Comparison of quantum, semiclassical and classical methods in hydrogen broadening of nitrogen lines

We use an accurate N₂-H₂ab initio potential energy surface (PES) in order to inter-compare various methods commonly employed to calculate pressure broadening coefficients. Close-coupling (CC) calculations of the collisional linewidths of the isotropic Raman lines of N₂ perturbed by H₂ are performed for temperatures between 77 and 2000 K. The CC results compare well with available experimental values. Three less exact methods of calculation are also used: the full classical (FC) model of Gordon, the semiclassical (SC) formalism of Robert and Bonamy and the quantum dynamical coupled states (CS) method. The CS method provides good agreement with CC calculations for all studied temperatures, FC calculations can be considered as accurate above room temperature while the SC method gives overestimated values by about 20-30% in all cases. The temperature dependences of pressure broadening coefficients provided by each method are very similar at elevated (above room) temperatures.     

On the accuracy of classical, semiclassical and quantum methods in collision line broadening calculations: Comparative analysis for C2H2-Ar, He systems

Accuracies of classical, semiclassical and quantum methods are comprehensively examined in calculations of impact line widths of C₂H₂ molecules perturbed by Ar and He. The field of comparative study covers both infrared absorption and Raman scattering lines of acetylene having rotational quantum number J=0-30 at temperatures 173 and 296 K. Calculations have been made by fully classical method and by three basic least approximate semiclassical methods, namely, Neilsen-Gordon (NG) method, peaking approximation (PA) and Smith-Giraud-Cooper (SGC) method. Most accurate ab initio potential energy surfaces (PES) of Yang et al. (1996) [21] and Mozsynski et al. (1995) [22] have been applied to model C₂H₂-Ar and C₂H₂-He interactions. The comparison has been made also with available experimental data and with the results of rigorous fully quantum-mechanical calculations within close coupling and coupled states approaches in identical conditions. Semiclassical methods are proved to be not so much accurate as it is generally believed since all they gave in the cases considered seriously underestimated results. The fundamental issue of the adequacy of simplified trajectories in collision broadening calculations is finally reasonably solved. In cases of C₂H₂-Ar and C₂H₂-He systems the use of the “exact” isotropic trajectories (i.e. driven only by the isotropic part of PES) is the main reason of failing of NG, PA and SGC methods. Thus the neglecting of back-influence of the RT exchange on the classical path is a principal defect of semiclassical methods. Finally, the application of simplified trajectories is recognized as inadequate and risky in broadening calculations for molecules having relatively small rotational constants when accurate ab initio PES are applied.     

Collisional line widths of autoperturbed N2: Measurements and quantum calculations

In this work we present new experimental and theoretical values for the line broadening coefficients of the Q-branch Raman lines of autoperturbed N₂. For the experimental determination of the coefficients, high resolution stimulated Raman spectra of the Q-branch of N₂ at different pressures were obtained at 77, 194 and 298 K. Simultaneously, quantum dynamical calculations, performed on two potential energy surfaces, were carried out for the system between 77 and 298 K, rendering a set of theoretical line broadening coefficients that could be directly compared to those obtained from the present measurements and the previous ones. Within the limit of considering the colliding molecules distinguishable we discuss the ortho and para contributions to the pressure broadening cross-sections. Because such calculations are time consuming we indicate routes to circumvent this difficulty. We observe a reasonable agreement between theoretical and experimental values of the collisional line broadening coefficients at all the studied temperatures.     

Experimental line broadening and line shift coefficients of the acetylene ν1 + ν3 band pressurized by hydrogen and deuterium and comparison with calculations

Theoretical and experimental values have been determined for the pressure broadening of the ν₁ + ν₃ band of acetylene by hydrogen and deuterium at 195 K, and experimental values of the pressure shifts have been determined. Theoretical values have been calculated on the basis of a recent potential energy surface using the close coupling scheme. We discuss the detailed contribution of the various rotational angular momenta of the perturbing gas and the ortho and para contribution to the total pressure broadening cross-sections. We give routes to circumvent the computational cost of such calculations. Experimental values have been measured using a tunable diode laser spectrometer assuming a Voigt line shape. These pressure broadening parameters are compared with measurements performed recently at room temperature and with present measurements performed at 195 K in the ν₁ + ν₃ band of acetylene. A satisfactory agreement is obtained with the present results and available ones at 295 K.     

The classical skeleton of open quantum chaotic maps

We have studied two complementary decoherence measures, purity and fidelity, for a generic diffusive noise in two different chaotic systems (the baker map and the cat map). For both quantities, we have found classical structures in quantum mechanics-the scar functions-that are specially stable when subjected to environmental perturbations. We show that these quantum states constructed on classical invariants are the most robust significant quantum distributions in generic dissipative maps.     

Path integral approach for Stark broadening of Lyman lines in hydrogen plasma

New results for Lyman lines from hydrogen plasmas are presented using the path integral approach. The influence of plasma components (electrons and ions) on the radiator is analysed separately. The ionic contribution is treated within the path integral approach, while the electronic contribution is estimated by the standard collision operator. The Stark effect, including the ion quadrupole contribution, is considered. The time‐dependent ionic microfield is treated within the path integral approximation using the model microfield method (MMM). The comparison with the quantum statistical approach is performed using a wide range of temperatures (T = 10⁴–10⁷ K) and electron densities (N_e = 10²³–10²⁶ m^?3). Good agreement is mainly obtained for low density and high temperature.     

q-Deformation of algebraic structures of quantum and classical mechanics

There exists a coassociative and cocommutative coproduct in the linear space spanned by the two algebraic products of a classical Hamilton algebra (the algebraic structure underlying classical mechanics [1]). The transition from classical to quantum Hamilton algebra (the algebraic structure underlying quantum mechanics) is anħ-deformation which preserves not only the Lie property of the classical Hamilton algebra but also the coassociativity and cocommutativity of the above coproduct. By explicit construction we obtain the algebraic structures of theq-deformed Hamilton algebras which preserve the said properties of the coproduct. Some algorithms of these structures are obtained and their implications discussed. The problem of consistency of time evolution with theq-deformed kinematical structure is discussed. A characteristic distinction between the parametersħ andq is brought out to stress the fact thatq cannot be regarded as a fundamental constant.     

Accuracy of semiclassical dynamics in the presence of chaos

We review some of the issues facing semiclassical methods in classically chaotic systems, then demonstrate the long-time accuracy of semiclassical propagation of a nonstationary wave packet using the quantum baker's map of Balazs and Voros. We show why some of the standard arguments against the efficacy of semiclassical dynamics for long-time chaotic motion are incorrect.     

Nitrogen-induced broadening and shifts of rotation-vibrational lines in the fundamental, first, second and third overtone bands of HI

We report experimental results on the previously unknown broadening and shifting coefficients in the fundamental and three overtone vibration-rotation bands of the HI molecule in mixtures with nitrogen gas. Our data are compared with the previously published results for the fundamental bands of the HF and HCl molecules. It is shown that the line shifts are dominated by the vibrational dependence of the isotropic part of the intermolecular interaction potential.     

Line broadening and shift coefficients of acetylene at 1550 nm

Pressure broadening and shift coefficients have been measured for the ν₁ + ν₃ band of acetylene, C₂H₂, broadened by N₂, H₂, D₂, air, and the noble gases at 295 K. Coefficients are reported for lines between 6470 and 6612 cm⁻¹ (1512-1546 nm). The pressure broadening coefficients are in general agreement with those reported for other vibrational bands, indicating that they are insensitive to vibrational excitation. The pressure shift coefficients, by contrast, are found to differ substantially among vibrational bands.     

Zwitters: Particles between quantum and classical

We describe both quantum particles and classical particles in terms of a classical statistical ensemble, with a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same quantum formalism. Quantum particles are characterized by a specific choice of observables and time evolution of the probability density. Then interference and tunneling are found within classical statistics. Zwitters are (effective) one-particle states for which the time evolution interpolates between quantum and classical particles. Experimental bounds on a small parameter can test quantum mechanics.     

A semiclassical approach to the ground state and density oscillations of quantum dots

A semiclassical Thomas–Fermi method, including a Weizsäcker gradient term, is implemented to describe ground states of two-dimensional nanostructures of arbitrary shape. Time-dependent density oscillations are addressed in the same spirit using the corresponding semiclassical time-dependent equations. The validity of the approximations is tested, both for ground state and density oscillations, compared with the available microscopic Kohn–Sham solutions.     

Magneto-transport study of Landau level broadening in a gated AlGaAs/GaAs parabolic quantum well structure

We study the Landau level broadening by analyzing the Shubnikov-de Haas oscillations in a gated AlGaAs/GaAs parabolic quantum well structure when only one electronic subband is occupied. Small-angle scattering is determined to be important in this system. The Shubnikov-de Haas oscillations are described equally well by employing Gaussian or Lorentzian broadening of the Landau levels at low magnetic field where the quantum localization effect is not important. A possible explanation is that the electron-electron interactions lead to the overlapping of adjacent Landau levels and one can not distinguish between the two broadening types.     

Theoretical analysis of collisional shift and broadening of antiprotonic helium spectral lines

Effect of medium density on shift and broadening of ( ) spectral lines is considered in the framework of binary-collision approximation with an effective ( )–He potential including the long-range attraction and short-range repulsion. Quantum calculations of the scattering phase shifts at reasonable values of the potential parameters allow to explain the main features of the observed density effect on the shape of ( ) spectral lines in low-temperature helium. This revised version was published online in August 2006 with corrections to the Cover Date.     

Twofold-broken rational tori and the uniform semiclassical approximation

We investigate broken rational tori consisting of a chain of four (rather than two) periodic orbits. The normal form that describes this configuration is identified and used to construct a uniform semiclassical approximation, which can be utilized to improve trace formulae. An accuracy gain can be achieved even for the situation when two of the four orbits are ghosts. This is illustrated for a model system, the kicked top. Received 3 August 1999     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

Dissipative chaotic quantum maps: Expectation values, correlation functions and the invariant state

I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the Frobenius-Perron operator, if . Several consequences arise: the Wigner transform of the invariant density matrix is a smeared out version of the classical strange attractor; time dependent expectation values and correlation functions of observables can be evaluated via hybrid quantum-classical formulae in which the quantum character enters only via the initial Wigner function. If a classical phase-space distribution is chosen for the latter or if the map is iterated sufficiently many times the formulae become entirely classical, and powerful classical trace formulae apply. Received 7 October 1999