Truncating the number of Fourier modes to −N ≤ j, k ≤ N, this matrix eigenvalue problem can be solved by MATLAB. Linear stability analysis We now turn to address the linear stability analysis on the above stationary solutions of Eq. (7) and verify them via direct numerical ...
the random matrixTis said to belong to the truncated orthogonal, unitary, or symplectic ensemble (denoted TOE, TUE, or TSE, respectively). These ensembles were introduced and studied in the works [44,45,69]. WhenMis fixed and\(N \rightarrow \infty \), after suitable rescaling they recover...
Since only matrix elements are measurable, we can use the differing inner products to transform from one formalism to the other, as we saw in Equation (59). Thus, we really have two parametrisations of the same formalism. In one, we can simplify calculations by using the fact that all ...