Generalized Heisenberg Algebras and Fibonacci Series

We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two previous levels. This happens, for example, for systems having the energy spectrum given by Fibonacci sequence. Moreover, the algebraic structure depends on two functions f(x) and g(x). When these two functions are linear we classify, analysing the stability of the fixed points of the functions, the possible representations for this algebra.Comment: 24 pages, 2 figures, subfigure.st

Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems

We introduce a one-parameter generalized oscillator algebra A(k) (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter k. We define an (Hamiltonian) operator associated with A(k) and examine the degeneracies of its spectrum. For the finite (when k < 0) and the infinite (when k > 0 or = 0) representations of A(k), we construct the associated phase operators and build temporally stable phase states as eigenstates of the phase operators. To overcome the difficulties related to the phase operator in the infinite-dimensional case and to avoid the degeneracy problem for the finite-dimensional case, we introduce a truncation procedure which generalizes the one used by Pegg and Barnett for the harmonic oscillator. This yields a truncated generalized oscillator algebra A(k,s), where s denotes the truncation order. We construct two types of temporally stable states for A(k,s) (as eigenstates of a phase operator and as eigenstates of a polynomial in the generators of A(k,s)). Two applications are considered in this article. The first concerns physical realizations of A(k) and A(k,s) in the context of one-dimensional quantum systems with finite (Morse system) or infinite (Poeschl-Teller system) discrete spectra. The second deals with mutually unbiased bases used in quantum information.Comment: Accepted for publication in Journal of Physics A: Mathematical and Theoretical as a pape

A Method Based on a Nonlinear Generalized Heisenberg Algebra to Study the Molecular Vibrational Spectrum

We propose a method, based on a Generalized Heisenberg Algebra (GHA), to reproduce the anharmonic spectrum of diatomic molecules. The theoretical spectrum generated by GHA allows us to fit the experimental data and to obtain the dissociation energy for the carbon monoxide molecule. Our outcomes are more accurate than the standard models used to study molecular vibrations, namely the Morse and the $q$-oscillator models and comparable to the perturbed Morse model proposed by Huffaker \cite{hf}, for the first experimental levels. The dissociation energy obtained here is more accurate than all previous models

Coherent state of a nonlinear oscillator and its revival dynamics

The coherent state of a nonlinear oscillator having a nonlinear spectrum is constructed using Gazeau Klauder formalism. The weighting distribution and the Mandel parameter are studied. Details of the revival structure arising from different time scales underlying the quadratic energy spectrum are investigated by the phase analysis of the autocorrelation function

Natural chain-breaking antioxidants and their synthetic analogs as modulators of oxidative stress

Oxidative stress is associated with the increased production of reactive oxygen species or with a significant decrease in the effectiveness of antioxidant enzymes and nonenzymatic defense. The penetration of oxygen and free radicals in the hydrophobic interior of biological membranes initiates radical disintegration of the hydrocarbon “tails” of the lipids. This process is known as “lipid peroxidation”, and the accumulation of the oxidation products as peroxides and the alde-hydes and acids derived from them are often used as a measure of oxidative stress levels. In total, 40 phenolic antioxidants were selected for a comparative study and analysis of their chain-breaking antioxidant activity, and thus as modulators of oxidative stress. This included natural and natural-like ortho-methoxy and ortho-hydroxy phenols, nine of them newly synthesized. Applied experimental and theoretical methods (bulk lipid autoxidation, chemiluminescence, in silico methods such as density functional theory (DFT) and quantitative structure–activity relationship ((Q)SAR) modeling) were used to clarify their structure–activity relationship. Kinetics of non-inhibited and inhibited lipid oxidation in close connection with inhibitor transformation under oxidative stress is considered. Special attention has been paid to chemical reactions resulting in the initiation of free radicals, a key stage of oxidative stress. Effects of substituents in the side chains and in the phenolic ring of hydroxylated phenols and biphenols, and the concentration were discussed

Active Membrane Fluctuations Studied by Micropipet Aspiration

We present a detailed analysis of the micropipet experiments recently reported in J-B. Manneville et al., Phys. Rev. Lett. 82, 4356--4359 (1999), including a derivation of the expected behaviour of the membrane tension as a function of the areal strain in the case of an active membrane, i.e., containing a nonequilibrium noise source. We give a general expression, which takes into account the effect of active centers both directly on the membrane, and on the embedding fluid dynamics, keeping track of the coupling between the density of active centers and the membrane curvature. The data of the micropipet experiments are well reproduced by the new expressions. In particular, we show that a natural choice of the parameters quantifying the strength of the active noise explains both the large amplitude of the observed effects and its remarkable insensitivity to the active-center density in the investigated range. [Submitted to Phys Rev E, 22 March 2001]Comment: 14 pages, 5 encapsulated Postscript figure

Hydrodynamic mobility of confined polymeric particles, vesicles, and cancer cells in a square microchannel

The transport of deformable objects, including polymer particles, vesicles, and cells, has been a subject of interest for several decades where the majority of experimental and theoretical studies have been focused on circular tubes. Due to advances in microfluidics, there is a need to study the transport of individual deformable particles in rectangular microchannels where corner flows can be important. In this study, we report measurements of hydrodynamic mobility of confined polymeric particles, vesicles, and cancer cells in a linear microchannel with a square cross-section. Our operating conditions are such that the mobility is measured as a function of geometric confinement over the range 0.3 < λ < 1.5 and at specified particle Reynolds numbers that are within 0.1 < Rep < 2.5. The experimental mobility data of each of these systems is compared with the circular-tube theory of Hestroni, Haber, and Wacholder [J. Fluid Mech. 41, 689–705 (1970)] with modifications made for a square cross-section. For polymeric particles, we find that the mobility data agrees well over a large confinement range with the theory but under predicts for vesicles. The mobility of vesicles is higher in a square channel than in a circular tube, and does not depend significantly on membrane mechanical properties. The mobility of cancer cells is in good agreement with the theory up to λ ≈ 0.8, after which it deviates. Comparison of the mobility data of the three systems reveals that cancer cells have higher mobility than rigid particles but lower than vesicles, suggesting that the cell membrane frictional properties are in between a solid-like interface and a fluid bilayer. We explain further the differences in the mobility of the three systems by considering their shape deformation and surface flow on the interface. The results of this study may find potential applications in drug delivery and biomedical diagnostics

All-sky search for short gravitational-wave bursts in the second Advanced LIGO and Advanced Virgo run

We present the results of a search for short-duration gravitational-wave transients in the data from the second observing run of Advanced LIGO and Advanced Virgo. We search for gravitational-wave transients with a duration of milliseconds to approximately one second in the 32-4096 Hz frequency band with minimal assumptions about the signal properties, thus targeting a wide variety of sources. We also perform a matched-filter search for gravitational-wave transients from cosmic string cusps for which the waveform is well modeled. The unmodeled search detected gravitational waves from several binary black hole mergers which have been identified by previous analyses. No other significant events have been found by either the unmodeled search or the cosmic string search. We thus present the search sensitivities for a variety of signal waveforms and report upper limits on the source rate density as a function of the characteristic frequency of the signal. These upper limits are a factor of 3 lower than the first observing run, with a 50% detection probability for gravitational-wave emissions with energies of ∼10-9 Mc2 at 153 Hz. For the search dedicated to cosmic string cusps we consider several loop distribution models, and present updated constraints from the same search done in the first observing run