Landau-Zener problem for energies close to potential crossing points

We examine one overlooked in previous investigations aspect of well - known Landau - Zener (LZ) problem, namely, the behavior in the intermediate, i.e. close to a crossing point, energy region, when all four LZ states are coupled and should be taken into account. We calculate the 4 x 4 connection matrix in this intermediate energy region, possessing the same block structure as the known connection matrices for the tunneling and in the over-barrier regions of the energy, and continously matching those in the corresponding energy regions.Comment: 5 pages, 1 figur

Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations

We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is therefore realized either along one trajectory or along two equivalent paths. Zero point fluctuations smear out the sharp transition between these two regimes and lead to a certain crossover behavior. When the two saddle points are inequivalent one can also have a first order transition related to the fact that one of the two trajectories becomes unstable. We illustrate these results by numerical investigations. Even though a specific model is investigated here, the approach is quite general and has potential applicability for various systems in physics and chemistry exhibiting multi-stability and tunneling phenomena.Comment: 11 pages, 8 eps figures, Revtex-

Semiclassical approach to states near potential barrier top

16 pages, 10 eps figures, Revtex, submitted to Phys. Rev. AWithin the framework of the instanton approach we present analytical results for the following model problems: (i) particle penetration through a parabolic potential barrier, where the instanton solution practically coincides with the exact (quantum) one; (ii) descriptions of highly excited states in two types of anharmonic potentials: double-well $X^4$, and decay $X^3$. For the former case the instanton method reproduces accurately not only single well and double-well quantization but as well a crossover region (in the contrast with the standard WKB approach which fails to describe the crossover behavior), and for the latter case the instanton method allows to study resonance broadening and collapse phenomena. We investigate also resonance tunneling, playing a relevant role in many semiconducting devices. We show that in a broad region of energies the instanton approach gives exact (quantum) results. Applications of the method and of the results may concern the various systems in physics, chemistry and biology exhibiting double level behavior and resonance tunneling