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 model of ultrafast photoisomerization reactions

In this letter we propose a model which explains ultrafast and efficient photoisomerization reactions as driven by transitions between quasistationary states of one dimensional (1D) double well potential of an excited electronic state. This adiabatic potential is formed as a result of doubly crossing of a decay diabatic potential of the ground electronic state and a bound diabatic potential of the excited state. We calculate the eigenstates and eigenfunctions using the semiclassical connection matrices at the turning and crossing points and the shift matrices between these points. The transitions between the localized in the wells below the adiabatic barrier states are realized by the tunneling and by the double non-adiabatic transitions via the crossing points processes. Surprisingly the behavior with the maximum transition rate keeps going even for the states relatively far above the barrier (2 -4 times the barrier height). Even though a specific toy model is investigated here, when properly interpreted it yields quite reasonable values for a variety of measured quantities, such as a reaction quantum yield, and conversion time.Comment: 9 pages, 5 figures. accepted to Chem. Phys. Letters (2005

New mechanism for non-trivial intra-molecular vibrational dynamics

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state, coupled to all other intra-molecular vibrational states of the same molecule, and also to its environment. Molecular states forming the first reservoir are characterised by a discrete dense spectrum, whereas the environment reservoir states form a continuous spectrum. Assuming the equidistant reservoir states we find the exact analytical solution of the quantum dynamic equations. System reservoirs couplings yield to spontaneous decay of the states, whereas system-reservoir exchange leads to recurrence cycles and Loschmidt echo and double resonances at the interlevel reservoir transitions. Due to these couplings the system $S$ time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are four possible dynamic regimes of the evolution: (i) - independent of the environment exponential decay suppressing backward transitions, (ii) Loschmidt echo regime, (iii) - incoherent dynamics with multicomponent Loschmidt echo, when the system state exchanges its energy with many states of the reservoir, (iv) - cycle mixing regime, when the long term system dynamics appear to be random. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.Comment: 11 pages, 2 figure

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

Dynamic and spectral mixing in nanosystems

In the framework of simple spin-boson Hamiltonian we study an interplay between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian describes an initial vibrational state coupled to discrete dense spectrum reservoir. The reservoir states are formed by three sequences with rationally independent periodicities typical for vibrational states in many nanosize systems. We show that quantum evolution of the system is determined by a dimensionless parameter which is characteristic number of the reservoir states relevant for the initial vibrational level dynamics. Our semi-quantitative analytic results are confirmed by numerical solution of the equation of motion. We anticipate that predicted in the paper both kinds of stochastic-like behavior (namely, due to spectral mixing and recurrence cycle dynamic mixing) can be observed by femtosecond spectroscopy methods in nanosystems.Comment: 6 pages, 4 figure