136 research outputs found
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
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
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
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
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
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
Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
The phenomenon of super-radiance (Dicke effect, coherent spontaneous
radiation by a gas of atoms coupled through the common radiation field) is well
known in quantum optics. The review discusses similar physics that emerges in
open and marginally stable quantum many-body systems. In the presence of open
decay channels, the intrinsic states are coupled through the continuum. At
sufficiently strong continuum coupling, the spectrum of resonances undergoes
the restructuring with segregation of very broad super-radiant states and
trapping of remaining long-lived compound states. The appropriate formalism
describing this phenomenon is based on the Feshbach projection method and
effective non-Hermitian Hamiltonian. A broader generalization is related to the
idea of doorway states connecting quantum states of different structure. The
method is explained in detail and the examples of applications are given to
nuclear, atomic and particle physics. The interrelation of the collective
dynamics through continuum and possible intrinsic many-body chaos is studied,
including universal mesoscopic conductance fluctuations. The theory serves as a
natural framework for general description of a quantum signal transmission
through an open mesoscopic system.Comment: 85 pages, 10 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
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