Transfer of a wave packet in double-well potential

Ultrashort, nearly unipolar electric field pulses are used to produce novel dynamic states in Rydberg atoms. A single 500 fsec field pulse redistributes essentially all of the population from a single stationary Rydberg state to hundreds of different final states. The dynamic evolution of the nonstationary wave packet is monitored using a second, time-delayed pulse. The time-dependent momentum-space probability distribution of the wave packet can be retrieved experimentally using a classical impulse approximation.

Cased petroleum wells must be logged to determine the bonding and hydraulic isolation properties of the sealing material and to determine the structural integrity status. Although ultrasonic pitch-catch logging in single-casing geometries has been widely studied and is commercially available, this is not the case for logging in double-casing geometries despite its increasing importance in plug and abandonment operations. It is therefore important to investigate whether existing logging tools can be used in such geometries. Using a finite-element model of a double-casing geometry with a two-receiver pitch-catch setup, we have simulated through-tubing logging, with fluid between the two casings. We found that there appears a cascade of leaky Lamb wave packets on both casings, linked by leaked wavefronts. By varying the geometry and materials in the model, we have examined the effect on the pulse received from the second wave packet on the inner casing, sometimes known as the third interface echo. The amplitude of this pulse was found to contain information on the bonded material in the outer annulus. Much stronger amplitude variations were found with two equally thick casings than with a significant thickness difference; relative thickness differences of up to one-third were simulated. Finally, we have developed a simple mathematical model of the wave packets’ time evolution to encapsulate and validate our understanding of the wave packet cascade. This model shows a more complex time evolution in the later wave packets than the exponentially attenuated primary packet, which is currently used for single-casing logging. This indicates that tools with more than two receivers, which could measure wave packets’ amplitude at more than two points along their time evolution, would be able to draw more information from these later packets. The model was validated against simulations, finding good agreement when the underlying assumptions of the model were satisfied.

We present a quantum mechanical wave packet study for the unimolecular dissociation of a triatomic molecule into an atom and a diatom. The 3D potential energy surface used in the dynamics calculations is that of the B̃ state of water corresponding to the second absorption band. Both OH stretching coordinates and the bending angle are included. What is not taken into account is the strong nonadiabatic coupling to the lower-lying à and X̃ states which in reality drastically shortens the lifetime in the B̃ state. For this reason the present study is not a realistic account of the dissociation dynamics of water in the 122 nm band. It is, however, a representational investigation of a unimolecular reaction evolving on a realistic potential energy surface without barrier. The main focus is the resonance structure of the absorption spectrum and the final rotational state distributions of the OH fragment. The total absorption spectrum as well as the partial dissociation cross sections for individual rotational states of OH show drastic fluctuations caused by overlapping resonances. The widths of the individual resonances increase, on average, with the excess energy which has the consequence that the cross sections become gradually smoother. Although the low-energy part of the spectrum is rather irregular, it shows ‘‘clumps’’ of resonances with an uniform spacing of ∼0.1 eV. They are discussed in the context of IVR and a particular unstable periodic orbit. In accordance with the fluctuations in the partial dissociation cross sections as functions of the excess energy the final rotational state distributions show pronounced, randomlike fluctuations which are extremely sensitive on the energy. The average is given by the statistical limit (PST), in which all levels are populated with equal probability. With increasing excess energy the distributions more and more exhibit dynamical features which are reminiscent of direct dissociation like rainbows and associated interferences. Classical trajectories for small excess energies are chaotic, as tested by means of the rotational excitation function, but become gradually more regular with increasing energy. Our wave packet calculations hence demonstrate how the transition from the chaotic to the regular regime shows up in a fully quantum mechanical treatment. The results of the present investigation are in qualitative accord with recent measurements for the unimolecular dissociation of NO2.

On the wave height distribution of waves and wave packets around a reef lagoon of the South China Sea

We show that, when a spatially localised electric pulse is applied at the edge of a quantum spin Hall system, electron wavepackets of the helical states can be photoexcited by purely intra-branch electrical transitions, without invoking the bulk states or the magnetic Zeeman coupling. In particular, as long as the electric pulse remains applied, the photoexcited densities lose their character of right- and left-movers, whereas after the ending of the pulse they propagate in opposite directions without dispersion, i.e. maintaining their space profile unaltered. Notably we find that, while the momentum distribution of the photoexcited wave packets depends on the temperature $T$ and the chemical potential $\mu$ of the initial equilibrium state and displays a non-linear behavior on the amplitude of the applied pulse, in the mesoscopic regime the space profile of the wave packets is independent of $T$ and $\mu$. Instead, it depends purely on the applied electric pulse, in a linear manner, as a signature of the chiral anomaly characterising massless Dirac electrons. We also discuss how the photoexcited wave packets can be tailored with the electric pulse parameters, for both low and finite frequencies.

ABSTRACTWe report a rigorous computational treatment of quantum dynamics of cold ions in a double-well trap using the time-dependent Schrödinger equation. Our method employs a numerically accurate approach that avoids approximations, such as assumption of weak coupling between the wells; normal mode nature of vibrations; or harmonic approximation for energy spectrum of the double-well system. Our goal is to reproduce, from first principles, the process of energy swaps between the wells observed in the experiments at NIST [Nature 471, 196 (2011)] and Innsbruck [Nature 471, 200 (2011)]. The model parameters and the initial conditions are carefully chosen to mimic experimental conditions. We obtain accurate energies and wave functions of the system numerically, and study the evolution of motional wave packets to provide new insight. This model reproduces experimental results obtained by NIST and Innsbruck in detail. We explain the energy transfer in terms of wave packet dynamics in the asymmetric potential energy well. We also show that, for a localised initial wave packet, this phenomenon can be interpreted using the terms of classical dynamics, such as trajectory of motion governed by the well-known simple principle: the angle of reflection equals the angle of incidence.

The ultrafast vibrational-electronic relaxation upon excitation into the singlet (1)A(2u) (dσ*→pσ) excited state of the d(8)-d(8) binuclear complex [Pt(2)(P(2)O(5)H(2))(4)](4-) has been investigated in different solvents by femtosecond polychromatic fluorescence up-conversion and femtosecond broadband transient absorption (TA) spectroscopy. Both sets of data exhibit clear signatures of vibrational relaxation and wave packet oscillations of the Pt-Pt stretch vibration in the (1)A(2u) state with a period of 224 fs, that decay on a 1-2 ps time scale, and of intersystem crossing (ISC) into the (3)A(2u) state. The vibrational relaxation and ISC times exhibit a pronounced solvent dependence. We also extract from the TA measurements the spectral distribution of the wave packet at a given delay time, which reflects the distribution of Pt-Pt bond distances as a function of time, i.e., the structural dynamics of the system. We clearly establish the vibrational relaxation and coherence decay processes, and we demonstrate that PtPOP represents a clear example of a harmonic oscillator that does not comply with the optical Bloch description due to very efficient coherence transfer between vibronic levels. We conclude that a direct Pt-solvent energy dissipation channel accounts for the vibrational cooling in the singlet state. ISC from the (1)A(2u) to the (3)A(2u) state is induced by spin-vibronic coupling with a higher-lying triplet state and/or (transient) symmetry breaking in the (1)A(2u) excited state. The particular structure, energetics, and symmetry of the molecule play a decisive role in determining the relatively slow rate of ISC, despite the large spin-orbit coupling strength of the Pt atoms.

The generation and dynamics of plasmon wave packets in single gold nanorods were observed at a spatiotemporal scale of 100 nm and 10 fs via time-resolved near-field optical microscopy. Following simultaneous excitation of two plasmon modes of a nanorod with an ultrashort near-field pulse, a decay and revival feature of the time-resolved signal was obtained, which reflected the reciprocating motion of the wave packet. The time-resolved near-field images were also indicative of the wave packet motion. At some period of time after the excitation, the spatial features of the two modes appeared alternately, showing motion of plasmonic wave crests along the rod. The wave packet propagation was clearly demonstrated from this observation with the aid of a simulation model. The present experimental scheme opens the door to coherent control of plasmon-induced optical fields in a nanometer spatial scale and femtosecond temporal scale.

A portion of the CO dimer millimeter wave absorption spectrum has been studied by using our highly sensitive intracavity-jet OROTRON spectrometer in the frequency range from 131 to 174 GHz. By varying the CO concentration in the Ne/CO gas mixture feeding the supersonic jet expansion, the effective temperature of the beam could be changed, revealing a correlation between the observed line intensity and the relative energy of the respective lower state energy levels. Using this temperature dependence and the technique of combination differences together with the data from the infrared study of Brookes and McKellar [J. Chem. Phys. 111, 7321 (1999)], out of over 200 observed transitions, a total of 19 lines could be assigned. All assigned millimeter-wave transitions are tunneling transitions. They belong to four subbands, which connect seven lower energy levels with A+ symmetry to ten previously unknown upper energy levels with A− symmetry. The A+ and A− separation signifies the tunneling splitting of the CO stretching ground state vCO=0 energy levels. The energies of all levels were determined to microwave accuracy. The discovered energy levels fall into two substates, corresponding to the projection K=0 and to K=1 of the total angular momentum J onto the intermolecular axis. The effective intermolecular CO–CO separation for these new K=0 and K=1 states is 4.26 and 4.17 Å, respectively.

The wave packet perturbation energy propagation and accumulation signal during continuing heavy rain process in west of Sichuan Basin from September 22, 2008 to September 27, 2008 is analyzed and predicted in wave-packet propagation diagnosis method by making use of NCEP/NCAR reanalysis materials. According to the analysis, the distribution and propagation of wave packet can obviously reflect features of generation, lasting and ending of the rain. The high value area of the wave packet is basically consistent with heavy rain areas. The heavy rain process is generally generated in high value period or high phase of the wave packet perturbation energy accumulation. According to the meridional and zonal propagation features of the wave packet value, the continuing heavy rain process in west of Sichuan Basin from September 22, 2008 to September 27, 2008 was mainly affected by West Pacific subtropical high, cold air in northern regions and plateau regions, two water vapor channels from Bay of Bengal and South Sea to the basin as well as Typhoon Hagupit. The evolution of wave packet is meaningful for prediction.

A semiquantal analysis of condensed phase chemical dynamics, outlined recently for a double-well linearly coupled to dissipative harmonic bath, is formulated in detail to clarify its general features as well as the specifics of the linear and quadratic coupling cases. The theory may be called a "semiquantal time-dependent Hartree (SQTDH)" approach, as it assumes a factorized product of the squeezed coherent state wave packets for the variational subspace of the many-dimensional time-dependent wave function. Due to this assumption, it straightforwardly satisfies the canonicity condition introduced by Marumori et al. is described by a set of Hamilton equations of motion in an extended phase space that includes auxiliary coordinates representing the wave packet widths. The potential in the extended phase space provides a pictorial understanding of the quantum effects affected due to the bath coupling, e.g., suppression of the wave packet spreading in terms of the potential wall developing along the auxiliary coordinates. The idea is illustrated by prototypical models of quartic double-well and cubic metastable potentials linearly and quadratically coupled to the bath. Further applications and extensions, where the SQTDH method will offer a practical approach for introducing quantum effects into realistic molecular dynamics simulations, are also discussed.

A time dependent wave packet approach to gas–surface scattering is presented. This semiclassical method is based on Gaussian wave functions whose average positions and momenta are those of classical trajectories. The initial states are represented as superpositions of Gaussian wave packets. These wave packets are propagated individually and after the collision, the scattering information is extracted by projecting them onto the final states in a coherent way, according to the initial expansion coefficients. The powerful new approach allows the treatment of surface imperfections as well as the inclusion of more degrees of freedom of the surface or the gas particle. The accuracy of the present semiclassical method is tested by a comparison with exact quantal calculations for He–LiF diffractive scattering and in most cases excellent agreement is found. In addition, the wave packet approach is used to calculate diffraction probabilities at high energies and to examine the interference structure of the scattered particles as a function of the size of the surface from which the scattering occurs.

With the progression of age, the rate and rhythm of breathing decrease during sleep, sleep disorders increase. Sleep apnea is a sleep disorder that is characterized by respiratory arrest during sleep. Aim: To investigate sleep apnea status and related factors of elderly individuals Method: The sample of study, consists of 72 elders who remain in four different rest homes, voluntarily agree to participate in study. Data were collected by using Berlin Sleep Apnea Form, Geriatric Depression Scale (GDS) and the Visual Similarity Scale Results: The mean age of cases was72,6±7,7and54.2%were female. It was found that 68%of the participants had chronic disease,41.3%had smoked and52.9%had high risk for sleep apnea. The majority of the participants had high fatigue levels and low energy levels. Risk of sleep apnea was higher in males. There was a strong positive correlation between sleep apnea and fatigue levels and a negative correlation with energy level(r As the level of fatigue increases and the energy level decreases, the riskof sleep apnea increases. It was found that the individuals who were moderate and over-dependent had a higher risk of sleep apnea compared to individuals who were mildly dependent and fully independent(p Patients with depression, DM and HT have high risk of sleep apnea compared to those without. Smoking was effective on sleep apnea. In addition, the individuals who were exposed to passive smoking were found to have a higher risk of sleep apnea(p Weight gain was associated with a high rate of sleep apnea(r Conclusion: Gender, high fatigue, low energy and dependence level, chronic diseases (depression, DM, HT), exposure to passive smoking, weight gain increase the risk of sleep apnea in elderly individuals.

It is shown that for a three-dimensional harmonic oscillator there exist families of Gaussian wave packets that retain their shape during the time evolution, i.e., the wave packet rotates around its center without spreading or deforming. This generalizes the concept of coherent vibrational motion to coherent rotational motion.

The interaction of a model atom with very intense radiation fields is well approximated by a map that describes a free particle being kicked periodically by a double-well potential. Both the classical and quantum versions of the map are studied and are shown to provide a compact description of high-field stabilization in this strongly perturbed quantum system. In particular, we find that the ``stabilized'' wave function results from the excitation of a superposition of eigenstates of the periodic, time-evolution operator that are localized near classically unstable and weakly stable orbits. These ``scarred'' wave functions correspond to localized wave packets that oscillate back and forth in the strong external field while in the neighborhood of the attractive Coulomb field. The periodic bremsstrahlung, emitted as this wave packet passes the nucleus, provides a distinct experimental signature of the stabilized state.