Open Systems

Abstract

This chapter is intended to make some basic concepts clear. First of all, there is an inherent problem in defining quantum transport which in mesoscopic systems could be flow of charge or current. Second, quantum mechanical operators are mostly unbounded operators that model the continuum and it is important to study the problem using first quantization and a basic introduction will be given as to how to treat boundary conditions leading to continuity of wavefunctions and conservation of currents. This will encompass the situation when we will have evanescent modes in the system. Such evanescent modes will become very important in later chapters. Also, a typical thermodynamic property, i.e., magnetization of a mesoscopic system due to AB effect will be explained in detail using continuum approach. Special emphasis will be given to explain the topological nature of the problem.