Salvador Godoy

Theory of high temperature superconductivity

1. Introduction. 2. Superconducting Transitions. 3. Bloch Electrons. 4. Phonon Exchange Attraction. 5. Quantum Statistical Theory. 6. Cooper Pairs (Pairons). 7. Superconductors at 0 K. 8. Quantum Statistics of Composites. 9. Bose-Einstein Condensation. 10. The Energy Gap Equations. 11. Pairon Energy Gaps and Heat Capacity. 12. Quantum Tunneling. 13. Flux Quantization. 14. Ginzburg-Landau Theory. 15. Josephson Effects. 16. Compound Superconductors. 17. Lattice Structures of Cuprates. 18. High-Tc Superconductors Below Tc. 19. Doping Dependence of Tc. 20. Transport Properties Above Tc. 21. Out-of-Plane Transport. 22. Seebeck Coefficient (Thermopower). 23. Magnetic Susceptibility. 24. Infrared Hall Effect. 25. d-Wave Cooper Pairs. 26. Connections with Other Theories. 27. Summary and Remarks. Appendix A. References. Bibliography. Index.

A quantum random‐walk model for tunneling diffusion in a 1D lattice. A quantum correction to Fick’s law

With the help of quantum‐scattering‐theory methods and the approximation of stationary phase, a one‐dimensional coherent random‐walk model which describes both tunneling and scattering above the potential diffusion of particles in a periodic one‐dimensional lattice is proposed. The walk describes for each lattice cell, the time evolution of modulating amplitudes of two opposite‐moving Gaussian wave packets as they are scattered by the potential barriers. Since we have a coherent process, interference contributions in the probabilities bring about strong departures from classical results. In the near‐equilibrium limit, Fick’s law and its associated Landauer diffusion coefficient are obtained as the incoherent contribution to the quantum current density along with a novel coherent contribution which depends on the lattice properties as [(1−R)/R]1/2.

STUDY OF A LORENTZ-GAS BASED ON CORRELATED WALKS

The dynamics of a Lorentz‐gas molecule is simulated in terms of correlated walks on cubic lattices. For a finite lattice with reflecting boundary, the ergodicity is established so that the probability distribution in position and direction approaches a stationary state which is homogeneous (site‐independent) and isotropic (direction‐independent). Exact expressions for probability distribution in direction are obtained for simple, body‐centered, and face‐centered cubic lattices. They approach equilibrium exponentially with a different number of relaxation times depending on the lattice. The directional probabilities for a single‐site lattice with reflecting boundary approach equilibrium in an oscillatory manner. The Boltzmann H‐function for this system, however, shows a monotonic behavior, and coincides with the H‐function for the same system with periodic boundary. The parameters in the model, step length and unit time, can be eliminated in the kinetic theoretical limit. In this limit, the diffusion coeff...

HELIX-COIL TRANSITION OF POLYPEPTIDES ON THE BASIS OF CORRELATED WALKS

The helix‐coil transition of polypeptides is treated on the basis of the correlated walk model which incorporates both the physical shape (helix or coil) and the hydrogen bonding. The statistical mechanical calculations reproduce the essential features of the classic theory established by Zimm and Bragg. Moreover, the nucleation parameter σ, which represents the degree of difficulty for forming a first helical turn, is related to the probability γ′ of the model polymer making the correct turn: σ = γ′3. In the model in which the hydrogen bonding is attained only after three successive correct turns, the numerical value for the probability γ′ obtained after comparison with the optical rotation study of the poly‐γ‐benzyl‐l‐glutamate by Doty and Yang is found to be 0.010. This value is compatible with the detailed molecular calculations by Scherag and his collaborators, but it is about one‐sixth of the value which results from γ′ = 3√σ with σ = 2×10−4 obtained in the truncated Z–B model. This difference arise...

Quantum statistical effects of the motion of an oscillator interacting with a radiation field

The motion of a quantum oscillator interacting with a quantized radiation field is studied. The exact solution shows that the motion of the oscillator is described by a Langevin-type equation in which the friction and the effective frequency depend on time. The physical conditions under which these properties become constant are studied. The stochastic force becomes a gaussian process and in the limit of long times and weak coupling, has an autocorrelation function with the usual delta behavior.

MESOSCOPIC DIFFUSION AS A NON-MARKOV PROCESS

We use both classical and quantum S-matrix theories to derive expressions for the ballistic diffusion current of a 1D mesoscopic crystalline solid. For both theories, we get the same local Fick’s law, thus proving that local Fick’s law and its associate local diffusion coefficient are incoherent results. The non-local Landauer diffusion coefficient is an incoherent result valid only for solids with a length larger than the coherence length. For solids with a length less than the coherence length, we show that quantum interference gives a new contribution for the non-local diffusion coefficient.

Bloch electron dynamics

AbstractNew equations of motion for a Bloch electron [momentump=hk,energy εn(p),zone number n, charge -e]:

Quantum statistical foundation to the Fermi liquid model and Ginzburg-Landau wave function

m_j \frac{{dv_j }}{{dt}} = - e(E + v \times B)_j