The aim of understanding any anomaly in physics is required to go deeper into the fundamental aspect of it. Lev Landau, one of the grand masters of theoretical physics once pointed out- ‘Physics is mainly an experimental science. It consists of ‘more than measurements’. The word ‘more’ implies a great deal of fundamental understanding. In the present context we begin with some fundamental understanding of a physical system as the title implies.
Over the last several decades, interest in quasi-one dimensional charge transport has progressed from the seminal discoveries of Landauer quantization of conductance as a function of carrier density, to significant finer- scale phenomena [1-3]. Those include: (i) fractional conductance, or “0.7 anomaly”; (ii) zero-bias anomaly; (iii) Rashba-effect anomalies; and (iv) apparent violation of the Landauer upper bound on conductance. In this talk I present a very short summary of the first three items. The last anomaly, which remained theoretically unexamined until recently, is discussed in detail with emphasis on novel low- dimensional physics.