Hidden facts in Landau-Zener transitions revealed by the Riccati Equation
arXiv:2502.04033 · doi:10.1103/nqgc-w1ns
Abstract
We express the dynamics of the two probability amplitudes in the elementary Landau-Zener problem in terms of the solution of the corresponding Riccati differential equation and identify three key features: (i) The solution of the Riccati equation provides the bridge between the two probability amplitudes. (ii) Neglecting the non-linearity in the Riccati equation is equivalent to the Markov approximation which yields the exact asymptotic expression for one of the probability amplitudes, and (iii) the Riccati equation identifies the origin of the failure of the Markov approximation not being able to provide us in general with the correct asymptotic expression of the other probability amplitude. Our approach relies on approximate yet analytical solutions of the Riccati equation in different time regimes, highlighting the impact of its non-linear nature on the time evolution of the system.
28 pages, 10 figures
References in corpus (13)
- Atom Interferometers
- Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
- Dissipative Landau-Zener transitions of a qubit: bath-specific and universal behavior
- Landau-Zener transitions in qubits controlled by electromagnetic fields
- Large-amplitude driving of a superconducting artificial atom: Interferometry, cooling, and amplitude spectroscopy
- Majorana's approach to nonadiabatic transitions validates the adiabatic-impulse approximation
- Landau-Zener transitions in an open multilevel quantum system
- Noise-resistant Landau-Zener sweeps from geometrical curves
- Riccati equation and the problem of decoherence
- Tuning the initial phase to control the final state of a driven qubit
- Partial Landau-Zener transitions and applications to qubit shuttling
- Angular Bloch Oscillations and their applications
- Mutual neutralization of C and C ions: Excitation energies and state-selective rate coefficients