855 research outputs found
A Complexity Measure for Continuous Time Quantum Algorithms
We consider unitary dynamical evolutions on n qubits caused by time dependent
pair-interaction Hamiltonians and show that the running time of a parallelized
two-qubit gate network simulating the evolution is given by the time integral
over the chromatic index of the interaction graph. This defines a complexity
measure of continuous and discrete quantum algorithms which are in exact
one-to-one correspondence. Furthermore we prove a lower bound on the growth of
large-scale entanglement depending on the chromatic index.Comment: 6 pages, Revte
Dynamical large deviations for a boundary driven stochastic lattice gas model with many conserved quantities
We prove the dynamical large deviations for a particle system in which
particles may have different velocities. We assume that we have two infinite
reservoirs of particles at the boundary: this is the so-called boundary driven
process. The dynamics we considered consists of a weakly asymmetric simple
exclusion process with collision among particles having different velocities
Dose Optimization for Using the Contrast Agent Gadofosveset in Magnetic Resonance Imaging (MRI) of Domestic Pig Brain
Pigs are useful models in stroke research, and Magnetic Resonance Imaging (MRI) is a useful tool for measurements of brain pathophysiology. Perfusion Weighed Imaging (PWI) with standard Gd-based chelates (i.e. gadobutrol) provides crucial information about breakdown of the Blood-Brain-Barrier (BBB) in patients. Gadofosveset is also a Gd-based contrast agent, but with a higher binding to serum albumin. The prolonged plasma-half life of gadofosveset allows the acquisition of steady state angiographies, which may increase the sensitivity for detection of BBB leakage. We hypothesize that the contrast dosage with gadofosveset can be optimized for PWI and subsequent steady-state Magnetic Resonance Angiography (MRA) in pigs. Anesthetized domestic pigs (females; N=6) were MRI scanned four times in one day: they were initially imaged during a standard gadobutrol bolus injection (0.1 mmol/kg). Then they received three successive gadofosveset bolus injections of varying dosages (0.015-0.09 mmol/kg). Based on projection from our data, we suggest that a bolus injection of 0.0916 mmol/kg gadofosveset would yield contrast similar to that of a standard dose of 0.1 mmol/kg gadobutrol in dynamic susceptibility contrast MRI at 3 T. In conclusion, our results demonstrate the feasibility of gadofosveset based PWI in pig brain research. The relaxation and plasma half-life properties allow detailed steady-state MRA angiographies and may prove useful in detecting subtle BBB disruption of significance in stroke models and human patients
Adaptive filtering techniques for gravitational wave interferometric data: Removing long-term sinusoidal disturbances and oscillatory transients
It is known by the experience gained from the gravitational wave detector
proto-types that the interferometric output signal will be corrupted by a
significant amount of non-Gaussian noise, large part of it being essentially
composed of long-term sinusoids with slowly varying envelope (such as violin
resonances in the suspensions, or main power harmonics) and short-term ringdown
noise (which may emanate from servo control systems, electronics in a
non-linear state, etc.). Since non-Gaussian noise components make the detection
and estimation of the gravitational wave signature more difficult, a denoising
algorithm based on adaptive filtering techniques (LMS methods) is proposed to
separate and extract them from the stationary and Gaussian background noise.
The strength of the method is that it does not require any precise model on the
observed data: the signals are distinguished on the basis of their
autocorrelation time. We believe that the robustness and simplicity of this
method make it useful for data preparation and for the understanding of the
first interferometric data. We present the detailed structure of the algorithm
and its application to both simulated data and real data from the LIGO 40meter
proto-type.Comment: 16 pages, 9 figures, submitted to Phys. Rev.
A theory of intense-field dynamic alignment and high harmonic generation from coherently rotating molecules and interpretation of intense-field ultrafast pump-probe experiments
A theory of ultra-fast pump-probe experiments proposed by us earlier [F.H.M.
Faisal et al., Phys. Rev. Lett. 98, 143001 (2007) and F.H.M. Faisal and A.
Abdurrouf, Phys. Rev. Lett. 100, 123005 (2008)] is developed here fully and
applied to investigate the phenomena of dynamic alignment and high harmonic
generation (HHG) from coherently rotating linear molecules. The theory provides
essentially analytical results for the signals that allow us to investigate the
simultaneous dependence of the HHG signals on the two externally available
control parameters, namely, the relative angle between the polarizations, and
the delay-time between the two pulses. It is applied to investigate the
characteristics of high harmonic emission from nitrogen and oxygen molecules
that have been observed experimentally in a number of laboratories. The results
obtained both in the time-domain and in the frequency-domain are compared with
the observed characteristics as well as directly with the data and are found to
agree remarkably well. In addition we have predicted the existence of a "magic"
polarization angle at which all modulations of the harmonic emission from
nitrogen molecule changes to a steady emission at the harmonic frequency. Among
other things we have also shown a correlation between the existence of the
"magic" or critical polarization angles and the symmetry of the active
molecular orbitals, that is deemed to be useful in connection with the "inverse
problem" of molecular imaging from the HHG data.Comment: 31 pages, 22 figures, and 140 equation
Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
The set of doubly-stochastic quantum channels and its subset of mixtures of
unitaries are investigated. We provide a detailed analysis of their structure
together with computable criteria for the separation of the two sets. When
applied to O(d)-covariant channels this leads to a complete characterization
and reveals a remarkable feature: instances of channels which are not in the
convex hull of unitaries can return to it when either taking finitely many
copies of them or supplementing with a completely depolarizing channel. In
these scenarios this implies that a channel whose noise initially resists any
environment-assisted attempt of correction can become perfectly correctable.Comment: 31 page
Quaternion-Octonion Unitary Symmetries and Analogous Casimir Operators
An attempt has been made to investigate the global SU(2) and SU(3) unitary
flavor symmetries systematically in terms of quaternion and octonion
respectively. It is shown that these symmetries are suitably handled with
quaternions and octonions in order to obtain their generators, commutation
rules and symmetry properties. Accordingly, Casimir operators for SU(2)and
SU(3) flavor symmetries are also constructed for the proper testing of these
symmetries in terms of quaternions and octonions
The Stokes and Poisson problem in variable exponent spaces
We study the Stokes and Poisson problem in the context of variable exponent
spaces. We prove the existence of strong and weak solutions for bounded domains
with C^{1,1} boundary with inhomogenous boundary values. The result is based on
generalizations of the classical theories of Calderon-Zygmund and
Agmon-Douglis-Nirenberg to variable exponent spaces.Comment: 20 pages, 1 figur
Magnetic phases and reorientation transitions in antiferromagnetically coupled multilayers
In antiferromagnetically coupled superlattices grown on (001) faces of cubic
substrates, e.g. based on materials combinations as Co/Cu, Fe/Si, Co/Cr, or
Fe/Cr, the magnetic states evolve under competing influence of bilinear and
biquadratic exchange interactions, surface-enhanced four-fold in-plane
anisotropy, and specific finite-size effects. Using phenomenological
(micromagnetic) theory, a comprehensive survey of the magnetic states and
reorientation transitions has been carried out for multilayer systems with even
number of ferromagnetic sub-layers and magnetizations in the plane. In
two-layer systems (N=2) the phase diagrams in dependence on components of the
applied field in the plane include ``swallow-tail'' type regions of
(metastable) multistate co-existence and a number of continuous and
discontinuous reorientation transitions induced by radial and transversal
components of the applied field. In multilayers (N \ge 4) noncollinear states
are spatially inhomogeneous with magnetization varying across the multilayer
stack. For weak four-fold anisotropy the magnetic states under influence of an
applied field evolve by a complex continuous reorientation into the saturated
state. At higher anisotropy they transform into various inhomogeneous and
asymmetric structures. The discontinuous transitions between the magnetic
states in these two-layers and multilayers are characterized by broad ranges of
multi-phase coexistence of the (metastable) states and give rise to specific
transitional domain structures.Comment: Manuscript 34 pages, 14 figures; submitted for publicatio
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