Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Patch dynamics and metapopulation theory: the case of successional species

We present a mathematical framework that combines extinction-colonization dynamics with the dynamics of patch succession. We draw an analogy between the epidemiological categorization of individuals (infected, susceptible, latent and resistant) and the patch structure of a spatially heterogeneous landscape (occupied-suitable, empty-suitable, occupied-unsuitable and empty-unsuitable). This approach allows one to consider life-history attributes that influence persistence in patchy environments (e.g., longevity, colonization ability) in concert with extrinsic processes (e.g., disturbances, succession) that lead to spatial heterogeneity in patch suitability. It also allows the incorporation of seed banks and other dormant life forms, thus broadening patch occupancy dynamics to include sink habitats. We use the model to investigate how equilibrium patch occupancy is influenced by four critical parameters: colonization rate? extinction rate, disturbance frequency and the rate of habitat succession. This analysis leads to general predictions about how the temporal scaling of patch succession and extinction-colonization dynamics influences long-term persistence. We apply the model to herbaceous, early-successional species that inhabit open patches created by periodic disturbances. We predict the minimum disturbance frequency required far viable management of such species in the Florida scrub ecosystem. (C) 2001 Academic Press.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

The effect of resource aggregation at different scales: Optimal foraging behavior of Cotesia rubecula

Resources can be aggregated both within and between patches. In this article, we examine how aggregation at these different scales influences the behavior and performance of foragers. We developed an optimal foraging model of the foraging behavior of the parasitoid wasp Cotesia rubecula parasitizing the larvae of the cabbage butterfly Pieris rapae. The optimal behavior was found using stochastic dynamic programming. The most interesting and novel result is that the effect of resource aggregation within and between patches depends on the degree of aggregation both within and between patches as well as on the local host density in the occupied patch, but lifetime reproductive success depends only on aggregation within patches. Our findings have profound implications for the way in which we measure heterogeneity at different scales and model the response of organisms to spatial heterogeneity.

NMR structure and backbone dynamics of a concatemer of epidermal growth factor homology modules of the human low-density lipoprotein receptor

The ligand-binding region of the low-density lipoprotein (LDL) receptor is formed by seven N-terminal, imperfect, cysteine-rich (LB) modules. This segment is followed by an epidermal growth factor precursor homology domain with two N-terminal, tandem, EGF-like modules that are thought to participate in LDL binding and recycling of the endocytosed receptor to the cell surface. EGF-A and the concatemer, EGF-AB, of these modules were expressed in Escherichia coli. Correct protein folding of EGF-A and the concatemer EGF-AB was achieved in the presence or absence of calcium ions, in contrast to the LB modules, which require them for correct folding. Homonuclear and heteronuclear H-1-N-15 NMR spectroscopy at 17.6 T was used to determine the three-dimensional structure of the concatemer. Both modules are formed by two pairs of short, anti-parallel beta -strands. In the concatemer, these modules have a fixed relative orientation, stabilized by calcium ion-binding and hydrophobic interactions at the interface. N-15 longitudinal and transverse relaxation rates, and {H-1}-N-15 heteronuclear NOEs were used to derive a model-free description of the backbone dynamics of the molecule. The concatemer appears relatively rigid, particularly near the calcium ion-binding site at the module interface, with an average generalized order parameter of 0.85 +/- 0.11. Some mutations causing familial hypercholesterolemia may now be rationalized. Mutations of D41, D43 and E44 in the EGF-B calcium ion-binding region may affect the stability of the linker and thus the orientation of the tandem modules. The diminutive core also provides little structural stabilization, necessitating the presence of disulfide bonds. The structure and dynamics of EGF-AB contrast with the N-terminal LB modules, which require calcium ions both for folding to form the correct disulfide connectivities and for maintenance of the folded structure, and are connected by highly mobile linking peptides. (C) 2001 Academic Press.

Enzymology, structure, and dynamics of acetohydroxy acid isomeroreductase

Acetohydroxy acid isomeroreductase is a key enzyme involved in the biosynthetic pathway of the amino acids isoleucine, valine, and leucine. This enzyme is of great interest in agrochemical research because it is present only in plants and microorganisms, making it a potential target for specific herbicides and fungicides. Moreover, it catalyzes an unusual two-step reaction that is of great fundamental interest. With a view to characterizing both the mechanism of inhibition by potential herbicides and the complex reaction mechanism, various techniques of enzymology, molecular biology, mass spectrometry, X-ray crystallography, and theoretical simulation have been used. The results and conclusions of these studies are described briefly in this paper.

Structural Dynamics in (ND4)2[Cu(D2O)6](SO4)2

The extended X-ray absorption fine structure spectroscopy (EXAFS) of (ND4)(2)[CU(D2O)(6)](SO4)(2) at 5, 14,100, 200, and 298 K is reported. This indicates that the Cu-O bond lengths of the Cu(D2O)(6)(2+) ion do not change significantly within this temperature range, which contrasts with EPR results and X-ray and neutron diffraction experiments, which imply that two of the Cu-(D2O) bonds converge in length as the temperature is raised. The EXAFS measurements thus confirm that the bond distances yielded by the diffraction experiments refer to the average positions of ligands involved in a dynamic equilibrium in which the directions of the long and intermediate bonds of the Jahn-Teller distorted Cu(D2O)(6)(2+) ion are interchanged in the crystal lattice. Analysis of the displacement parameters is consistent with this interpretation, as are the wave functions calculated using a model involving Jahn-Teller vibronic coupling and the influence of lattice strain interactions.

Quantum criticality

We investigate the theory of quantum fluctuations in non-equilibrium systems having large critical fluctuations. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, and also to envisage future tests of quantum theory in regions of macroscopic quantum fluctuations. A long-term objective of this research is to identify suitable physical systems in which macroscopic 'Schrodinger cat'-like behaviour may be observed. We investigate two systems in particular of much current experimental interest, namely the degenerate parametric oscillator near threshold, and the evaporatively cooled (BEC). We compare the results obtained in the positive-P representation, as a fully quantum mechanical calculation, with the truncated Wigner phase space equation, also known as semi-classical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. In the region where the largest quantum fluctuations and Schrodinger cat-like behaviour might be expected, we find that the quantum predictions correspond very closely to the semi-classical theory. Nature abhors observing a Schrodinger car.

Haptic information stabilizes and destabilizes coordination dynamics

Goal-directed, coordinated movements in humans emerge from a variety of constraints that range from 'high-level' cognitive strategies based oil perception of the task to 'low-level' neuromuscular-skeletal factors such as differential contributions to coordination from flexor and extensor muscles. There has been a tendency in the literature to dichotomize these sources of constraint, favouring one or the other rather than recognizing and understanding their mutual interplay. In this experiment, subjects were required to coordinate rhythmic flexion and extension movements with an auditory metronome, the rate of which was systematically increased. When subjects started in extension on the beat of the metronome, there was a small tendency to switch to flexion at higher rates, but not vice versa. When subjects: were asked to contact a physical stop, the location of which was either coincident with or counterphase to the auditor) stimulus, two effects occurred. When haptic contact was coincident with sound, coordination was stabilized for both flexion and extension. When haptic contact was counterphase to the metronome, coordination was actually destabilized, with transitions occurring from both extension to flexion on the beat and from flexion to extension on the beat. These results reveal the complementary nature of strategic and neuromuscular factors in sensorimotor coordination. They also suggest the presence of a multimodal neural integration process-which is parametrizable by rate and context - in which intentional movement, touch and sound are bound into a single, coherent unit.

Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach

We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD's) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine how the CQD system state depends on the actual current through the PC device, we use the so-called quantum trajectory method to derive the zero-temperature conditional master equation. We first treat the electron tunneling through the PC barrier as a classical stochastic point process (a quantum-jump model). Then we show explicitly that our results can be extended to the quantum-diffusive limit when the average electron tunneling rate is very large compared to the extra change of the tunneling rate due to the presence of the electron in the dot closer to the PC. We find that in both quantum-jump and quantum-diffusive cases, the conditional dynamics of the CQD system can be described by the stochastic Schrodinger equations for its conditioned state vector if and only if the information carried away from the CQD system by the PC reservoirs can be recovered by the perfect detection of the measurements.

Stochastic Schrodinger equation approach to quantum noise in resonant tunneling current

We apply the quantum trajectory method to current noise in resonant tunneling devices. The results from dynamical simulation are compared with those from unconditional master equation approach. We show that the stochastic Schrodinger equation approach is useful in modeling the dynamical processes in mesoscopic electronic systems.