853 research outputs found
Time delay for one-dimensional quantum systems with steplike potentials
This paper concerns time-dependent scattering theory and in particular the
concept of time delay for a class of one-dimensional anisotropic quantum
systems. These systems are described by a Schr\"{o}dinger Hamiltonian with a potential converging to different limits
and as and respectively. Due to the
anisotropy they exhibit a two-channel structure. We first establish the
existence and properties of the channel wave and scattering operators by using
the modern Mourre approach. We then use scattering theory to show the identity
of two apparently different representations of time delay. The first one is
defined in terms of sojourn times while the second one is given by the
Eisenbud-Wigner operator. The identity of these representations is well known
for systems where vanishes as (). We show
that it remains true in the anisotropic case , i.e. we prove
the existence of the time-dependent representation of time delay and its
equality with the time-independent Eisenbud-Wigner representation. Finally we
use this identity to give a time-dependent interpretation of the
Eisenbud-Wigner expression which is commonly used for time delay in the
literature.Comment: 48 pages, 1 figur
On the Localization of One-Photon States
Single photon states with arbitrarily fast asymptotic power-law fall-off of
energy density and photodetection rate are explicitly constructed. This goes
beyond the recently discovered tenth power-law of the Hellwarth-Nouchi photon
which itself superseded the long-standing seventh power-law of the Amrein
photon.Comment: 7 pages, tex, no figure
Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian
We consider the hamiltonian operator associated with planar sec- tions of
infinitely long cylindrical solenoids and with a homogeneous magnetic field in
their interior. First, in the Sobolev space , we characterize all
generalized boundary conditions on the solenoid bor- der compatible with
quantum mechanics, i.e., the boundary conditions so that the corresponding
hamiltonian operators are self-adjoint. Then we study and compare the
scattering of the most usual boundary con- ditions, that is, Dirichlet, Neumann
and Robin.Comment: 40 pages, 5 figure
Rigorous Real-Time Feynman Path Integral for Vector Potentials
we will show the existence and uniqueness of a real-time, time-sliced Feynman
path integral for quantum systems with vector potential. Our formulation of the
path integral will be derived on the transition probability amplitude via
improper Riemann integrals. Our formulation will hold for vector potential
Hamiltonian for which its potential and vector potential each carries at most a
finite number of singularities and discontinuities
The EPATH trial
Observational studies suggested a link between bone disease and left
ventricular (LV) dysfunction that may be pronounced in hyperparathyroid
conditions. We therefore aimed to test the hypothesis that circulating markers
of bone turnover correlate with LV function in a cohort of patients with
primary hyperparathyroidism (pHPT). Cross-sectional data of 155 subjects with
pHPT were analyzed who participated in the “Eplerenone in Primary
Hyperparathyroidism” (EPATH) Trial. Multivariate linear regression analyses
with LV ejection fraction (LVEF, systolic function) or peak early transmitral
filling velocity (e’, diastolic function) as dependent variables and
N-terminal propeptide of procollagen type 1 (P1NP), osteocalcin (OC), bone-
specific alkaline phosphatase (BALP), or beta-crosslaps (CTX) as the
respective independent variable were performed. Analyses were additionally
adjusted for plasma parathyroid hormone, plasma calcium, age, sex, HbA1c, body
mass index, mean 24-hours systolic blood pressure, smoking status, estimated
glomerular filtration rate, antihypertensive treatment, osteoporosis
treatment, 25-hydroxy vitamin D and N-terminal pro-brain B-type natriuretic
peptide. Independent relationships were observed between P1NP and LVEF
(adjusted β-coefficient = 0.201, P = 0.035) and e’ (β = 0.188, P = 0.042),
respectively. OC (β = 0.192, P = 0.039) and BALP (β = 0.198, P = 0.030) were
each independently related with e’. CTX showed no correlations with LVEF or
e’. In conclusion, high bone formation markers were independently and
paradoxically related with better LV diastolic and, partly, better systolic
function, in the setting of pHPT. Potentially cardio-protective properties of
stimulated bone formation in the context of hyperparathyroidism should be
explored in future studies
The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I
We exemplify the way the rigged Hilbert space deals with the
Lippmann-Schwinger equation by way of the spherical shell potential. We
explicitly construct the Lippmann-Schwinger bras and kets along with their
energy representation, their time evolution and the rigged Hilbert spaces to
which they belong. It will be concluded that the natural setting for the
solutions of the Lippmann-Schwinger equation--and therefore for scattering
theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur
The various power decays of the survival probability at long times for free quantum particle
The long time behaviour of the survival probability of initial state and its
dependence on the initial states are considered, for the one dimensional free
quantum particle. We derive the asymptotic expansion of the time evolution
operator at long times, in terms of the integral operators. This enables us to
obtain the asymptotic formula for the survival probability of the initial state
, which is assumed to decrease sufficiently rapidly at large .
We then show that the behaviour of the survival probability at long times is
determined by that of the initial state at zero momentum . Indeed,
it is proved that the survival probability can exhibit the various power-decays
like for an arbitrary non-negative integers as ,
corresponding to the initial states with the condition as .Comment: 15 pages, to appear in J. Phys.
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