22 research outputs found
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
Coherent oscillations and incoherent tunnelling in one - dimensional asymmetric double - well potential
For a model 1d asymmetric double-well potential we calculated so-called
survival probability (i.e. the probability for a particle initially localised
in one well to remain there). We use a semiclassical (WKB) solution of
Schroedinger equation. It is shown that behaviour essentially depends on
transition probability, and on dimensionless parameter which is a ratio of
characteristic frequencies for low energy non-linear in-well oscillations and
inter wells tunnelling. For the potential describing a finite motion
(double-well) one has always a regular behaviour. For the small value of the
parameter there is well defined resonance pairs of levels and the survival
probability has coherent oscillations related to resonance splitting. However
for the large value of the parameter no oscillations at all for the survival
probability, and there is almost an exponential decay with the characteristic
time determined by Fermi golden rule. In this case one may not restrict oneself
to only resonance pair levels. The number of perturbed by tunnelling levels
grows proportionally to the value of this parameter (by other words instead of
isolated pairs there appear the resonance regions containing the sets of
strongly coupled levels). In the region of intermediate values of the parameter
one has a crossover between both limiting cases, namely the exponential decay
with subsequent long period recurrent behaviour.Comment: 19 pages, 7 figures, Revtex, revised version. Accepted to Phys. Rev.
Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution
We study equilibrium properties of a catalytically-activated annihilation reaction taking place on a one-dimensional chain of length () in which some segments (placed at random, with mean concentration
) possess special, catalytic properties. Annihilation reaction takes place,
as soon as any two particles land onto two vacant sites at the extremities
of the catalytic segment, or when any particle lands onto a vacant site on
a catalytic segment while the site at the other extremity of this segment is
already occupied by another particle. Non-catalytic segments are inert with
respect to reaction and here two adsorbed particles harmlessly coexist. For
both "annealed" and "quenched" disorder in placement of the catalytic segments,
we calculate exactly the disorder-average pressure per site. Explicit
asymptotic formulae for the particle mean density and the compressibility are
also presented.Comment: AMSTeX, 27 pages + 4 figure
The manipulation of massive ro-vibronic superpositions using time-frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS): from quantum control to quantum computing
Molecular ro-vibronic coherences, joint energy-time distributions of quantum
amplitudes, are selectively prepared, manipulated, and imaged in
Time-Frequency-Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS)
measurements using femtosecond laser pulses. The studies are implemented in
iodine vapor, with its thermally occupied statistical ro-vibrational density
serving as initial state. The evolution of the massive ro-vibronic
superpositions, consisting of 1000 eigenstates, is followed through
two-dimensional images. The first- and second-order coherences are captured
using time-integrated frequency-resolved CARS, while the third-order coherence
is captured using time-gated frequency-resolved CARS. The Fourier filtering
provided by time integrated detection projects out single ro-vibronic
transitions, while time-gated detection allows the projection of arbitrary
ro-vibronic superpositions from the coherent third-order polarization. Beside
the control and imaging of chemistry, the controlled manipulation of massive
quantum coherences suggests the possibility of quantum computing. We argue that
the universal logic gates necessary for arbitrary quantum computing - all
single qubit operations and the two-qubit controlled-NOT (CNOT) gate - are
available in time resolved four-wave mixing in a molecule. The molecular
rotational manifold is naturally "wired" for carrying out all single qubit
operations efficiently, and in parallel. We identify vibronic coherences as one
example of a naturally available two-qubit CNOT gate, wherein the vibrational
qubit controls the switching of the targeted electronic qubit.Comment: PDF format. 59 pages, including 22 figures. To appear in Chemical
Physic