103 research outputs found
Quasi-bound states in continuum
We report the prediction of quasi-bound states (resonant states with very
long lifetimes) that occur in the eigenvalue continuum of propagating states
for a wide region of parameter space. These quasi-bound states are generated in
a quantum wire with two channels and an adatom, when the energy bands of the
two channels overlap. A would-be bound state that lays just below the upper
energy band is slightly destabilized by the lower energy band and thereby
becomes a resonant state with a very long lifetime (a second QBIC lays above
the lower energy band).Comment: 4 pages, 4figures, 1 tabl
Complex Energy Spectrum and Time Evolution of QBIC States in a Two-Channel Quantum wire with an Adatom Impurity
We provide detailed analysis of the complex energy eigenvalue spectrum for a
two-channel quantum wire with an attached adatom impurity. The study is based
on our previous work [Phys. Rev. Lett. 99, 210404 (2007)], in which we
presented the quasi-bound states in continuum (or QBIC states). These are
resonant states with very long lifetimes that form as a result of two
overlapping continuous energy bands one of which, at least, has a divergent van
Hove singularity at the band edge. We provide analysis of the full energy
spectrum for all solutions, including the QBIC states, and obtain an expansion
for the complex eigenvalue of the QBIC state. We show that it has a small decay
rate of the order , where is the coupling constant. As a result of
this expansion, we find that this state is a non-analytic effect resulting from
the van Hove singularity; it cannot be predicted from the ordinary perturbation
analysis that relies on Fermi's golden rule. We will also numerically
demonstrate the time evolution of the QBIC state using the effective potential
method in order to show the stability of the QBIC wave function in comparison
with that of the other eigenstates.Comment: Around 20 pages, 50 total figure
Strongly Coupled Matter-Field and Non-Analytic Decay Rate of Dipole Molecules in a Waveguide
The decay rate \gam of an excited dipole molecule inside a waveguide is
evaluated for the strongly coupled matter-field case near a cutoff frequency
\ome_c without using perturbation analysis. Due to the singularity in the
density of photon states at the cutoff frequency, we find that \gam depends
non-analytically on the coupling constant as . In contrast
to the ordinary evaluation of \gam which relies on the Fermi golden rule
(itself based on perturbation analysis), \gam has an upper bound and does not
diverge at \ome_c even if we assume perfect conductance in the waveguide
walls. As a result, again in contrast to the statement found in the literature,
the speed of emitted light from the molecule does not vanish at \ome_c and is
proportional to which is on the order of m/s for
typical dipole molecules.Comment: 4 pages, 2 figure
Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. III: potential function in local stochastic dynamics and in steady state of Boltzmann-Gibbs type distribution function
From a logic point of view this is the third in the series to solve the
problem of absence of detailed balance. This paper will be denoted as SDS III.
The existence of a dynamical potential with both local and global meanings in
general nonequilibrium processes has been controversial. Following an earlier
explicit construction by one of us (Ao, J. Phys. {\bf A37}, L25 '04,
arXiv:0803.4356, referred to as SDS II), in the present paper we show
rigorously its existence for a generic class of situations in physical and
biological sciences. The local dynamical meaning of this potential function is
demonstrated via a special stochastic differential equation and its global
steady-state meaning via a novel and explicit form of Fokker-Planck equation,
the zero mass limit. We also give a procedure to obtain the special stochastic
differential equation for any given Fokker-Planck equation. No detailed balance
condition is required in our demonstration. For the first time we obtain here a
formula to describe the noise induced shift in drift force comparing to the
steady state distribution, a phenomenon extensively observed in numerical
studies. The comparison to two well known stochastic integration methods, Ito
and Stratonovich, are made ready. Such comparison was made elsewhere (Ao, Phys.
Life Rev. {\bf 2} (2005) 117. q-bio/0605020).Comment: latex. 13 page
On the Thermal Symmetry of the Markovian Master Equation
The quantum Markovian master equation of the reduced dynamics of a harmonic
oscillator coupled to a thermal reservoir is shown to possess thermal symmetry.
This symmetry is revealed by a Bogoliubov transformation that can be
represented by a hyperbolic rotation acting on the Liouville space of the
reduced dynamics. The Liouville space is obtained as an extension of the
Hilbert space through the introduction of tilde variables used in the
thermofield dynamics formalism. The angle of rotation depends on the
temperature of the reservoir, as well as the value of Planck's constant. This
symmetry relates the thermal states of the system at any two temperatures. This
includes absolute zero, at which purely quantum effects are revealed. The
Caldeira-Leggett equation and the classical Fokker-Planck equation also possess
thermal symmetry. We compare the thermal symmetry obtained from the Bogoliubov
transformation in related fields and discuss the effects of the symmetry on the
shape of a Gaussian wave packet.Comment: Eqs.(64a), (65a)-(68) are correcte
Nontrivial eigenvalues of the Liouvillian of an open quantum system
We present methods of finding complex eigenvalues of the Liouvillian of an
open quantum system. The goal is to find eigenvalues that cannot be predicted
from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type
quantum dot with an infinitely long lead. We suggest the existence of the
non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that
the original problem reduces to the problem of a two-particle Hamiltonian with
a two-body interaction and the other way is to show that diagram expansion of
the Green's function has correlation between the bra state and the ket state.
We also introduce the integral equations equivalent to the original eigenvalue
problem.Comment: 5 pages, 2 figures, proceeding
A Quantum Anti-Zeno Paradox
We establish an exact differential equation for the operator describing
time-dependent measurements continuous in time and obtain a series solution.
Suppose the projection operator is measured
continuously from t = 0 to T, where E is a projector leaving the initial state
unchanged and U(t) a unitary operator obeying U(0) = 1 and some smoothness
conditions in t. We prove that the probability of always finding E(t) = 1 from
t = 0 to T is unity. If , the watched kettle is sure to `boil'.Comment: 10 pages,late
Influence of the detector's temperature on the quantum Zeno effect
In this paper we study the quantum Zeno effect using the irreversible model
of the measurement. The detector is modeled as a harmonic oscillator
interacting with the environment. The oscillator is subjected to the force,
proportional to the energy of the measured system. We use the Lindblad-type
master equation to model the interaction with the environment. The influence of
the detector's temperature on the quantum Zeno effect is obtained. It is shown
that the quantum Zeno effect becomes stronger (the jump probability decreases)
when the detector's temperature increases
Projection Postulate and Atomic Quantum Zeno Effect
The projection postulate has been used to predict a slow-down of the time
evolution of the state of a system under rapidly repeated measurements, and
ultimately a freezing of the state. To test this so-called quantum Zeno effect
an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295 (1990)) in
which an atomic-level measurement was realized by means of a short laser pulse.
The relevance of the results has given rise to controversies in the literature.
In particular the projection postulate and its applicability in this experiment
have been cast into doubt. In this paper we show analytically that for a wide
range of parameters such a short laser pulse acts as an effective level
measurement to which the usual projection postulate applies with high accuracy.
The corrections to the ideal reductions and their accumulation over n pulses
are calculated. Our conclusion is that the projection postulate is an excellent
pragmatic tool for a quick and simple understanding of the slow-down of time
evolution in experiments of this type. However, corrections have to be
included, and an actual freezing does not seem possible because of the finite
duration of measurements.Comment: 25 pages, LaTeX, no figures; to appear in Phys. Rev.
- …