525 research outputs found
Adiabatic theorem for non-hermitian time-dependent open systems
In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic
theorem for systems subjected to time periodic fields holds only for bound
systems and not for open ones (where ionization and dissociation take place)
[D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here
with the help of the (t,t') formalism combined with the complex scaling method
we derive an adiabatic theorem for open systems and provide an analytical
criteria for the validity of the adiabatic limit. The use of the complex
scaling transformation plays a key role in our derivation. As a numerical
example we apply the adiabatic theorem we derived to a 1D model Hamiltonian of
Xe atom which interacts with strong, monochromatic sine-square laser pulses. We
show that the gener- ation of odd-order harmonics and the absence of
hyper-Raman lines, even when the pulses are extremely short, can be explained
with the help of the adiabatic theorem we derived
A global biogeocenotical biosphere simulation
This model of the D. Forrester type, constructed in differential equations, predicts the food and mineral supply for the factors biosphere population, depending on two socio-economic factors, until about the year 2500. If contemporary rates of natural resources utilization are maintained and there is no management of the environment, food resources will begin to limit human population growth after 2200, and mineral resources will after 2300. A decrease in the biosphere pollution, increase in effective agricultural production, and discovery of new energy sources may forestall or completely avert the onset of a crisis situation. Conservation measures, according to the model, are to a considerable extent realizable only if carried out simultaneously in both areas
Amplification of High Harmonics Using Weak Perturbative High Frequency Radiation
The mechanism underlying the substantial amplification of the high-order
harmonics q \pm 2K (K integer) upon the addition of a weak seed XUV field of
harmonic frequency q\omega to a strong IR field of frequency \omega is analyzed
in the framework of the quantum-mechanical Floquet formalism and the
semiclassical re-collision model. According to the Floquet analysis, the
high-frequency field induces transitions between several Floquet states and
leads to the appearance of new dipole cross terms. The semiclassical
re-collision model suggests that the origin of the enhancement lies in the
time-dependent modulation of the ground electronic state induced by the XUV
field.Comment: 8 pages, 2 figure
Strong impact of light induced conical intersections on the spectrum of diatomic molecules
We show that dressing of diatomic molecules by running laser waves gives rise
to conical intersections (CIs). Due to presence of such CIs, the rovibronic
molecular motions are strongly coupled. A pronounced impact of the CI on the
spectrum of molecule is demonstrated via numerical calculation for weak
and moderate laser intensity, and an experiment is suggested on this basis. The
position of the light induced CI and the strength of its non-adiabatic
couplings can be chosen by changing the frequency and intensity of the used
running laser wave. This offers new possibilities to control the photo-induced
rovibronic molecular dynamics.Comment: 4 pages, 7 figure
Mechanism of Molecular Orientation by Single-cycle Pulses
Significant molecular orientation can be achieved by time-symmetric
single-cycle pulses of zero area, in the THz region. We show that in spite of
the existence of a combined time-space symmetry operation, not only large peak
instantaneous orientations but also nonzero time-average orientations over a
rotational period can be obtained. We show that this unexpected phenomenon is
due to interferences among eigenstates of the time-evolution operator, as was
described previously for transport phenomena in quantum ratchets. This
mechanism also works for sequences of identical pulses, spanning a rotational
period. This fact can be used to obtain a net average molecular orientation
regardless of the magnitude of the rotational constant.Comment: Published version may be found at
(URL:http://link.aip.org/link?/JCP/137/044303). Substantial changes with
respect to previous versions, including new titl
Breakdown of adiabatic transfer of light in waveguides in the presence of absorption
In atomic physics, adiabatic evolution is often used to achieve a robust and
efficient population transfer. Many adiabatic schemes have also been
implemented in optical waveguide structures. Recently there has been increasing
interests in the influence of decay and absorption, and their engineering
applications. Here it is shown that even a small decay can significantly
influence the dynamical behaviour of a system, above and beyond a mere change
of the overall norm. In particular, a small decay can lead to a breakdown of
adiabatic transfer schemes, even when both the spectrum and the eigenfunctions
are only sightly modified. This is demonstrated for the generalization of a
STIRAP scheme that has recently been implemented in optical waveguide
structures. Here the question how an additional absorption in either the
initial or the target waveguide influences the transfer property of the scheme
is addressed. It is found that the scheme breaks down for small values of the
absorption at a relatively sharp threshold, which can be estimated by simple
analytical arguments.Comment: 8 pages, 7 figures, revised and extende
Mixed-state evolution in the presence of gain and loss
A model is proposed that describes the evolution of a mixed state of a
quantum system for which gain and loss of energy or amplitude are present.
Properties of the model are worked out in detail. In particular, invariant
subspaces of the space of density matrices corresponding to the fixed points of
the dynamics are identified, and the existence of a transition between the
phase in which gain and loss are balanced and the phase in which this balance
is lost is illustrated in terms of the time average of observables. The model
is extended to include a noise term that results from a uniform random
perturbation generated by white noise. Numerical studies of example systems
show the emergence of equilibrium states that suppress the phase transition.Comment: 5 pages, 2 figures (published version
Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution
The solutions of the time independent Schrodinger equation for non-Hermitian
(NH) Hamiltonians have been extensively studied and calculated in many
different fields of physics by using L^2 methods that originally have been
developed for the calculations of bound states. The existing non-Hermitian
formalism breaks down when dealing with wavepackets(WP). An open question is
how time dependent expectation values can be calculated when the Hamiltonian is
NH ? Using the F-product formalism, which was recently proposed, [J. Phys.
Chem., 107, 7181 (2003)] we calculate the time dependent expectation values of
different observable quantities for a simple well known study test case model
Hamiltonian. We carry out a comparison between these results with those
obtained from conventional(i.e., Hermitian) quantum mechanics (QM)
calculations. The remarkable agreement between these results emphasizes the
fact that in the NH-QM, unlike standard QM, there is no need to split the
entire space into two regions; i.e., the interaction region and its
surrounding. Our results open a door for a type of WP propagation calculations
within the NH-QM formalism that until now were impossible.Comment: 20 pages, 5 Postscript figures. To be Published in Physical Review
Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime
We study the transmission through different small systems as a function of
the coupling strength to the two attached leads. The leads are identical
with only one propagating mode in each of them. Besides the
conductance , we calculate the phase rigidity of the scattering wave
function in the interior of the system. Most interesting results are
obtained in the regime of strongly overlapping resonance states where the
crossover from staying to traveling modes takes place. The crossover is
characterized by collective effects. Here, the conductance is plateau-like
enhanced in some energy regions of finite length while corridors with zero
transmission (total reflection) appear in other energy regions. This
transmission picture depends only weakly on the spectrum of the closed system.
It is caused by the alignment of some resonance states of the system with the
propagating modes in the leads. The alignment of resonance states
takes place stepwise by resonance trapping, i.e. it is accompanied by the
decoupling of other resonance states from the continuum of propagating modes.
This process is quantitatively described by the phase rigidity of the
scattering wave function. Averaged over energy in the considered energy window,
is correlated with . In the regime of strong coupling, only two
short-lived resonance states survive each aligned with one of the channel wave
functions . They may be identified with traveling modes through the
system. The remaining trapped narrow resonance states are well separated
from one another.Comment: Resonance trapping mechanism explained in the captions of Figs. 7 to
11. Recent papers added in the list of reference
Calculating resonance positions and widths using the Siegert approximation method
Here we present complex resonance states (or Siegert states), that describe
the tunneling decay of a trapped quantum particle, from an intuitive point of
view which naturally leads to the easily applicable Siegert approximation
method that can be used for analytical and numerical calculations of complex
resonances of both the linear and nonlinear Schr\"odinger equation. Our
approach thus complements other treatments of the subject that mostly focus on
methods based on continuation in the complex plane or on semiclassical
approximations.Comment: 15 pages, 1 figure, contains MATLAB source code; new version with
additional illustration
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