157 research outputs found
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
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
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-
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
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