Voltage fluctuations in a four-terminal quantum device with orthogonal, unitary or symplectic symmetry

Abstract

The statistical fluctuations of the voltage across a quantum wire in a four-terminal arrangement, where two of the terminals are used as probes while the other two are used to establish a flux current, is studied in the single channel case. The quantum wire to be measured consists of a chaotic microcavity or a disordered conductor in the presence of one of the three symmetry classes: orthogonal, unitary, or symplectic. Using the circular ensembles of random matrix theory or the Dorokov–Mello–Pereyra–Kumar (DMPK) equation, the statistical distribution of the voltage is reduced to quadratures for noninvasive probes which is solved numerically. Numerical simulations from random matrix theory or for the DMPK equation are performed for any coupling strength of the probes. For the chaotic cavity the effect of the symmetry class is clearly manifested through the weak and weak anti-localization phenomena for the orthogonal and symplectic symmetry classes, respectively. A similar effect is found, but with respect to the degree of disorder in a quantum wire as it evolves from strong to weak disorder: a simple correspondence between the label of the symmetry class and the degree of disorder, is found.