Sagnik-Luis • Presnentation for Katarzyna • Sept 17, 2024
Avalanche
stability of the
Anderson
Model
Hamiltonians
Dries I:
Dries II:
Luis:
H = \frac{1}{2} \sum_{i=1}^{L-1} \left( c_i^\dagger c_{i+1} + c_i c_{i+1}^\dagger \right)+\sum_{i=1}^{L}\frac{1}{2}(1-2 c_i^\dagger c_i)
Lindbladians
\frac{d}{dt}\rho(t) = \mathcal{L}[\rho]
\\\mathcal{L}[\rho]=-i[H,\rho(t)] + \sum_{j} \left( J_{j}\rho(t)J_{j}^{\dagger} - \frac{1}{2}\{J_{j}^{\dagger}J_{j},\rho(t)\} \right)
Decay channels on first spin
J_i=(X_1,Y_1,Z_1)
Dries Sels:
Scaling of decay rate; Jordan Wignered
Scaling with system size, scaled decay rates
Eigenscatters
Avalanche-Kataryna
By Sagnik Ghosh
