Loris Ferrari

A defect theory of the viscosity in glass-forming liquids

Abstract The viscosity of glass-forming liquids is calculated at constant volume, according to the assumption that intrinsic defects are exponentially distributed in energy. Under suitable conditions, it is shown that the viscosity displays a Vogel-Fulcher behaviour and a cross-over to an Arrhenius regime at lower temperatures. For a different choice of the parameters, a new cooperative expression of the viscosity is found, which is not of Vogel-Fulcher type but fits again an Arrhenius behaviour at lower temperatures.

Bound states and expansion dynamics of interacting bosons on a one-dimensional lattice

The expansion dynamics of bosonic gases in optical lattices has recently been the focus of increasing attention, both experimental and theoretical. We consider, by means of numerical Bethe ansatz, the expansion dynamics of initially confined wave packets of two interacting bosons on a lattice. We show that a correspondence between the asymptotic expansion velocities and the projection of the evolved wave function over the bound states of the system exists, clarifying the existing picture for such situations. Moreover, we investigate the role of the lattice in this kind of evolution.

Ab initio analysis of the x-ray absorption spectrum of the myoglobin–carbon monoxide complex: Structure and vibrations

We present a comparison between

The Heisenberg uncertainty principle demonstrated with an electron diffraction experiment

\text{Fe}\text{ }K

Approaching Bose?Einstein condensation

-edge x-ray absorption spectra of carbonmonoxy\char21{}myoglobin and its simulation based on density-functional theory determination of the structure and vibrations and spectral simulation with multiple-scattering theory. An excellent comparison is obtained for the main part of the molecular structure without any structural fitting parameters. The geometry of the CO ligand is reliably determined using a synergic approach to data analysis. The methodology underlying this approach is expected to be especially useful in similar situations in which high-resolution data for structure and vibrations are available.

Long wavelength approximation of transport processes in a single-band crystal

An experiment analogous to the classical diffraction of light from a circular aperture has been realized with electrons. The results are used to introduce undergraduate students to the wave behaviour of electrons. The diffraction fringes produced by the circular aperture are compared to those predicted by quantum mechanics and are exploited to present and discuss the Heisenberg uncertainty principle.

Chemical and structural disorder effects on the Curie temperature

Bose–Einstein condensation (BEC) is discussed at the level of an advanced course of statistical thermodynamics, clarifying some formal and physical aspects that are usually not covered by the standard pedagogical literature. The non-conventional approach adopted starts by showing that the continuum limit, in certain cases, cancels out the crucial role of the bosonic ground level. If so, a correct treatment of the problem, including the ground level population N0 by construction, leads to BEC in a straightforward way. For a density of states of the form G()∝γ, the chemical potential µ is explicitly calculated as a function of the temperature T and of the number N of bosons, for various significant values of the positive exponent γ. In the thermodynamic limit, in which the boson number N diverges and BEC is a sharp process, the chemical potential µ is a singular function of T at the critical temperature TB, determined by an appropriate critical exponent. The condensate population N0 is studied analytically and numerically as a function of the temperature, for various values of N and for different γ. This provides an accurate description of the way BEC approaches the character of a sharp phase transition. Some aspects of the real experiments on BEC, involving a finite number of bosons, are also illustrated.

Coherent absorption of energy by electrons in a time-dependent oscillating magnetic field

The single band, long wavelength approximation (SBA?LWA) is currently used in textbooks as a quasi-free-particle picture of the motion in a quantum crystal. The resulting transport process might thereby look a trivial issue. In contrast, we shall show that the SBA?LWA hides some controversial aspects that should be clarified at the level of an advanced course of condensed matter physics, and refer to the incompleteness of the SBA representation. In particular, it will be shown that the single-band velocity v1B, expressed in terms of the projectors on the Bloch states, cannot be a transport velocity in a full sense, since the resulting current violates the continuity equation. The drawback manifests itself as a ?lost? current Jlost, which provides a non conventional estimate of the limits of accuracy of SBA?LWA. The vanishing of Jlost corresponds to the effective mass approximation in which the dispersion relation can be reduced to a quadratic form in the (pseudo) momentum components. In practice, the quantity transported by v1B is not the bare mass, but the effective mass, until this notion does make sense. Recalling that the non-quadratic expression of the relativistic kinetic energy leads to a difference between the rest and moving mass, the notion of the lost current is finally used as a non-conventional approach to relativistic quantum mechanics, with special reference to Dirac?s theory.

Reduction method for the linear quantum or classical oscillator with time-dependent frequency, damping, and driving

The disorder effects on the Curie temperature of ferromagnetic and ferroelectric systems are studied by factorizing the spin–spin (or dipole–dipole) interaction into a chemical (on-site) and a structural (off-site) part. Assuming the statistical independence of the two contributions, the Curie temperature Tc is calculated in the limit of small disorder and in the mean-field approximation. The chemical disorder always enhances Tc . In the absence of spin waves (Ising-like systems), the structural disorder enhances Tc in turn. The only negative contribution to Tc is found in Heisenberg-like systems, and is ascribed to the interplay between structural disorder and spin waves. A comparison is made with other mean-field theories that adopt a different representation of the disorder. The application of the results obtained to real systems is considered, with special reference to recent experimental data on ferroelectric perovskites. An approximate expression, consistent with the mean-field approach, is suggested to estimate the relative weight of the chemical and structural disorder effects, even when an exact factorization is impossible, as is the case of the exchange interactions.

QUANTUM OSCILLATOR WITH FLUCTUATING TIME-DEPENDENT FREQUENCY

The exponential absorption of energy, characteristic of the harmonic oscillator with time-dependent fluctuating frequency [L. Ferrari, Phys. Rev. B 56, 593 (1997)], is applied to electrons in a large constant magnetic field, with a small oscillating perturbation added. Physical conditions are given, for the model to be implementable in practical cases. These conditions turn out to be accessible to conventional techniques, not too different from those used to detect the de Haas\char21{}van Alphen effect. The main effect predicted is an increase of the electronic density of states at the Fermi level, with a parallel increase of the temperature, both saturating at asymptotic values. Some consequences of the effect on the properties of hydrogenated metals are discussed.