Adiabatic switching in time-dependent Fourier grid Hamiltonian method: some test cases

Quantum dynamics of a system of coupled nonlinear oscillators: Spectral and information entropy‐based analysis

“…It would be interesting to compare the dynamical pictures provided by C (τ) and C I (τ). The nonlinear perturbation can be switched on either suddenly or adiabatically, possibly affecting the evolution in different ways 11, 12. For adiabatic switching, the evolution equation to be solved is given by where $\hat{H}$ ( t ) = $\hat{H}$ 0 + η( t ) ∑ i λ i $\hat{x}$ with η( t ) = 0 at t = 0, and η( t ) = 1 at t = T (the switching time).…”

“…For adiabatic switching, the evolution equation to be solved is given by where $\hat{H}$ ( t ) = $\hat{H}$ 0 + η( t ) ∑ i λ i $\hat{x}$ with η( t ) = 0 at t = 0, and η( t ) = 1 at t = T (the switching time). Special forms of η( t ) that are known to ensure adiabatic passage should be used 11, 12. In either case (i.e., sudden or adiabatic switching), we propose to examine the correlation function for spectral or information entropy C (τ) as functions of τ.…”

Time‐dependent Fourier grid Hamiltonian method for studying the curve crossing dynamics: Dynamics of predissociation of NaI

“…We note here that our TDFGH method 12, 13 followed naturally from its time‐independent version originally proposed by Marston and Balint‐Kurti 14. It has found many applications in 1‐ and 2‐D problems 15–18. To the best of our knowledge, it has never been explored in the context of following nuclear dynamics.…”

Tunneling in 2-D quantum dots via quantum adiabatic switching route

“…Does it tunnel into the new classically forbidden zones or remain confined to the initial well? We may make use of the idea of quantum adiabatic switching [43][44][45][46][47][48][49][50][51][52] and solve the appropriate evolution equation starting from an eigenstate of the Hamiltonian describing the initial structure (H i ) and monitoring the growth of the probability of finding the electron in the new classically forbidden zones defined by the final Hamiltonian (H f ). This can be done for any state of the dot selectively and gives us insight into how the disposition of unperturbed states of the Hamiltonian get dynamically distorted during the quasi adiabatic evolution.…”