THE PARTITION-FUNCTION FOR AN ANYON-LIKE OSCILLATOR

We compute the partition function of an anyon-like harmonic oscillator. The well known results for both the bosonic and fermionic oscillators are then re-obtained as particular cases of our function. The technique we employ is a non-relativistic version of the Green function method used in the computation of one-loop effective actions of quantum field theory.

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

Faddeev-jackiw formalism for A topological-like oscillator in planar dimensions

The problem of a harmonic oscillator coupling to an electromagnetic potential plus a topological-like (Chern-Simons) massive term, in two-dimensional space, is studied in the light of the symplectic formalism proposed by Faddeev and Jackiw for constrained systems.

Trapping of a particle in a short-range harmonic potential well

Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed. © 2012 Springer Science+Business Media, LLC.

Multipartite entanglement in harmonic oscillators subjected to dissipative quantum dynamics

Una detallada descripción de la dinámica de bajas energías del entrelazamiento multipartito es proporcionada para sistemas armónicos en una gran variedad de escenarios disipativos. Sin hacer ninguna aproximación central, esta descripción yace principalmente sobre un conjunto razonable de hipótesis acerca del entorno e interacción entorno-sistema, ambas consistente con un análisis lineal de la dinámica disipativa. En la primera parte se deriva un criterio de inseparabilidad capaz de detectar el entrelazamiento k-partito de una extensa clase de estados gausianos y no-gausianos en sistemas de variable continua. Este criterio se emplea para monitorizar la dinámica transitiva del entrelazamiento, mostrando que los estados no-gausianos pueden ser tan robustos frente a los efectos disipativos como los gausianos. Especial atención se dedicada a la dinámica estacionaria del entrelazamiento entre tres osciladores interaccionando con el mismo entorno o diferentes entornos a distintas temperaturas. Este estudio contribuye a dilucidar el papel de las correlaciones cuánticas en el comportamiento de la corrientes energéticas.

Hidden vorticity in binary Bose-Einstein condensates

We consider a binary Bose-Einstein condensate (BEC) described by a system of two-dimensional (2D) Gross-Pitaevskii equations with the harmonic-oscillator trapping potential. The intraspecies interactions are attractive, while the interaction between the species may have either sign. The same model applies to the copropagation of bimodal beams in photonic-crystal fibers. We consider a family of trapped hidden-vorticity (HV) modes in the form of bound states of two components with opposite vorticities S(1,2) = +/- 1, the total angular momentum being zero. A challenging problem is the stability of the HV modes. By means of a linear-stability analysis and direct simulations, stability domains are identified in a relevant parameter plane. In direct simulations, stable HV modes feature robustness against large perturbations, while unstable ones split into fragments whose number is identical to the azimuthal index of the fastest growing perturbation eigenmode. Conditions allowing for the creation of the HV modes in the experiment are discussed too. For comparison, a similar but simpler problem is studied in an analytical form, viz., the modulational instability of an HV state in a one-dimensional (1D) system with periodic boundary conditions (this system models a counterflow in a binary BEC mixture loaded into a toroidal trap or a bimodal optical beam coupled into a cylindrical shell). We demonstrate that the stabilization of the 1D HV modes is impossible, which stresses the significance of the stabilization of the HV modes in the 2D setting.

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Optimal estimation of one-parameter quantum channels

We explore the task of optimal quantum channel identification and in particular, the estimation of a general one-parameter quantum process. We derive new characterizations of optimality and apply the results to several examples including the qubit depolarizing channel and the harmonic oscillator damping channel. We also discuss the geometry of the problem and illustrate the usefulness of using entanglement in process estimation.

Determination of the force constant of a single-beam gradient trap by measurement of backscattered light

A single-beam gradient trap could potentially be used to hold a stylus for scanning force microscopy. With a view to development of this technique, we modeled the optical trap as a harmonic oscillator and therefore characterized it by its force constant. We measured force constants and resonant frequencies for 1-4-mu m-diameter polystyrene spheres in a single-beam gradient trap using measurements of back-scattered light. Force constants were determined with both Gaussian and doughnut laser modes, with powers of 3 and 1 mW, respectively. Typical values for spring constants were measured to be between 10(-6) and 4 x 10(-6) N/m. The resonant frequencies of trapped particles were measured to be between 1 and 10 kHz, and the rms amplitudes of oscillations were estimated to be around 40 nm. Our results confirm that the use of the doughnut mode for single-beam trapping is more efficient in the axial direction. (C) 1996 Optical Society of America.

Modeling upper eyelid kinematics during spontaneous and reflex blinks

To test a mathematical model for measuring blinking kinematics. Spontaneous and reflex blinks of 23 healthy subjects were recorded with two different temporal resolutions. A magnetic search coil was used to record 77 blinks sampled at 200 Hz and 2 kHz in 13 subjects. A video system with low temporal resolution (30 Hz) was employed to register 60 blinks of 10 other subjects. The experimental data points were fitted with a model that assumes that the upper eyelid movement can be divided into two parts: an impulsive accelerated motion followed by a damped harmonic oscillation. All spontaneous and reflex blinks, including those recorded with low resolution, were well fitted by the model with a median coefficient of determination of 0.990. No significant difference was observed when the parameters of the blinks were estimated with the under-damped or critically damped solutions of the harmonic oscillator. On the other hand, the over-damped solution was not applicable to fit any movement. There was good agreement between the model and numerical estimation of the amplitude but not of maximum velocity. Spontaneous and reflex blinks can be mathematically described as consisting of two different phases. The down-phase is mainly an accelerated movement followed by a short time that represents the initial part of the damped harmonic oscillation. The latter is entirely responsible for the up-phase of the movement. Depending on the instantaneous characteristics of each movement, the under-damped or critically damped oscillation is better suited to describe the second phase of the blink. (C) 2010 Elsevier B.V. All rights reserved.

The relationship between two types of upper eyelid movements: Saccades and pursuit

PURPOSE. To establish the relationship between upper eyelid saccades and upper eyelid pursuit movements. METHODS. Upper eyelid saccades and periodic sinusoidal upper eyelid pursuit movements were recorded in a sample of controls and patients with Graves upper eyelid retraction. A video-computerized system was used to register both types of movements that accompanied 60 of eye rotation across the upper and lower hemifields. The forced harmonic oscillator model was used to fit saccadic and pursuit movements. RESULTS. Mean mid-pupil eyelid distance for the Graves patients (6.6 +/- 1.1 mm) was significantly higher than for the controls (4.6 +/- 0.8 mm; t = 7.18; P < 0.00001). Despite the difference in the upper eyelid resting position, saccades and pursuit eyelid movements of both groups were extremely well fitted by underdamped solutions and steady forced solutions of the harmonic oscillator model, respectively. For the controls, the amplitude of the pursuit movements was well correlated with the upward and downward saccades. The amplitude of the eyelid movements of the Graves patients (saccades and pursuit) was significantly reduced compared with that of the controls. CONCLUSIONS. Saccadic and pursuit movements of the upper eyelid can be described by the harmonic oscillator model. In healthy subjects and Graves patients, the amplitude of pursuit lid movements is correlated to the saccade amplitude. Pursuit eyelid movements are more difficult to register than saccades, and their measurements do not allow clear separation of the relaxation and contraction properties of the upper eyelid retractors.

Study of vanadium doped ZnO films prepared by dc reactive magnetron sputtering at different substrate temperatures

ZnO films doped with vanadium (ZnO:V) have been prepared by dc reactive magnetron sputtering technique at different substrate temperatures (RT–500 C). The effects of the substrate temperature on ZnO:V films properties have been studied. XRD measurements show that only ZnO polycrystalline structure has been obtained, no V2O5 or VO2 crystal phase can be observed. It has been found that the film prepared at low substrate temperature has a preferred orientation along the (002) direction. As the substrate temperature is increased, the (002) peak intensity decreases. When the substrate temperature reaches the 500 C, the film shows a random orientation. SEM measurements show a clear formation of the nano-grains in the sample surface when the substrate temperature is higher than 400 C. The optical properties of the films have been studied by measuring the specular transmittance. The refractive index has been calculated by fitting the transmittance spectra using OJL model combined with harmonic oscillator.

Homeostatic and circadian contribution to EEG and molecular state variables of sleep regulation.

STUDY OBJECTIVES: Besides their well-established role in circadian rhythms, our findings that the forebrain expression of the clock-genes Per2 and Dbp increases and decreases, respectively, in relation to time spent awake suggest they also play a role in the homeostatic aspect of sleep regulation. Here, we determined whether time of day modulates the effects of elevated sleep pressure on clock-gene expression. Time of day effects were assessed also for recognized electrophysiological (EEG delta power) and molecular (Homer1a) markers of sleep homeostasis. DESIGN: EEG and qPCR data were obtained for baseline and recovery from 6-h sleep deprivation starting at ZT0, -6, -12, or -18. SETTING: Mouse sleep laboratory. PARTICIPANTS: Male mice. INTERVENTIONS: Sleep deprivation. RESULTS: The sleep-deprivation induced changes in Per2 and Dbp expression importantly varied with time of day, such that Per2 could even decrease during sleep deprivations occurring at the decreasing phase in baseline. Dbp showed similar, albeit opposite dynamics. These unexpected results could be reliably predicted assuming that these transcripts behave according to a driven damped harmonic oscillator. As expected, the sleep-wake distribution accounted for a large degree of the changes in EEG delta power and Homer1a. Nevertheless, the sleep deprivation-induced increase in delta power varied also with time of day with higher than expected levels when recovery sleep started at dark onset. CONCLUSIONS: Per2 and delta power are widely used as exclusive state variables of the circadian and homeostatic process, respectively. Our findings demonstrate a considerable cross-talk between these two processes. As Per2 in the brain responds to both sleep loss and time of day, this molecule is well positioned to keep track of and to anticipate homeostatic sleep need. CITATION: Curie T; Mongrain V; Dorsaz S; Mang GM; Emmenegger Y; Franken P. Homeostatic and circadian contribution to EEG and molecular state variables of sleep regulation. SLEEP 2013;36(3):311-323.

Average ground-state energy of finite Fermi systems

Semiclassical theories such as the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard-wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.

Structure and Stability of 3He Droplets

We have studied the structure of 3He droplets at zero temperature using a density functional approach plus a configuration interaction calculation in an harmonic oscillator major shell. The most salient feature of open shell drops is that the valence atoms couple their spins to the maximum value compatible with Pauli's principle, building a large magnetic moment. We have determined that 29 atoms constitute the smallest self-bound droplet.