3,351 research outputs found
Phase rigidity and avoided level crossings in the complex energy plane
We consider the effective Hamiltonian of an open quantum system, its
biorthogonal eigenfunctions and define the value that characterizes the
phase rigidity of the eigenfunctions . In the scenario with
avoided level crossings, varies between 1 and 0 due to the mutual
influence of neighboring resonances. The variation of may be
considered as an internal property of an {\it open} quantum system. In the
literature, the phase rigidity of the scattering wave function
is considered. Since can be represented in the interior
of the system by the , the phase rigidity of the
is related to the and therefore also to the mutual
influence of neighboring resonances. As a consequence, the reduction of the
phase rigidity to values smaller than 1 should be considered, at least
partly, as an internal property of an open quantum system in the overlapping
regime. The relation to measurable values such as the transmission through a
quantum dot, follows from the fact that the transmission is, in any case,
resonant with respect to the effective Hamiltonian. We illustrate the relation
between phase rigidity and transmission numerically for small open
cavities.Comment: 6 pages, 3 figure
Whispering gallery modes in open quantum billiards
The poles of the S-matrix and the wave functions of open 2D quantum billiards
with convex boundary of different shape are calculated by the method of complex
scaling. Two leads are attached to the cavities. The conductance of the
cavities is calculated at energies with one, two and three open channels in
each lead. Bands of overlapping resonance states appear which are localized
along the convex boundary of the cavities and contribute coherently to the
conductance. These bands correspond to the whispering gallery modes appearing
in the classical calculations.Comment: 9 pages, 3 figures in jpg and gif forma
Conductance of Open Quantum Billiards and Classical Trajectories
We analyse the transport phenomena of 2D quantum billiards with convex
boundary of different shape. The quantum mechanical analysis is performed by
means of the poles of the S-matrix while the classical analysis is based on the
motion of a free particle inside the cavity along trajectories with a different
number of bounces at the boundary. The value of the conductance depends on the
manner the leads are attached to the cavity. The Fourier transform of the
transmission amplitudes is compared with the length of the classical paths.
There is good agreement between classical and quantum mechanical results when
the conductance is achieved mainly by special short-lived states such as
whispering gallery modes (WGM) and bouncing ball modes (BBM). In these cases,
also the localization of the wave functions agrees with the picture of the
classical paths. The S-matrix is calculated classically and compared with the
transmission coefficients of the quantum mechanical calculations for five modes
in each lead. The number of modes coupled to the special states is effectively
reduced.Comment: 19 pages, 6 figures (jpg), 2 table
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
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
Nonlinear acousto-electric transport in a two-dimensional electron system
We study both theoretically and experimentally the nonlinear interaction
between an intense surface acoustic wave and a two-dimensional electron plasma
in semiconductor-piezocrystal hybrid structures. The experiments on hybrid
systems exhibit strongly nonlinear acousto-electric effects. The plasma turns
into moving electron stripes, the acousto-electric current reaches its maximum,
and the sound absorption strongly decreases. To describe the nonlinear
phenomena, we develop a coupled-amplitude method for a two-dimensional system
in the strongly nonlinear regime of interaction. At low electron densities the
absorption coefficient decreases with increasing sound intensity, whereas at
high electron density the absorption coefficient is not a monotonous function
of the sound intensity. High-harmonic generation coefficients as a function of
the sound intensity have a nontrivial behavior. Theory and experiment are found
to be in a good agreement.Comment: 27 pages, 6 figure
Observation of resonance trapping in an open microwave cavity
The coupling of a quantum mechanical system to open decay channels has been
theoretically studied in numerous works, mainly in the context of nuclear
physics but also in atomic, molecular and mesoscopic physics. Theory predicts
that with increasing coupling strength to the channels the resonance widths of
all states should first increase but finally decrease again for most of the
states. In this letter, the first direct experimental verification of this
effect, known as resonance trapping, is presented. In the experiment a
microwave Sinai cavity with an attached waveguide with variable slit width was
used.Comment: to be published in Phys. Rev. Let
Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths
A phenomenological schematic model of multipole giant resonances (GR) is
considered which treats the external interaction via common decay channels on
the same footing as the coherent part of the internal residual interaction. The
damping due to the coupling to the sea of complicated states is neglected. As a
result, the formation of GR is governed by the interplay and competition of two
kinds of collectivity, the internal and the external one. The mixing of the
doorway components of a GR due to the external interaction influences
significantly their multipole strengths, widths and positions in energy. In
particular, a narrow resonance state with an appreciable multipole strength is
formed when the doorway components strongly overlap.Comment: 20 pages, LaTeX, 3 ps-figures, to appear in PRC (July 1997
Resonant-state expansion of the Green's function of open quantum systems
Our series of recent work on the transmission coefficient of open quantum
systems in one dimension will be reviewed. The transmission coefficient is
equivalent to the conductance of a quantum dot connected to leads of quantum
wires. We will show that the transmission coefficient is given by a sum over
all discrete eigenstates without a background integral. An apparent
"background" is in fact not a background but generated by tails of various
resonance peaks. By using the expression, we will show that the Fano asymmetry
of a resonance peak is caused by the interference between various discrete
eigenstates. In particular, an unstable resonance can strongly skew the peak of
a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical
Physics as an article in the Proceedings for PHHQP 2010
(http://www.math.zju.edu.cn/wjd/
Interfering Doorway States and Giant Resonances. II: Transition Strengths
The mixing of the doorway components of a giant resonance (GR) due to the
interaction via common decay channels influences significantly the distribution
of the multipole strength and the energy spectrum of the decay products of the
GR. The concept of the partial widths of a GR becomes ambiguous when the mixing
is strong. In this case, the partial widths determined in terms of the - and
-matrices must be distinguished. The photoemission turns out to be most
sensitive to the overlapping of the doorway states. At high excitation
energies, the interference between the doorway states leads to a restructuring
towards lower energies and apparent quenching of the dipole strength.Comment: 17 pages, LaTeX, 5 figures as JPEG, to appear in PRC (July 1997
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