F. Napoli

Functional integral methods in the theory of the Anderson model

Abstract The use of the functional integration technique applied to the problem of local moment formation in the Anderson model is reviewed in this paper. The different approximations are discussed, in order to clarify both their internal consistency and relations among them. Connection with the ordinary diagrammatic approach is made by summarizing and extending previous treatments done on this subject; and the difference between the one-field and the two-field approaches is explained in terms of the ‘unphysical diagrams’ generated by the first. The results for the magnetic susceptibility are presented for each approximation discussed in the paper, both in the strong magnetic and in the non-magnetic regime; while it is shown that no reliable approximation has been developed for the intermediate coupling situation. Finally the Kondo effect is discussed within the functional integration scheme and application of the method to the study of superconducting magnetic alloys is reviewed.

Electron transport properties of MgB2 in the normal state

Abstract:We report measurements of the resistivity, ρ, and the Seebeck coefficient, S, of a MgB2 sintered sample, and compare S with theoretical calculations based on precise electronic structure calculations. ρ is fitted well by a generalized Bloch-Grüneisen equation with a Debye temperature ΘR of 1050 K. S is given by the sum of a diffusive and a phonon drag term and the behavior in the temperature region Tc < T < 0.1ΘR follows the relationship AT+BT3. The phonon drag term indicates a strong electron-phonon interaction. The diffusive term, compared with calculations, suggests that σ bands give the main contribution to the Seebeck effect.We report measurements of the resistivity, ; and the Seebeck coecient, S; of aM gB 2 sintered sample, and compare S with theoretical calculations based on precise electronic structure calculations. is tted well by a generalized Bloch-Gruneisen equation with a Debye temperatureR of 1050 K.S is given by the sum of a diusive and a phonon drag term and the behavior in the temperature region Tc <T <0:1R follows the relationship AT +BT 3 . The phonon drag term indicates a strong electron-phonon interaction. The diusive term, compared with calculations, suggests that bands give the main contribution to the Seebeck eect.

Spin‐Singlet Pairing of Composite Fermions

Interactions between composite fermions in a two-dimensional electron gas in a strong perpendicular magnetic field at a Landau level filling factor 1/2 are investigated. It is shown that for antiparallel spins and momenta of the quasi-particles the interplay between Coulomb interaction and fluctuations of the gauge field leads to an attractive effective interaction in the long-wavelength limit. It is argued that this can give rise to a ground state of spin-singlet pairs. A quantitative estimate for the pair-breaking gap is provided. Experimental implications are discussed.

Specific heat and “susceptibility” in the Yu and Anderson model

Abstract Starting from the expression of the partition function Z for a local oscillator interacting with an electron gas expressed in terms of that of a classical “Coulomb” gas, we have calculated the specific heat and the displacive response by an approximated evaluation of such Z . Analogies of the present problem with the Kondo effect are briefly discussed.

Quantum diffusion of a heavy particle moving in a periodic potential and interacting with an electron gas

Abstract We study the diffusion of a heavy particle moving in a strongly corrugated periodic potential and interacting with an electronic bath. Using a path-integral approach we are able to integrate out the electrons and to derive an effective action for the particle in two different limiting cases: (i) arbitrary large coupling between heavy particles and electrons and linear dissipation, and (ii) weak coupling and nonlinear dissipation. In the first case we obtain an effective action for the particle of the Caldeira-Leggett ohmic form, with a friction coefficient equal to that of a classical Brownian particle in a fermionic bath. In the second case we obtain a nonlinear, but still ohmic, dissipative term. Using an instanton approach we evaluate the mobility (and the diffusion coefficient) of the particle, whose temperature dependence shows a cross-over from diffusive to localized behaviour at a critical value of the friction, which is different in the two considered cases. Finally we discuss whether the friction can reach such a critical value, and we arrive at the conclusion that this might happen only for a rather high spin degeneracy.

Phonon assisted quantum diffusion in a periodic potential

We study the diffusion of a quantum heavy particle moving in a one dimensional strongly corrugated periodic potential, and interacting with a phonon bath.By integrating out the phonons degrees of freedom we derive an effective action functional for the particle, which includes a non-local self-interacting term whose strength is proved to be the classical friction coefficient η.Using an instanton approach we express the velocity-velocity correlation function, and thus the mobility, of the brownian particle in terms of the charge density-density correlation function of a classical Coulomb gas, which in the strong corrugation limit has a very low fugacity.By making a virial expansion in the gas fugacity we evaluate the static mobility μ of the brownian particle as a function of the temperature, and we find two different behaviours: a “diffusive” behaviour at low friction, where μ decreases withT, and a “localised” behaviour at high friction, where μ increases withT.The cross-over between the two régimes takes place at a critical friction η0, corresponding to the Kosterlitz-Thouless transition for the Coulomb gas.

Linear mobility for coherent quantum tunneling in a periodic potential

The dynamics of a quantum particle moving in a tight binding lattice and coupled to an ohmic heat bath is investigated. Imaginary-time functional integral methods are utilized to determine the self-energy of the velocity-velocity correlation function for weak damping and arbitrary temperatures. Recent results for the linear mobility atT=0 and high temperatures are confirmed and extended to intermediate temperatures. The dominant corrections to the zero temperature mobility are given in terms of a power law.

Evidences for non-Fermi liquid behavior of quantum wires

Abstract The present understanding of the physics of correlated electrons in quantum wires is explained by using two representative examples. Non-Fermi liquid collective excitations are obtained within the Luttinger liquid model. Charge and spin density modes are considered and compared with the data from resonant Raman scattering experiments. The results indicate that interactions dominate the low-frequency collective modes. The interplay in DC-transport between interaction, spin, backscattering by impurities and inhomogeneity is discussed and compared with recent experiments.

Composite Fermions with Spin at

Acknowledgment This work has been supported by the European Union via the TMR and RTN programmes (FMRX-CT98-0180, HPRN-CT2000-00144), by the Deutsche Forschungsgemeinschaft within the Schwerpunkt “Quanten-Hall-Effekt” of the Universit¨at Hamburg, and by the Italian MURST via PRIN00.

ν=1/2

Abstract We develop a theory for the collective excitations in a quantum wire with two occupied subbands. The dispersion relations of the intra- and inter-subband spin and charge modes are determined as a function of the interaction strength. The hitherto unexplained “single particle excitations”, which appear near resonance, independently of the relative polarization of incoming and outgoing light, are shown to originate from higher order spin density excitations.