Counter-propagating Wave Packets Research Articles

Counter-propagating wave packets in the quantum transition state approach to reactive scattering.

The quantum transition state concept provides an intuitive and numerically efficient framework for the description of quantum state-resolved reactive scattering and thermal reaction processes. Combining multiconfigurational time-dependent Hartree wave packet dynamics calculations with a flux correlation function based analysis, rigorous full-dimensional calculations of initial state-selected and state-to-state reaction probabilities for six atom reactions are feasible. In these calculations, a set of wave packets is generated in the transition state region, propagated into the asymptotic area, and analyzed. In the present work, an alternative approach which employs counter-propagating sets of wave packets is introduced. Outgoing wave packets started in the transition state region are matched with incoming wave packets generated in the reactant (or product) asymptotic area. Studying the H + CH4 → H2 + CH3 reaction as a prototypical example, one finds that the incoming wave packets can be propagated closely up to the transition state region with minor numerical effort. Employing cross correlation functions of incoming and outgoing wavefunctions, the propagation times required for the outgoing wave packet and thus the numerical costs of the entire calculation can be reduced significantly. Detailed full-dimensional calculations studying initial state-selected reaction probabilities for the H + CH4 → H2 + CH3 reaction are presented to illustrate the new approach. It is found that converged results can be obtained using shorter propagation times of the outgoing wave packets and less single-particle functions.

Quantum Interference, Hidden Symmetries: Theory and Experimental Facts

The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple mathematical idea of linearly combining vectors in a Hilbert space. Specifically, the discussion turns around the connection between symmetries characterizing the wave function and the behavior in time displayed by the quantum flux when the latter is analyzed in terms of streamlines (Bohmian trajectories). This is illustrated with a series of analytical results and numerical simulations, which include Young’s two-slit experiment, counter-propagating wave packets, grating diffiraction and quantum carpets (e.g., Talbot carpets), and diffiraction under confinement conditions. From the analysis presented it follows that quantum paradoxes appear whenever symmetries related to interference are neglected in the interpretation and understanding of the corresponding phenomena.

Investigating Puzzling Aspects of the Quantum Theory by Means of Its Hydrodynamic Formulation

Bohmian mechanics, a hydrodynamic formulation of the quantum theory, constitutes a useful tool to understand the role of the phase as the mechanism responsible for the dynamical evolution displayed by quantum systems. This role is analyzed and discussed here in the context of quantum interference, considering to this end two well-known scenarios, namely Young’s two-slit experiment and Wheeler’s delayed choice experiment. A numerical implementation of the first scenario is used to show how interference in a coherent superposition of two counter-propagating wave packets can be seen and explained in terms of an effective model consisting of a single wave packet scattered off an attractive hard wall. The outcomes from this model are then applied to the analysis of Wheeler’s delayed choice experiment, also recreated by means of a reliable realistic simulation. Both examples illustrate quite well how the Bohmian formulation helps to explain in a natural way (and therefore to demystify) aspects of the quantum theory typically regarded as paradoxical. In other words, they show that a proper understanding of quantum phase dynamics immediately removes any trace of unnecessary artificial wave-particle arguments.

Mesoscopic transport and interferometry with wave packets of ultracold atoms: Effects of quantum coherence and interactions

We propose a way to simulate mesoscopic transport processes with counterpropagating wave packets of ultracold atoms in quasi-one-dimensional (1D) waveguides and show quantitative agreement with analytical results. The method allows the study of a broad range of transport processes at the level of individual modes, not possible in electronic systems. Typically suppressed effects of quantum coherence become manifest, along with the effects of tunable interactions, which can be used to develop a simpler type of sensitive atom interferometer.

Precise relative rotation sensing using slow light

A novel relative rotation sensor based on slow light is proposed and analysed. A theoretical analysis shows that the high sensitivity of the proposed rotation sensor is achieved through an electromagnetically-induced-transparency medium. Unlike the tradition detection method, the idea of rotation sensing is to detect group delay between counter-propagating wave packets. It can be used to realize an ultra-precise rotation sensor.

Dark soliton past a finite-size obstacle

We consider the collision of a dark soliton with an obstacle in a quasi-one-dimensional Bose condensate. We show that in many respects the soliton behaves as an effective classical particle of mass twice the mass of a bare particle, evolving in an effective potential which is a convolution of the actual potential describing the obstacle. Radiative effects beyond this approximation are also taken into account. The emitted waves are shown to form two counterpropagating wave packets, both moving at the speed of sound. We determine, at leading order, the total amount of radiation emitted during the collision and compute the acceleration of the soliton due to the collisional process. It is found that the radiative process is quenched when the velocity of the soliton reaches the velocity of sound in the system.

Incompressible MHD Turbulence

AbstractThe inertial range of incompressible MHD turbulence is most conveniently described in terms of counter propagating waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves. MHD turbulence is anisotropic with energy cascading more rapidly along k⊥ than along k‖. Anisotropy increases with k⊥ such that the excited modes are confined inside a cone bounded by . The opening angle of the cone, , defines the scale dependent anisotropy. MHD turbulence is generically strong in the sense that the waves which comprise it are critically damped. Nevertheless, deep inside the inertial range, turbulent fluctuations are small. Their energy density is less than that of the background field by a factor θ2(k⊥) « 1. MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating wave packets. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping’s shear and slow waves for its dilatation. The former exceeds the latter by θ−1 (k⊥) » 1 which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics.

The Long Wave Limit for a Boussinesq Equation

We consider the long wave limit for a Boussinesq equation. It is shown that for spatially localized initial conditions the dynamics are under a Korteweg--de Vries (KdV) regime on a large time interval; i.e., in this limit the solutions split up into two counterpropagating wave packets, where each of the wave packets evolve independently and approximately as a solution of a KdV equation. For the proof, exact estimates between the long wave solutions of the Boussinesq equation and the approximations obtained via the decoupled set of KdV equations are demonstrated. We expect that this result holds for the water wave problem, too.

Traveling-wave decomposition of surface displacements associated with scattering by a cylindrical shell: Numerical evaluation displaying guided forward and backward wave properties

Internal displacements of spherical shells subjected to steady sound waves in water have previously been computed by other researchers [e.g., R. Hickling et al., J. Acoust. Soc. Am. 92, 499 (1992)]. Such displacements can be perplexing to directly interpret with a guided wave representation because of the superposition of counterpropagating waves in a steady-state analysis. In this research the surface displacements of a cylinder were evaluated since they can be mathematically decomposed into counterpropagating circumferential traveling waves. (Unlike an analogous decomposition for spheres, the traveling-wave amplitudes in the cylinder case are regular at 0 and 180 deg.) By limiting attention to the radial displacements of the outer surface, it was also possible to display the response to short-tone bursts and thereby distinguish between counterpropagating wave packets. Both the steady-state and burst response situations clearly manifest waves launched on the shell. Shells studied include 2.5% and 10% thick SS304 shells with coincidence frequency excitations of the subsonic a0− Lamb wave and high-frequency (near kLh≊π) excitation of a negative group velocity Lamb wave.

Counterpropagating periodic pulses in coupled Ginzburg-Landau equations

A recently observed stable regime in the form of periodically colliding counterpropagating wave packets (pulses) in an annular convection channel at very small positive overcriticalities is described analytically in terms of coupled Ginzburg-Landau equations. First, the existence of this regime is demonstrated in the framework of the simplest system including only the group-velocity difference, weak gain, and nonlinear dissipative coupling between two modes. In this approximation, the shape of the counterpropagating waves remains indefinite. It is demonstrated that additional dispersive terms, regarded as a small perturbation, provide shaping of the wave packets and also give rise to the deviation of the phase velocity from that for purely linear waves.

Integrable models of nondispersive four-wave interaction

The coherent interaction of two pairs of counter-propagating wave packets is considered. The sum or difference of the carrying frequencies of these packets in each pair is close to the frequency of a two-level transition. It is supposed that the medium is dispersionless. We show that under some physically realisable restrictions the corresponding evolution equations may be integrated by the inverse scattering transform method.