130 research outputs found
Influence of branch points in the complex plane on the transmission through double quantum dots
We consider single-channel transmission through a double quantum dot system
consisting of two single dots that are connected by a wire and coupled each to
one lead. The system is described in the framework of the S-matrix theory by
using the effective Hamiltonian of the open quantum system. It consists of the
Hamiltonian of the closed system (without attached leads) and a term that
accounts for the coupling of the states via the continuum of propagating modes
in the leads. This model allows to study the physical meaning of branch points
in the complex plane. They are points of coalesced eigenvalues and separate the
two scenarios with avoided level crossings and without any crossings in the
complex plane. They influence strongly the features of transmission through
double quantum dots.Comment: 30 pages, 14 figure
The brachistochrone problem in open quantum systems
Recently, the quantum brachistochrone problem is discussed in the literature
by using non-Hermitian Hamilton operators of different type. Here, it is
demonstrated that the passage time is tunable in realistic open quantum systems
due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton
operator. As an example, the numerical results obtained by Bulgakov et al. for
the transmission through microwave cavities of different shape are analyzed
from the point of view of the brachistochrone problem. The passage time is
shortened in the crossover from the weak-coupling to the strong-coupling regime
where the resonance states overlap and many branch points (exceptional points)
in the complex plane exist. The effect can {\it not} be described in the
framework of standard quantum mechanics with Hermitian Hamilton operator and
consideration of matrix poles.Comment: 18 page
Two-color interference stabilization of atoms
The effect of interference stabilization is shown to exist in a system of two
atomic levels coupled by a strong two-color laser field, the two frequencies of
which are close to a two-photon Raman-type resonance between the chosen levels,
with open channels of one-photon ionization from both of them. We suggest an
experiment, in which a rather significant (up to 90%) suppression of ionization
can take place and which demonstrates explicitly the interference origin of
stabilization. Specific calculations are made for H and He atoms and optimal
parameters of a two-color field are found. The physics of the effect and its
relation with such well-known phenomena as LICS and population trapping in a
three-level system are discussed.Comment: the paper includes 1 TeX file and 16 picture
Dynamics of quantum systems
A relation between the eigenvalues of an effective Hamilton operator and the
poles of the matrix is derived which holds for isolated as well as for
overlapping resonance states. The system may be a many-particle quantum system
with two-body forces between the constituents or it may be a quantum billiard
without any two-body forces. Avoided crossings of discrete states as well as of
resonance states are traced back to the existence of branch points in the
complex plane. Under certain conditions, these branch points appear as double
poles of the matrix. They influence the dynamics of open as well as of
closed quantum systems. The dynamics of the two-level system is studied in
detail analytically as well as numerically.Comment: 21 pages 7 figure
S-matrix theory for transmission through billiards in tight-binding approach
In the tight-binding approximation we consider multi-channel transmission
through a billiard coupled to leads. Following Dittes we derive the coupling
matrix, the scattering matrix and the effective Hamiltonian, but take into
account the energy restriction of the conductance band. The complex eigenvalues
of the effective Hamiltonian define the poles of the scattering matrix. For
some simple cases, we present exact values for the poles. We derive also the
condition for the appearance of double poles.Comment: 29 pages, 9 figures, submitted to J. Phys. A: Math. and Ge
High resolution X-ray emission spectra from picosecond laser irradiated Ge targets
Investigations of a high resolution X-ray emission spectrum in the range 0.66–0.75 nm obtained by irradiating a Germanium target with high-power p-polarized, 40 picosecond laser radiation at 532 nm wavelength was done. Spectra in the wavelength region of 2l-4l′ and 2l-5l′ L-shell transitions in F-like, Ne-like and Na-like germanium ions were recorded using the FSSR-2D spectrometer equipped with a spherically bent quartz crystal with a spectral resolution λ/Δλ better than 5000. Spectral lines were compared with theoretical values obtained using the LANL plasma kinetic code ATOMIC. Fair agreement between experimental and theoretical spectral lines has been observed, which allowed to measure enough high bulk electron temperature values of 560 eV and electron density of ∼1021 cm−3 in Ge plasma irradiated by rather small commercial high repetition rate Nd:YAG laser system
Effective Hamiltonian and unitarity of the S matrix
The properties of open quantum systems are described well by an effective
Hamiltonian that consists of two parts: the Hamiltonian of the
closed system with discrete eigenstates and the coupling matrix between
discrete states and continuum. The eigenvalues of determine the
poles of the matrix. The coupling matrix elements
between the eigenstates of and the continuum may be very
different from the coupling matrix elements between the eigenstates
of and the continuum. Due to the unitarity of the matrix, the
\TW_k^{cc'} depend on energy in a non-trivial manner, that conflicts with the
assumptions of some approaches to reactions in the overlapping regime. Explicit
expressions for the wave functions of the resonance states and for their phases
in the neighbourhood of, respectively, avoided level crossings in the complex
plane and double poles of the matrix are given.Comment: 17 pages, 7 figure
Projective Hilbert space structures at exceptional points
A non-Hermitian complex symmetric 2x2 matrix toy model is used to study
projective Hilbert space structures in the vicinity of exceptional points
(EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are
Puiseux-expanded in terms of the root vectors at the EP. It is shown that the
apparent contradiction between the two incompatible normalization conditions
with finite and singular behavior in the EP-limit can be resolved by
projectively extending the original Hilbert space. The complementary
normalization conditions correspond then to two different affine charts of this
enlarged projective Hilbert space. Geometric phase and phase jump behavior are
analyzed and the usefulness of the phase rigidity as measure for the distance
to EP configurations is demonstrated. Finally, EP-related aspects of
PT-symmetrically extended Quantum Mechanics are discussed and a conjecture
concerning the quantum brachistochrone problem is formulated.Comment: 20 pages; discussion extended, refs added; bug correcte
Interfering resonances in a quantum billiard
We present a method for numerically obtaining the positions, widths and
wavefunctions of resonance states in a two dimensional billiard connected to a
waveguide. For a rectangular billiard, we study the dynamics of three resonance
poles lying separated from the other ones. As a function of increasing coupling
strength between the waveguide and the billiard two of the states become
trapped while the width of the third one continues to increase for all coupling
strengths. This behavior of the resonance poles is reflected in the time delay
function which can be studied experimentally.Comment: 2 pages, 3 figure
Formation of the X-ray line emission spectrum of excimer laser-produced plasmas
Time- and space-integrated emission spectra measurements have been performed in plasma produced by 308 nm wavelength XeCl laser radiation (IL = (4–10)·1012 W/cm2, τ = 10 ns) and by 248 nm wavelength KrF laser pulse train radiation (IL = 5·1015 W/cm2, τ = 7 ps, 16 pulses in train) on CF2 plane target. Theoretical modelling of Lyman series and He-like ion resonance series of fluorine and its fit of experimental data show considerable differences in the absorption of laser radiation in the two plasmas
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