1,441 research outputs found
Influence of asymmetry and nodal planes on high-harmonic generation in heteronuclear molecules
The relation between high-harmonic spectra and the geometry of the molecular
orbitals in position and momentum space is investigated. In particular we
choose two isoelectronic pairs of homonuclear and heteronuclear molecules, such
that the highest occupied molecular orbital of the former exhibit at least one
nodal plane. The imprint of such planes is a strong suppression in the harmonic
spectra, for particular alignment angles. We are able to identify two distinct
types of nodal planes. If the nodal planes are determined by the atomic
wavefunctions only, the angle for which the yield is suppressed will remain the
same for both types of molecules. In contrast, if they are determined by the
linear combination of atomic orbitals at different centers in the molecule,
there will be a shift in the angle at which the suppression occurs for the
heteronuclear molecules, with regard to their homonuclear counterpart. This
shows that, in principle, molecular imaging, which uses the homonuclear
molecule as a reference and enables one to observe the wavefunction distortions
in its heteronuclear counterpart, is possible.Comment: 14 pages, 7 figures. Figs. 3, 5 and 6 have been simplified in order
to comply with the arXiv size requirement
High-harmonic generation from a confined atom
The order of high harmonics emitted by an atom in an intense laser field is
limited by the so-called cutoff frequency. Solving the time-dependent
Schr\"odinger equation, we show that this frequency can be increased
considerably by a parabolic confining potential, if the confinement parameters
are suitably chosen.
Furthermore, due to confinement, the radiation intensity remains high
throughout the extended emission range. All features observed can be explained
with classical arguments.Comment: 4 pages(tex files), 4 figures(eps files); added references and
comment
Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
We provide a reviewlike introduction into the quantum mechanical formalism
related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting
with the time-independent framework we explain how to determine an appropriate
domain of a non-Hermitian Hamiltonian and pay particular attention to the role
played by PT-symmetry and pseudo-Hermiticity. We discuss the time-evolution of
such systems having in particular the question in mind of how to couple
consistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate
the general formalism with three explicit examples: i) the generalized Swanson
Hamiltonians, which constitute non-Hermitian extensions of anharmonic
oscillators, ii) the spiked harmonic oscillator, which exhibits explicit
supersymmetry and iii) the -x^4-potential, which serves as a toy model for the
quantum field theoretical phi^4-theory.Comment: 14 pages, 3 figures, to appear in Laser Physics, minor typos
correcte
The periodic Anderson model from the atomic limit and FeSi
The exact Green's functions of the periodic Anderson model for
are formally expressed within the cumulant expansion in terms of an effective
cumulant. Here we resort to a calculation in which this quantity is
approximated by the value it takes for the exactly soluble atomic limit of the
same model. In the Kondo region a spectral density is obtained that shows near
the Fermi surface a structure with the properties of the Kondo peak.
Approximate expressions are obtained for the static conductivity
and magnetic susceptibility of the PAM, and they are employed to fit
the experimental values of FeSi, a compound that behaves like a Kondo insulator
with both quantities vanishing rapidly for . Assuming that the system
is in the intermediate valence region, it was possible to find good agreement
between theory and experiment for these two properties by employing the same
set of parameters. It is shown that in the present model the hybridization is
responsible for the relaxation mechanism of the conduction electrons.Comment: 26 pages and 8 figure
Time evolution of non-Hermitian Hamiltonian systems
We provide time-evolution operators, gauge transformations and a perturbative
treatment for non-Hermitian Hamiltonian systems, which are explicitly
time-dependent. We determine various new equivalence pairs for Hermitian and
non-Hermitian Hamiltonians, which are therefore pseudo-Hermitian and in
addition in some cases also invariant under PT-symmetry. In particular, for the
harmonic oscillator perturbed by a cubic non-Hermitian term, we evaluate
explicitly various transition amplitudes, for the situation when these systems
are exposed to a monochromatic linearly polarized electric field.Comment: 25 pages Latex, 1 eps figure, references adde
Classical and quantum-mechanical treatments of nonsequential double ionization with few-cycle laser pulses
We address nonsequential double ionization induced by strong, linearly
polarized laser fields of only a few cycles, considering a physical mechanism
in which the second electron is dislodged by the inelastic collision of the
first electron with its parent ion. The problem is treated classically, using
an ensemble model, and quantum-mechanically, within the strong-field and
uniform saddle-point approximations. In the latter case, the results are
interpreted in terms of "quantum orbits", which can be related to the
trajectories of a classical electron in an electric field. We obtain highly
asymmetric electron momentum distributions, which strongly depend on the
absolute phase, i.e., on the phase difference between the pulse envelope and
its carrier frequency. Around a particular value of this parameter, the
distributions shift from the region of positive to that of negative momenta, or
vice-versa, in a radical fashion. This behavior is investigated in detail for
several driving-field parameters, and provides a very efficient method for
measuring the absolute phase. Both models yield very similar distributions,
which share the same physical explanation. There exist, however, minor
discrepancies due to the fact that, beyond the region for which electron-impact
ionization is classically allowed, the yields from the quantum mechanical
computation decay exponentially, whereas their classical counterparts vanish.Comment: 12 pages revtex, 12 figures (eps files
Delta-Function Potential with a Complex Coupling
We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is
real, \delta(x) is the Dirac delta function, and z is an arbitrary complex
coupling constant. For a purely imaginary z, H has a (real) spectral
singularity at E=-z^2/4. For \Re(z)<0, H has an eigenvalue at E=-z^2/4. For the
case that \Re(z)>0, H has a real, positive, continuous spectrum that is free
from spectral singularities. For this latter case, we construct an associated
biorthonormal system and use it to perform a perturbative calculation of a
positive-definite inner product that renders H self-adjoint. This allows us to
address the intriguing question of the nonlocal aspects of the equivalent
Hermitian Hamiltonian for the system. In particular, we compute the energy
expectation values for various Gaussian wave packets to show that the
non-Hermiticity effect diminishes rapidly outside an effective interaction
region.Comment: Published version, 14 pages, 2 figure
Quantum impurity with 2/3 local moment in 1D quantum wires: an NRG study
We study a Kondo state that is strongly influenced by its proximity to an
w^-1/2 singularity in the metallic host density of states. This singularity
occurs at the bottom of the band of a 1D chain, for example. We first analyze
the non-interacting system: A resonant state e_d, located close to the band
singularity, suffers a strong `renormalization', such that a bound state is
created below the bottom of the band in addition to a resonance in the
continuum. When e_d is positioned right at the singularity, the spectral weight
of the bound state is 2/3, irrespective of its coupling to the conduction
electrons. The interacting system is modeled using the Single Impurity Anderson
Model, which is then solved using the Numerical Renormalization Group method.
We observe that the Hubbard interaction causes the bound state to suffer a
series of transformations, including level splitting, transfer of spectral
weight, appearance of a spectral discontinuity, changes in binding energy (the
lowest state moves farther away from the bottom of the band), and development
of a finite width. When e_d is away from the singularity and in the
intermediate valence regime, the impurity occupancy is lower. As e_d moves
closer to the singularity, the system partially recovers Kondo regime
properties, i.e., higher occupancy and lower Kondo temperature T_K. The
impurity thermodynamic properties show that the local moment fixed point is
also strongly affected by the existence of the bound state. When e_d is close
to the singularity, the local moment fixed point becomes impervious to charge
fluctuations (caused by bringing e_d close to the Fermi energy), in contrast to
the local moment suppression that occurs when e_d is away from the singularity.
We also discuss an experimental implementation that shows similar results to
the quantum wire, if the impurity's metallic host is an armchair graphene
nanoribbon.Comment: 13 pages, 20 figure
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