Transport phenomena and quantum phase transitions in mesoscopic systems

Shi-Liang Zhu

FRANCESCO IACHELLO

Teemu Ojanen

Mesoscopic physics and nanoelectronics concentrate on systems with dimensions somewhere between atomic and everyday macroscopic scale. Modern technology enables construction of submicron nanostructures where modeling based on classical physics has proven inadequate. It is possible to design electric circuits where dynamics of single electrons and photons are controlled using state-of-the-art experimental methods. For quantitative understanding of these systems it is necessary to resort to a quantum-mechanical description. Quantum phenomena, such as tunneling and a wave-like interference of particles, are essential ingredients of physics in mesoscopic systems. Field of mesoscopic physics contains a rich variety of topics ranging from fundamental condensed matter physics to quantum information processing and possible future technological applications. \n \nThis thesis presents theoretical studies of mesoscopic quantum phenomena in nanostructures and small electronic devices. We have focused on effects of environment fluctuations and investigated connections between fluctuations and transport phenomena. Decoherence in quantum bits (qubits) and quantum state engineering in superconducting circuits are also studied. The theoretical analysis in each case requires an open-system treatment. \n \nEffects of current fluctuations on quantum probe systems have been studied in detail. We have calculated transitions induced by current noise and discussed how these could be used for characterization of fluctuations. We have also shown that electric fluctuations play a key role in radiation and photon heat transport in nanostructures. Motivated by recent advances in mesoscopic electron-photon systems, we have studied a response of a coupled resonator-qubit system, squeezing of quantum fluctuations in small superconducting circuits and investigated decoherence in Josephson flux qubits.

Michael R. Geller

A novel chiral interferometer is proposed that allows for a direct measurement of the phase of the transmission coefficient for transport through a variety of mesoscopic structures in a strong magnetic field. The effects of electron-electron interaction on this phase are investigated with the use of finite-size bosonization techniques combined with perturbation theory resummation. New non-Fermi-liquid phenomena are predicted in the fractional quantum Hall effect regime that may be used to distinguish experimentally between Luttinger and Fermi liquids.

Y. Imry

Abstract This chapter will be devoted to mesoscopic effects which are not necessarily related to nonequilibrium or transport phenomena. Most of our discussion in the rest of this chapter will be concerned with electronic effects, often with fluctuations from sample to sample. We shall start here, however, by briefly reviewing more general finite-size effects due to ordinary thermodynamic fluctuations. Such fluctuations are usually negligible in the “thermodynamic limit,” as far as their contributions to, for example, intensive properties, or to the O(N)part of extensive ones are concerned. However, thermodynamic fluctuations may play an important role in special situations where large length scales exist in the system. We mention here two of these: the elimination of certain types of long-range order (and, therefore, phase transitions) in low-dimensional systems and the effects of finite sample sizes on regular phase transitions. There are several varieties of the former effects.

Nicola Lo Gullo