Cálculo semiclássico de transporte em sistemas caóticos - Oliveira, Lucas Henrique de (2023)
In this work, we study quantum transport through mesoscopic chaotic cavities coupled to the external environment through very long waveguides. For this purpose, we use a diagrammatic approach implemented through a matrix integral. Thus, due to this connection, a semiclassical physics problem is transformed into a problem of symmetric polynomials. Through this method, we obtain a perturbative series in the reflection probability of the barrier, where each term is exact in the numbers of channels of the waveguides. Considering the cavity with ideal input and output guides and a third guide coupled through a tunneling barrier, we obtained the mean values of various transport moments, including conductance and its variance, the Fano factor, and the third cumulant, all consistent with Random Matrix Theory predictions. For a cavity with two guides coupled by barriers, we obtained the conductance in the absence and presence of time-reversal symmetry. In the particular case where the barriers are identical, we obtained averages of a Schur function and a closed expression for the conductance that exhibits an exponential term for the reflection probability of the barrier and the total number of available channels, γ^M. In addition, we obtained the squared module of immanants, which are related to the transport moments from the perspective of identical particles.