Landau–Zener formula in a “non-adiabatic” regime for avoided crossings

Non–Adiabatic Transitions near Avoided Crossings: Theory and Numerics

We present a review of rigorous mathematical results about non– adiabatic transitions in molecular systems that are associated with avoided crossings of electron energy level surfaces. We then present a novel numerical technique for studying these transitions that is based on expansions in semiclassical wavepackets.

Non-adiabatic passage through an avoided crossing

By the application of an ultra fast magnetic field sweeping (2.0 × 105 T/sec) and the zero-field magnetic resonance (ZFMR)/FID techniques, we are able to probe the dynamics at the level anti-crossing region of the photo-excited triplet states of pentacene-h14 in p-terphenyl (PHPT) and pentacene-d14 in p-terphenyl (PDPT) systems. The crossing is a non-adiabatic passage at such a high jumping rat...

Avoided Crossings in Driven Systems

We characterize the avoided crossings in a two-parameter, time-periodic system which has been the basis for a wide variety of experiments. By studying these avoided crossings in the near-integrable regime, we are able to determine scaling laws for the dependence of their characteristic features on the non-integrability parameter. As an application of these results, the influence of avoided cros...

Bohr-Sommerfeld phases for avoided crossings

on the real line. Here Ĥ = (Ĥi,j)1≤i,j≤N is a matrix of semi-classical pseudodifferential operators of order 0 in 1 variable x with (Ĥi,j) ? = Ĥi,j. For applications, it will be important to consider the case where Ĥ = Ĥμ depends smoothly on a germ of parameters μ ∈ (R, 0). In our previous papers [5, 6], we derived normal forms near the eigenvalues crossings which allow to compute a local scatt...

Wavepacket propagation in D-dimensional non-adiabatic crossings Master Thesis