Investigating transition state resonances in the time domain by means of Bohmian mechanics: The F+HD reaction

In this work, we investigate the existence of transition state resonances on atom-diatom reactive collisions from a time-dependent perspective, stressing the role of quantum trajectories as a tool to analyze this phenomenon. As it is shown, when one focusses on the quantum probability current density, new dynamical information about the reactive process can be extracted. In order to detect the effects of the different rotational populations and their dynamics/coherences, we have considered a reduced two-dimensional dynamics obtained from the evolution of a full three-dimensional quantum time-dependent wave packet associated with a particular angle. This reduction procedure provides us with information about the entanglement between the radial degrees of freedom (r,R) and the angular one (\gamma), which can be considered as describing an environment. The combined approach here proposed has been applied to study the F+HD reaction, for which the FH+D product channel exhibits a resonance-mediated dynamics.Comment: 12 pages, 9 figure

Stability of stationary solutions of the Schrodinger-Langevin equation

The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by Liapunov's direct method. The results are demonstrated by numerical calculations on the example of the damped harmonic oscillator.Comment: revised, 12 pages, 7 figure

Relativistic quantum mechanics and the Bohmian interpretation

Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role, provides a viable interpretation of relativistic quantum mechanics. We formulate the Bohmian interpretation of many-particle wave functions in a Lorentz-covariant way. In contrast with the nonrelativistic case, the relativistic Bohmian interpretation may lead to measurable predictions on particle positions even when the conventional interpretation does not lead to such predictions.Comment: 10 pages, revised, to appear in Found. Phys. Let

Quantum interference within the complex quantum Hamilton-Jacobi formalism

Quantum interference is investigated within the complex quantum Hamilton-Jacobi formalism. As shown in a previous work [Phys. Rev. Lett. 102, 250401 (2009)], complex quantum trajectories display helical wrapping around stagnation tubes and hyperbolic deflection near vortical tubes, these structures being prominent features of quantum caves in space-time Argand plots. Here, we further analyze the divergence and vorticity of the quantum momentum function along streamlines near poles, showing the intricacy of the complex dynamics. Nevertheless, despite this behavior, we show that the appearance of the well-known interference features (on the real axis) can be easily understood in terms of the rotation of the nodal line in the complex plane. This offers a unified description of interference as well as an elegant and practical method to compute the lifetime for interference features, defined in terms of the average wrapping time, i.e., considering such features as a resonant process.Comment: revised version, 13 pages, 11 figures, 1 tabl

Astrocytic Ion Dynamics: Implications for Potassium Buffering and Liquid Flow

We review modeling of astrocyte ion dynamics with a specific focus on the implications of so-called spatial potassium buffering, where excess potassium in the extracellular space (ECS) is transported away to prevent pathological neural spiking. The recently introduced Kirchoff-Nernst-Planck (KNP) scheme for modeling ion dynamics in astrocytes (and brain tissue in general) is outlined and used to study such spatial buffering. We next describe how the ion dynamics of astrocytes may regulate microscopic liquid flow by osmotic effects and how such microscopic flow can be linked to whole-brain macroscopic flow. We thus include the key elements in a putative multiscale theory with astrocytes linking neural activity on a microscopic scale to macroscopic fluid flow.Comment: 27 pages, 7 figure

Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation

We discuss the particle method in quantum mechanics which provides an exact scheme to calculate the time-dependent wavefunction from a single-valued continuum of trajectories where two spacetime points are linked by at most a single orbit. A natural language for the theory is offered by the hydrodynamic analogy, in which wave mechanics corresponds to the Eulerian picture and the particle theory to the Lagrangian picture. The Lagrangian model for the quantum fluid may be developed from a variational principle. The Euler-Lagrange equations imply a fourth-order nonlinear partial differential equation to calculate the trajectories of the fluid particles as functions of their initial coordinates using as input the initial wavefunction. The admissible solutions are those consistent with quasi-potential flow. The effect of the superposition principle is represented via a nonclassical force on each particle. The wavefunction is computed via the standard map between the Lagrangian coordinates and the Eulerian fields, which provides the analogue in this model of Huygens principle in wave mechanics. The method is illustrated by calculating the time-dependence of a free Gaussian wavefunction. The Eulerian and Lagrangian pictures are complementary descriptions of a quantum process in that they have associated Hamiltonian formulations that are connected by a canonical transformation. The de Broglie-Bohm interpretation, which employs the same set of trajectories, should not be conflated with the Lagrangian version of the hydrodynamic interpretation. The theory implies that the mathematical results of the de Broglie-Bohm model may be regarded as statements about quantum mechanics itself rather than about its interpretation.Comment: 26 page

Efficacy of Synaptic Inhibition Depends on Multiple, Dynamically Interacting Mechanisms Implicated in Chloride Homeostasis

Chloride homeostasis is a critical determinant of the strength and robustness of inhibition mediated by GABAA receptors (GABAARs). The impact of changes in steady state Cl− gradient is relatively straightforward to understand, but how dynamic interplay between Cl− influx, diffusion, extrusion and interaction with other ion species affects synaptic signaling remains uncertain. Here we used electrodiffusion modeling to investigate the nonlinear interactions between these processes. Results demonstrate that diffusion is crucial for redistributing intracellular Cl− load on a fast time scale, whereas Cl−extrusion controls steady state levels. Interaction between diffusion and extrusion can result in a somato-dendritic Cl− gradient even when KCC2 is distributed uniformly across the cell. Reducing KCC2 activity led to decreased efficacy of GABAAR-mediated inhibition, but increasing GABAAR input failed to fully compensate for this form of disinhibition because of activity-dependent accumulation of Cl−. Furthermore, if spiking persisted despite the presence of GABAAR input, Cl− accumulation became accelerated because of the large Cl− driving force that occurs during spikes. The resulting positive feedback loop caused catastrophic failure of inhibition. Simulations also revealed other feedback loops, such as competition between Cl− and pH regulation. Several model predictions were tested and confirmed by [Cl−]i imaging experiments. Our study has thus uncovered how Cl− regulation depends on a multiplicity of dynamically interacting mechanisms. Furthermore, the model revealed that enhancing KCC2 activity beyond normal levels did not negatively impact firing frequency or cause overt extracellular K− accumulation, demonstrating that enhancing KCC2 activity is a valid strategy for therapeutic intervention