The multichannel Dirac equation with a random (matricial) mass
We have considered the Dirac equation with a Gaussian white noise N*N matrical mass in:
- Aurélien Grabsch and Christophe Texier,
Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model,
Europhys. Lett. 116, 17004 (2016)
cond-mat arXiv:1506.05322
The model presents interesting topological properties : as the ratio mass/disorder is tuned the systems exhibits a sequence of N topological phase transitions. The phase diagram (below) in the half plane (mass,disorder) presents N+1 sectors:
See also page “ products of random matrices ”
Wigner-Smith time delay matrix and Wigner time delay for semi-infinite multichannel disordered wires
(within the multichannel Schrödinger equation)
- Aurélien Grabsch and Christophe Texier,
Distribution of spectral linear statistics on random matrices beyond the large deviation function — Wigner time delay in multichannel disordered wires,
J. Phys. A : Math. Theor. 49, 465002 (2016)
cond-mat arXiv:1602.03370
- Aurélien Grabsch and Christophe Texier,
Wigner-Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity
J. Phys. A : Math. Theor. 53, 425003 (2020)
math-ph arXiv:2002.12077
see also page on » Wigner time delay in 1D «