Quantum initial value representations using approximate Bohmian trajectories

Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic description of quantum mechanics, are used to construct time-correlation functions in an initial value representation (IVR). The formulation is fully quantum mechanical and the resulting equations for the correlation functions are similar in form to their semi-classical analogs but do not require the computation of the stability or monodromy matrix or conjugate points. We then move to a {\em local} trajectory description by evolving the cumulants of the wave function along each individual path. The resulting equations of motion are an infinite hierarchy, which we truncate at a given order. We show that time-correlation functions computed using these approximate quantum trajectories can be used to accurately compute the eigenvalue spectrum for various potential systems.Comment: 7 pages, 6 figure

Car-Parrinello Molecular Dynamics on excited state surfaces

This paper describes a method to do ab initio molecular dynamics in electronically excited systems within the random phase approximation (RPA). Using a dynamical variational treatment of the RPA frequency, which corresponds to the electronic excitation energy of the system, we derive coupled equations of motion for the RPA amplitudes, the single particle orbitals, and the nuclear coordinates. These equations scale linearly with basis size and can be implemented with only a single holonomic constraint. Test calculations on a model two level system give exact agreement with analytical results. Furthermore, we examined the computational efficiency of the method by modeling the excited state dynamics of a one-dimensional polyene lattice. Our results indicate that the present method offers a considerable decrease in computational effort over a straight-forward configuration interaction (singles) plus gradient calculation performed at each nuclear configuration

Presynaptic facilitation at the crayfish neuromuscular junction: Role of calcium-activated potassium conductance

Membrane potential was recorded intracellularly near presynaptic terminals of the excitor axon of the crayfish opener neuromuscular junction (NMJ), while transmitter release was recorded postsynaptically. This study focused on the effects of a presynaptic calcium-activated potassium conductance, gK(Ca), on the transmitter release evoked by single and paired depolarizing current pulses. Blocking gK(Ca) by adding tetraethylammonium ion (TEA; 5-20 mM) to a solution containing tetrodotoxin and aminopyridines caused the relation between presynaptic potential and transmitter release to steepen and shift to less depolarized potentials. When two depolarizing current pulses were applied at 20-ms intervals with gK(Ca) not blocked, the presynaptic voltage change to the second (test) pulse was inversely related to the amplitude of the first (conditioning) pulse. This effect of the conditioning prepulse on the response to the test pulse was eliminated by 20 mM TEA and by solutions containing 0 mM Ca2+/1 mM EGTA, suggesting that the reduction in the amplitude of the test pulse was due to activation of gK(Ca) by calcium remaining from the conditioning pulse. In the absence of TEA, facilitation of transmitter release evoked by a test pulse increased as the conditioning pulse grew from -40 to -20 mV, but then decreased with further increase in the conditioning depolarization. A similar nonmonotonic relationship between facilitation and the amplitude of the conditioning depolarization was reported in previous studies using extracellular recording, and interpreted as supporting an additional voltagedependent step in the activation of transmitter release. We suggest that this result was due instead to activation of a gK(Ca) by the conditioning depolarization, since facilitation of transmitter release increased monotonically with the amplitude of the conditioning depolarization, and the early time course of the decay of facilitation was prolonged when gK(Ca) was blocked. The different time courses for decay of the presynaptic potential (20 ms) and facilitation (> 50 ms) suggest either that residual free calcium does not account for facilitation at the crayfish NMJ or that the transmitter release mechanism has a markedly higher affinity or stoichiometry for internal free calcium than does g K(Ca). Finally, our data suggest that the calcium channels responsible for transmitter release at the crayfish NMJ are not of the L, N, or T type.This work was partially supported by NIAAA grant AA0776 to G. D. Bittner.Neuroscienc

Maintenance and degradation of proteins in intact and severed axons: Implications for the mechanism of long-term survival of anucleate crayfish axons

Protein maintenance and degradation are examined in the severed distal (anucleate) portions of crayfish medial giant axons (MGAs), which remain viable for over 7 months following axotomy. On polyacrylamide gels, the silver-stained protein banding pattern of anucleate MGAs severed from their cell bodies for up to 4 months remains remarkably similar to that of intact MGAs. At 7 months postseverance, some (but not all) proteins are decreased in anucleate MGAs compared to intact MGAs. To determine the half-life of axonally transported proteins, we radiolabeled MGA cell bodies and monitored the degradation of newly synthesized transported proteins. Assuming exponential decay, proteins in the fast component of axonal transport have an average half-life of 14 d in anucleate MGAs and proteins in the slow component have an average half-life of 17 d. Such half-lives are very unlikely to account for the ability of anucleate MGAs to survive for over 7 months after axotomy.This work was supported by an ATP grant to G.D.B.Neuroscienc

Evolution of abilities to regenerate neurons in central nervous systems

This work was supported by a Kappa Kappa Gamma Graduate Fellowship Award to C. E. H. and NIH grant NS-11861 and RCDA NS-00070 to G. D. B.Neuroscienc

Facilitation of transmitter release at squid synapses

Facilitation is shown to decay as a compound exponential with two time constants (T1, T2) at both giant and non-giant synapses in squid steilate ganglia bathed in solutions having low extracellular calcium concentrations ([Ca++]o). Maximum values of facilitation (F~) were significantly larger, and T1 was significantly smaller in giant than non-giant synapses. Decreases in [Ca++]o or increases in [Mn++]o had variable effects on T1 and F1, whereas decreases in temperature increased T~ but had insignificant effects on/'1. The growth of facilitation during short trains of equal interval stimuli was adequately predicted by the linear summation model developed by Mallart and Martin (1967.J. Physiol. (Lond.). 193: 676-694) for frog neuromuscular junctions. This result suggests that the underlying mechanisms of facilitation are similar in squid and other synapses which release many transmitter quanta.This work was supported by National Science Foundation research grant GB-36949, National Research Council (Canada) and Grass Fellowships to Dr. Charlton, and a National Institutes of Health career award (NS-00070) to Dr. Bittner.Neuroscienc

Soot formation and burnout in flames

The amount of soot formed when burning a benzene/hexane mixture in a turbulent combustor was examined. Soot concentration profiles in the same combustor for kerosene fuel are given. The chemistry of the formation of soot precursors, the nucleation, growth and subsequent burnout of soot particles, and the effect of mixing on the previous steps were considered

River Bed Response to Channel Width Variation: Theory and Experiments (HES 49)

Illinois Water Resources Center (USGS Project 04 Contract 14-08-0004-G2017unpublishednot peer reviewe

Mechanisms for the maintenance and eventual degradation of neurofilament proteins in the distal segments of severed goldfish Mauthner axons

Cellular mechanisms that might affect the degradation of neurofilament proteins (NFPs) were examined in the distal segments of severed goldfish Mauthner axons (M-axons), which do not degenerate for more than 2 months after severance. Calpain levels, as determined by reactivity to a polyclonal antibody, remained constant for 80 d postseverance in distal segments of M-axons and then declined from 80 to 85 d postseverance. Calpain activity in rat brain, as determined by a spectrophotometric assay, was much higher than calpain activity in control and severed goldfish brain, spinal cord, muscle, or M-axons. Calpain activity was extremely low in M-axons compared with that in all other tissues and remained low for up to 80 d postseverance in distal segments of M-axons. Phosphorylated NFPs, as determined by Stains-All treatment of SDS gels, were maintained for up to 72 d postseverance and then decreased noticeably at 75 d postseverance when NFP breakdown products appeared on silver-stained gels. By 85 d postseverance, phosphorylated NFPs no longer were detected, and NFP breakdown products were the most prominent bands on silver-stained gels. These results suggest that the distal segments of M-axons survive for months after severance, because NFPs are maintained in a phosphorylated state that stabilizes and protects NFPs from degradation by low levels of calpain activity in the M-axon; the distal segments of severed M-axons degenerate eventually when NFPs no longer are maintained in a phosphorylated state and become susceptible to degradation, possibly by low levels of calpain activity in the M-axon.This work was supported by an Advanced Technology Project Grant to G.D.B.Neuroscienc