vapour coexistence curve towards the critical point. Coordination numbers ∼8-10 near melting then reduce, as the density is lowered, to 2 at or near the critical point.

In the centennial of Ettore Majorana's birth (1906-1938?), we re-examine some aspects of his fundamental scientific production in atomic and molecular physics, including a not well known short communication. There, Majorana critically discusses Fermi's solution of the celebrated Thomas-Fermi equation for electron screening in atoms and positive ions. We argue that some of Majorana's seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg-Majorana forces) in his later workson theoretical nuclear physics. In all his papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed., to appear in Found. Phys

The present study of small molecules containing silicon has been motivated by (a) the considerable interest being shown currently in the kinetics and reactivity of such molecules, and (b) the biotechnological potential of silicon-derivate surfaces as substrates in the adsorption of, for instance, amino acids and proteins. Therefore, we have studied by (i) a semi-empirical approach and (ii) an ab initio procedure employing low-order Moller-Plesset perturbation theory, the molecular correlation energies of some neutral closed and open shell silicon-containing molecules in the series SiXnYm. Procedure (i) is shown to have particular merit for the correlation of the ionic members studied in the above series, while the ab initio procedures employed come into their own for neutral species., Comment: Mol. Phys., to be published

The superconducting transition temperature Tc has earlier been correlated with coherence length and effective mass for a series of heavy Fermion (HF) materials at atmospheric pressure. Here, a further physical property, the dc electrical conductivity sigma(Tc), is one focal point, another being the pressure dependence of both Tc and sigma(Tc) for several HF materials. The relaxation time tau(Tc) is also studied in relation to an Uncertainty Principle limit, involving only the thermal energy kB Tc and Planck's constant., Comment: Supercond. Sci. Tech., to appear

Recent ab initio predictions concerning the metal-insulator (MI) transition in rings of the light alkali atoms, Li and Na, are compared and contrasted with experimental facts concerning diluted Rb and Cs alkalis. The main focus here is on the local coordination number as a function of density as these two heavy alkali metallic fluids are taken along the liquid-vapour coexistence curve towards the critical point, which in these cases coincides with the MI transition. Also recorded are the results of experiments in which Cs chains are observed at large interatomic spacing outside semiconducting substrates of InSb and GaAs.

In a recent study by Kornath et al. [J. Chem. Phys. 118 (2003) 6957], the Li_n clusters with n=2, 4 and 8 have been isolated in argon matrices at 15 K and characterized by Raman spectroscopy. This has prompted us to carry out a theoretical study on such clusters up to n=10, using Hartree-Fock theory, plus low-order Moeller-Plesset perturbation corrections. To check against the above study of Kornath et al., as a by-product we have made the same approximations for n=6 and 8 as we have for n=10. This has led us to emphasize trends with n through the Li_n clusters for (i) ground-state energy, (ii) HOMO-LUMO energy gap, (iii) dissociation energy, and (iv) Hartree-Fock eigenvalue sum. The role of electron correlation in distinguishing between low-lying isomers is plainly crucial, and will need a combination of experiment and theory to obtain decisive results such as that of Kornath et al. for Li_8. In particular, it is shown that Hartree-Fock theory plus bond order correlations does account for the experimentally observed symmetry T_d symmetry for Li_8., accepted for publication in J. Chem. Phys

For a given crystal structure, say body-centred-cubic, the many-body Hamiltonian in which nuclear and electron motions are to be treated from the outset on the same footing, has parameters, for the elements, which can be classified as (i) atomic mass M, (ii) atomic number Z, characterizing the external potential in which electrons move, and (iii) bcc lattice spacing, or equivalently one can utilize atomic volume, Omega. Since the thermodynamic quantities can be determined from H, we conclude that Tc, the superconducting transition temperature, when it is non-zero, may be formally expressed as Tc = Tc^(M) (Z, Omega). One piece of evidence in support is that, in an atomic number vs atomic volume graph, the superconducting elements lie in a well defined region. Two other relevant points are that (a) Tc is related by BCS theory, though not simply, to the Debye temperature, which in turn is calculable from the elastic constants C_{11}, C_{12}, and C_{44}, the atomic weight and the atomic volume, and (b) Tc for five bcc transition metals is linear in the Cauchy deviation C* = (C_{12} - C_{44})/(C_{12} + C_{44}). Finally, via elastic constants, mass density and atomic volume, a correlation between C* and the Debye temperature is established for the five bcc transition elements., EPJB, accepted

In the high-Tc cuprates, the unusual dependence of Tc on external pressure results from the combination of the nonmonotonic dependence of Tc on hole doping or hole-doping distribution among inequivalent layers, and from an ``intrinsic'' contribution. After reviewing our work on the interplay among Tc, hole content, and pressure in the bilayered and multilayered cuprate superconductors, we will discuss how the proximity to an electronic topological transition (ETT) may give a microscopic justification of the ``intrinsic'' pressure dependence of Tc in the cuprates. As a function of the proximity to an ETT, we recover a nonmonotonic behaviour of the superconducting gap at T=0, regardless of the pairing symmetry of the order parameter. This is in agreement with the trend observed for Tc as a function of pressure and other material specific quantities in several high-Tc cuprates. In the case of epitaxially strained cuprate thin films, we argue that an ETT can be driven by a strain-induced modification of the in-plane band structure, at constant hole content, at variance with a doping-induced ETT, as is usually assumed. We also find that an increase of the in-plane anisotropy enhances the effect of fluctuations above Tc on the normal-state transport properties, which is a fingerprint of quantum criticality at T=0., EHPRG Award Lecture, http://www.ehprg.org. To be published in J. Phys.: Cond. Matter

Imaging the effects of an impurity like Zn in high-T-c superconductors [Nature 61 (2000) 746] has rekindled interest in defect problems in the superconducting phase. This has prompted us here to re-examine the early work of March and Murray [Phys. Rev. 120 (1960) 830] on the linear response function in an initially translationally invariant Fermi gas. In particular, we present corresponding results for a superconductor at zero temperature, both in the s- and in the cl-wave case, and mention their direct physical relevance in the case when the impurity potential is highly localized. (C) 2002 Elsevier Science Ltd. All rights reserved.

We review a Ginzburg-Landau phenomenological model for the dependence of the critical temperature on microscopic strain in tetragonal high-T c cuprates. Such a model is in agreement with the experimental results for LSCO under epitaxial strain, as well as with the hydrostatic pressure dependence of T c in most cuprates. In particular, a nonmonotonic dependence of T c on hydrostatic pressure, as well as on in-plane or apical microstrain, is derived. From a microscopic point of view, such results can be understood as due to the proximity to an electronic topological transition (ETT). In the case of LSCO, we argue that such an ETT can be driven by a strain-induced modification of the band structure, at constant hole content, at variance with a doping-induced ETT, as is usually assumed.

The Gaussian Effective Potential in a fixed transverse unitarity gauge is studied for the static three-dimensional U(1) scalar electrodynamics (Ginzburg-Landau phenomenological theory of superconductivity). In the broken-symmetry phase the mass of the electromagnetic field (inverse penetration depth) and the mass of the scalar field (inverse correlation length) are both determined by solution of the coupled variational equations. At variance with previous calculations, the choice of a fixed unitarity gauge prevents from the occurrence of any unphysical degree of freedom. The theory provides a nice interpolation of the experimental data when approaching the critical region, where the standard mean-field method is doomed to failure.

The interlayer pair-tunneling (ILT) mechanism for high-$T_c$ superconductivity is able to predict the dependence of the (optimal) critical temperature Tc on the number of layers n within an homologous series of layered cuprate oxides. We generalize the mean-field procedure employed to evaluate Tc within an extended in-plane Hubbard model in presence of ILT, developed for a bilayer complex (n = 2), to the case of n = 3, 4 inequivalent superconducting layers. As a function of doping, we show how a nonuniform hole-content distribution among different layers affects Tc. In particular, depending on doping, the onset of superconductivity may be ruled by inner or outer layers. The latter result may be related to recent experimental data of Tc as a function of pressure in Tl- and Bi-based layered superconductors.

The review begins with a consideration of three forms of quantum information entropy associated with Shannon and Jaynes. For model two-electron spin compensated systems, some analytic progress is first reported. The Jaynes entropy is clearly related to correlation kinetic energy. A way of testing the usefulness of a known uncertainty principle inequality is proposed for a whole class of model two-electron atoms with harmonic confinement but variable electron-electron interaction. Emerging properties are then studied by reference to bcc Na at ambient pressure and its modeling by "jellium". Jellium itself has collective behavior with changes of the density, especially noteworthy being the discontinuity of the momentum distribution at the Fermi surface. This has almost reduced to zero at rs = 100 a.u., the neighborhood in which the quantal Wigner electron solid transition is known to occur. However, various workers have studied crystalline Na under pressure and their results are compared and contrasted. Work by DFT on K, Rb and Cs is discussed, but now with reduced density from the ambient pressure value. The crystalline results for the cohesive energy of these metals as a function of lattice parameters and local coordination number are shown to be closely reproduced by means of ground and excited states for dimer potential energy curves. Then, pair potentials for liquid Na and Be are reviewed, and compared with the results of computer simulations from the experimental structure factor for Na . Finally, magnetic field effects are discussed. First a phenomenological model of the metal-to-insulator transition is presented with an order parameter which is the discontinuity in the Fermi momentum distribution. Lastly, experiments on a two-dimensional electron assembly in a GaAs / AlGaAs heterojunction in a perpendicular magnetic field are briefly reviewed and then interpreted.

This extended abstract contains an outline of the work reported at the conference IQIS2018. We show that it is possible to exploit a thermalization process to extract work from a resource system R to a bipartite system S. To do this, we propose a simple protocol in a general setting in the presence of a single bath at temperature T and then examine it when S is described by the quantum Rabi model at T = 0 . We find the theoretical bounds of the protocol in the general case and we show that when applied to the Rabi model it gives rise to a satisfactory extraction of work and efficiency.

A method is presented for reducing a 3d-fold integral occurring in higher order many-body integrals for a d-dimensional electron gas to a double integral. The result is applied to the second order exchange energy for a d-dimensional uniform electron fluid. The cases \(d=2,3\) are examined in detail.