Y. Imry

Josephson behavior in small normal one-dimensional rings

Abstract Small and strictly one-dimensional rings of normal metal, driven by an external magnetic flux, act like superconducting rings with a Josephson junction, except that 2e is replaced by e.

Active Transmission Channels and Universal Conductance Fluctuations.

The transport through a segment of a disordered system is determined by the eigenvalues of a large random matrix. The effectively independent active transmission channels are associated with these eigenvalues which are closest to unity. A decreasing number of those survives when the systems length increases. They determine the conductance and its fluctuations, which are found to be independent, within broad limits, of the size, disorder and nature of the system. This universality is due to the strong correlations in the spectra of large random matrices, providing a new insight on and generalizing the extremely interesting recent results of Altschuler, Lee and Stone.

Conductance viewed as transmission

Early quantum theories of electrical conduction were semiclassical. Electrons were accelerated according to Bloch’s theorem; this was balanced by back scattering due to phonons and lattice defects. Cross sections for scattering, and band structures, were calculated quantum-mechanically, but the balancing process allowed only for occupation probabilities, not permitting a totally coherent process. Also, in most instances, scatterers at separate locations were presumed to act incoherently. Totally quantum-mechanical theories stem from the 1950s, and have diverse sources. Particularly intense concern with the need for more quantum mechanical approaches was manifested in Japan, and Kubo’s formulation became the most widely accepted version. Quantum theory, as described by the Schrodinger equation, is a theory of conservative systems, and does not allow for dissipation. The Schrodinger equation readily allows us to calculate polarizability for atoms, molecules, or other isolated systems that do not permit electrons to enter or leave. Kubo’s linear-response theory is essentially an extended theory of polarizability. Some supplementary handwaving is needed to calculate a dissipative effect such as conductance, for a sample with boundaries where electrons enter and leave (Anderson, 1997). After all, no theory that ignores the interfaces of a sample to the rest of its circuit can possibly calculate the resistance of such a sample of limited extent. Modern microelectronics has provided the techniques for fabricating very small samples. These permit us to study conductance in cases where the carriers have a totally quantum mechanically coherent history within the sample, making it essential to take the interfaces into account. Mesoscopic physics, concerned with samples that are intermediate in size between the atomic scale and the macroscopic one, can now demonstrate in manufactured structures much of the quantum mechanics we associate with atoms and molecules.

Random external fields

The various theoretical considerations for the effects of quenched random fields (RF) on second-order transitions as well as the experimental situation are briefly reviewed. Some of the physical realizations of the RF models are discussed, with an emphasis on solid-state first-order transitions in impure systems. The physical arguments for the RF effects in the bulk as well as on phase interfaces are discussed. In the latter case it is suggested that scattering experiments can probe the details of the interface fluctuations. The role of long relaxation times and metastability in Ising RF systems is emphasized.

Proton Dynamics in Hydrogen‐Bonded Ferroelectrics

A comparison between infrared absorption and neutron inelastic‐scattering measurements indicates the existence of a broad low‐energy (around 400 cm−1) protonic level in KH2PO4 above the Curie point. This level is only weakly discerned in the ir but is seen quite clearly in neutron scattering. The mode is explained as resulting from splitting of the ground level of the proton in a slightly asymmetric double minimum potential well where tunneling of the proton takes place. The asymmetry is caused by the interaction between the different protons, and it changes slowly with time as the result of the collective motions of the protons. Prominent changes in ir spectra in the 400‐cm−1 range were found on cooling through the Curie point, indicating the disappearance of the tunneling mode.This picture allows a simplified treatment of the system, leading to the existence of two correlated phase transition points, and a negative thermal expansion coefficient of the H bond at temperatures between these points. The two...

Three-terminal thermoelectric transport through a molecular junction

The thermoelectric transport through a molecular bridge is discussed, with an emphasis on the effects of inelastic processes of the transport electrons caused by the coupling to the vibrational modes of the molecule. In particular it is found that when the molecule is strongly coupled to a thermal bath of its own, which may be at a temperature different from those of the electronic reservoirs, a heat current between the molecule and the electrons can be converted into electric current. Expressions for the transport coefficients governing this conversion and similar ones are derived, and a possible scenario for increasing their magnitudes is outlined.

Transport at low temperature in amorphous magnetic metals (invited)

The scaling theory of conduction for a noninteracting electron gas in a disordered system at T = 0 is reviewed and the conductivity at various length scales obtained. The concepts of the mean free time between inelastic collisions and the corresponding inelastic length lin, are introduced. The conductivity for a dirty metal is obtained as a function of temperature at low temperatures in terms of lin(T). For the case of a disordered magnetic metal the effect of the temperature‐dependent magnetic disorder is introduced and several possible typical situations schematically analyzed. The effect of electron‐electron interactions is briefly discussed, as determining the effective inelastic length and a simple qualitative picture of conduction as a function of temperature suggested. Some cautionary remarks about the testing of these ideas by experiments are made.

Steady oscillatory states of a finite Josephson junction

Abstract Under the assumption that solutions have traveling-wave form, time-periodic solutions are found for the Josephson phase equation for a finite-length tunnel junction with uniform current feed and linear loss term. Exact current-voltage characteristics are found and compared with simple approximations. The complete current-velocity and mean-width-velocity curves for isolated fluxons are found. Comparison with characteristics for a finite junction shows that end effects obtained from analysis of a circuit model of the junction shows that end effects introduce lower- and upper-current thresholds.

On the statistical mechanics of coupled order parameters

Generalized Landau-Ginsburg models for systems with coupled order parameters are introduced. Detailed discussion is given for a particular model with biquadratic coupling between two (second-order) order parameters. This includes the complete, rather interesting, phase diagrams within the Landau-theory approximation and a discussion of fluctuation effects. For these, simple expectations are presented based on the topology of the Landau free-energy surfaces and renormalization group results including an identification of the limitations of the latter. It is argued that these models are very general and relevant to many systems of experimental interest.

Towards an explanation of the mesoscopic double-slit experiment: A new model for charging of a quantum Dot

For a quantum dot (QD) in the intermediate regime between integrable and fully chaotic, the widths of single-particle levels naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. In this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels, and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD.