2,195 research outputs found
Periodic and discrete Zak bases
Weyl's displacement operators for position and momentum commute if the
product of the elementary displacements equals Planck's constant. Then, their
common eigenstates constitute the Zak basis, each state specified by two phase
parameters. Upon enforcing a periodic dependence on the phases, one gets a
one-to-one mapping of the Hilbert space on the line onto the Hilbert space on
the torus. The Fourier coefficients of the periodic Zak bases make up the
discrete Zak bases. The two bases are mutually unbiased. We study these bases
in detail, including a brief discussion of their relation to Aharonov's modular
operators, and mention how they can be used to associate with the single degree
of freedom of the line a pair of genuine qubits.Comment: 15 pages, 3 figures; displayed abstract is shortened, see the paper
for the complete abstrac
Liquid mixing time and gas distribution in aerated multiple-impeller stirred tanks
Gas-liquid fluid dynamics and mass transfer are crucial aspects of aerobic fermentation and robust methodologies for their determination in industrial bioreactors are expected to provide significant improvements in many production processes. In this work, a gas-liquid stirred tank of high aspect ratio, that replicates the geometry of typical industrial aerated fermenters, is investigated. In particular, the liquid phase homogenization dynamics and the gas phase spatial distribution are determined. The selected methodology is based on the analysis of the conductivity measurements obtained by Electrical Resistance Tomography. The gas-liquid flow regimes and the mixing time are identified at various gas flow rates and impeller speeds, thus covering different gas-liquid regimes. Data col
lected with vertical and horizontal arrangements of the electrodes allow to obtain a
tailed picture of the equipment working mode and to gain insight into the gas-liquid flow dynamics under optically inaccessible conditions. Quantitative evaluation of the
bility of the collected data is attempted by comparing the results obtained with the
tical and horizontal arrangements in the same locations
Simultaneous measurement of coordinate and momentum on a von Neumann lattice
It is shown that on a finite phase plane the -coordinates and the sites
of a von Neumann lattice are conjugate to one another. This elementary result
holds when the number defining the size of the phase plane can be expressed
as a product, , with and being relatively prime.
As a consequence of this result a hitherto unknown wave function is defined
giving the probability of simultaneously measuring the momentum and coordinate
on the von Neumann lattice.Comment: Published in EPL 83 (2008) 1000
Biochemical correlates of cardiac hypertrophy. I. Experimental model; changes in heart weight, RNA content, and nuclear RNA polymerase activity
Cardiac hypertrophy occurred in mature rats after producing supravalvular aortic stenosis with a specially designed silver clip. For 2 weeks following this procedure, heart weight, body weight, and RNA content of the myocardium were serially determined. Heart weight and RNA content increased within 24 hours of aortic banding, reaching a maximal level in 2 days and remaining elevated during the 2 weeks of observation. Nuclei were isolated and purified from heart muscle homogenates, and changes in RNA polymerase activity following aortic banding were determined. The nearest neighbor frequency of the bases of the RNA synthesized by the polymerase from nuclear preparations was identical in both the banded animals and the sham-operated controls. Both groups could thus be compared on the basis of the enzyme assay. RNA polymerase activity in nuclei from the hearts of banded rats rose rapidly when compared with the activity in sham-operated rats; peak values were reached on the second day, the earliest detectable change being around 12 hours. The increase in RNA polymerase activity represents one of the earliest biochemical events that take place in the myocardium following aortic banding
The Postantibiotic Effect in the Treatment of Experimental Meningitis Caused by Streptococcus pneumoniae in Rabbits
The relevance of a postantibiotic effect in the treatment of pneumococcal meningitis was evaluated in a rabbit model. After administration of a single intravenous bolus of ampicillin at various dosages, such an effect was observed in all animals. The duration of this effect in vivo (2.5-18 hr) was consistently longer than that in vitro (1-4.3 hr); however, in rabbits the postantibiotic effect was eliminated by the administration of intravenous plus intracisternal β-lactamase. In an assessment of the potential therapeutic benefit of the postantibiotic effect, the efficacy of two regimens of treatment with different intervals between doses was compared. One group of animals received ampicillin every 4 hr and another every 12 hr. With sufficiently high doses, drug concentrations in cerebrospinal fluid exceeded the minimal bactericidal concentration for most of the 4-hr interval but for only about one-third of the 12-hr interval. The rate of cure was similar for the two regimens and approximated 100% when peak drug concentrations in cerebrospinal fluid exceeded the minimal bactericidal concentration by at least 10-fol
Algebraic Geometry Approach to the Bethe Equation for Hofstadter Type Models
We study the diagonalization problem of certain Hofstadter-type models
through the algebraic Bethe ansatz equation by the algebraic geometry method.
When the spectral variables lie on a rational curve, we obtain the complete and
explicit solutions for models with the rational magnetic flux, and discuss the
Bethe equation of their thermodynamic flux limit. The algebraic geometry
properties of the Bethe equation on high genus algebraic curves are
investigated in cooperationComment: 28 pages, Latex ; Some improvement of presentations, Revised version
with minor changes for journal publicatio
Area versus Length Distribution for Closed Random Walks
Using a connection between the -oscillator algebra and the coefficients of
the high temperature expansion of the frustrated Gaussian spin model, we derive
an exact formula for the number of closed random walks of given length and
area, on a hypercubic lattice, in the limit of infinite number of dimensions.
The formula is investigated in detail, and asymptotic behaviours are evaluated.
The area distribution in the limit of long loops is computed. As a byproduct,
we obtain also an infinite set of new, nontrivial identities.Comment: 17 page
Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
We present a unified theory for wave-packet dynamics of electrons in crystals
subject to perturbations varying slowly in space and time. We derive the
wave-packet energy up to the first order gradient correction and obtain all
kinds of Berry-phase terms for the semiclassical dynamics and the quantization
rule. For electromagnetic perturbations, we recover the orbital magnetization
energy and the anomalous velocity purely within a single-band picture without
invoking inter-band couplings. For deformations in crystals, besides a
deformation potential, we obtain a Berry-phase term in the Lagrangian due to
lattice tracking, which gives rise to new terms in the expressions for the
wave-packet velocity and the semiclassical force. For multiple-valued
displacement fields surrounding dislocations, this term manifests as a Berry
phase, which we show to be proportional to the Burgers vector around each
dislocation.Comment: 12 pages, RevTe
Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants
For a periodic Hamiltonian, periodic dynamical invariants may be used to
obtain non-degenerate cyclic states. This observation is generalized to the
degenerate cyclic states, and the relation between the periodic dynamical
invariants and the Floquet decompositions of the time-evolution operator is
elucidated. In particular, a necessary condition for the occurrence of cyclic
non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic
states are obtained for a magnetic dipole interacting with a precessing
magnetic field.Comment: Plain LaTeX, 13 pages, accepted for publication in J. Phys. A: Math.
Ge
Emergent Classicality via Commuting Position and Momentum Operators
Any account of the emergence of classicality from quantum theory must address
the fact that the quantum operators representing positions and momenta do not
commute, whereas their classical counterparts suffer no such restrictions. To
address this, we revive an old idea of von Neumann, and seek a pair of
commuting operators which are, in a specific sense, "close" to the
canonical non-commuting position and momentum operators, . The
construction of such operators is related to the problem of finding complete
sets of orthonormal phase space localized states, a problem severely limited by
the Balian-Low theorem. Here these limitations are avoided by restricting
attention to situations in which the density matrix is reasonably decohered
(i.e., spread out in phase space).Comment: To appear in Proceedings of the 2008 DICE Conferenc
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