On the efficient computation of recurrence relations

A new parallel algorithm for the solution of a general linear recurrence is described. Its relation to the work of Kogge and Stone is discussed

Quantum Flux and Reverse Engineering of Quantum Wavefunctions

An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent state projections on a quantum wavefunction. An extended definition of the flux operator is obtained using coherent states. We present a "processed Husimi" representation, which makes decisions using many Husimi projections at each location. The processed Husimi representation reverse engineers or deconstructs the wavefunction, yielding the underlying classical ray structure. Our approach makes possible interpreting the dynamics of systems where the probability flux is uniformly zero or strongly misleading. The new technique is demonstrated by the calculation of particle flow maps of the classical dynamics underlying a quantum wavefunction.Comment: Accepted to EP

Scarring by homoclinic and heteroclinic orbits

In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when associated closed circuits in phase space are properly quantized, thus introducing strong quantum correlations. The corresponding quantization rules are also established. This opens the door for developing computationally tractable methods to calculate eigenstates of chaotic systems.Comment: 5 pages, 4 figure

Phase-space correlations of chaotic eigenstates

It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in configuration space, they persist in the semiclassical limit. A quantitative theory is developed on the basis of Gaussian wavepacket dynamics and random-matrix arguments. The role of symmetries is discussed for the example of time-reversal invariance.Comment: Published version with minor corrections to version

Observing trajectories with weak measurements in quantum systems in the semiclassical regime

We propose a scheme allowing to observe the evolution of a quantum system in the semiclassical regime along the paths generated by the propagator. The scheme relies on performing consecutive weak measurements of the position. We show how weak trajectories" can be extracted from the pointers of a series of measurement devices having weakly interacted with the system. The properties of these "weak trajectories" are investigated and illustrated in the case of a time-dependent model system.Comment: v2: Several minor corrections were made. Added Appendix (that will appear as Suppl. Material). To be published in Phys Rev Let

Induced Nested Galactic Bars Inside Assembling Dark Matter Halos

We investigate the formation and evolution of nested bar systems in disk galaxies in a cosmological setting by following the development of an isolated dark matter (DM) and baryon density perturbation. The disks form within the assembling triaxial DM halos and the feedback from the stellar evolution is accounted for in terms of supernovae and OB stellar winds. Focusing on a representative model, we show the formation of an oval disk and of a first generation of nested bars with characteristic sub-kpc and a few kpc sizes. The system evolves through successive dynamical couplings and decouplings, forcing the gas inwards and settles in a state of resonant coupling. The inflow rate can support a broad range of activity within the central kpc, from quasar- to Seyfert-types, supplemented by a vigorous star formation as a by-product. The initial bar formation is triggered in response to the tidal torques from the triaxial DM halo, which acts as a finite perturbation. This first generation of bars does not survive for more than 4--5 Gyr: by that time the secondary bar has totally dissolved, while the primary one has very substantially weakened, reduced to a fat oval. This evolution is largely due to chaos introduced by the interaction of the multiple non-axisymmetric components.Comment: 4 pages, 4 figures, 1 mpeg animation. To be published by the Astrophysical Journal Letters. The animation can be found at http://www.pa.uky.edu/~shlosman/research/galdyn/movies.html Replaced with an updated version (small text corrections

Localization of Eigenfunctions in the Stadium Billiard

We present a systematic survey of scarring and symmetry effects in the stadium billiard. The localization of individual eigenfunctions in Husimi phase space is studied first, and it is demonstrated that on average there is more localization than can be accounted for on the basis of random-matrix theory, even after removal of bouncing-ball states and visible scars. A major point of the paper is that symmetry considerations, including parity and time-reversal symmetries, enter to influence the total amount of localization. The properties of the local density of states spectrum are also investigated, as a function of phase space location. Aside from the bouncing-ball region of phase space, excess localization of the spectrum is found on short periodic orbits and along certain symmetry-related lines; the origin of all these sources of localization is discussed quantitatively and comparison is made with analytical predictions. Scarring is observed to be present in all the energy ranges considered. In light of these results the excess localization in individual eigenstates is interpreted as being primarily due to symmetry effects; another source of excess localization, scarring by multiple unstable periodic orbits, is smaller by a factor of $\sqrt{\hbar}$.Comment: 31 pages, including 10 figure

Quantum mechanical and quasiclassical investigation of the time domain nonadiabatic dynamics of NO2 close to the bottom of the X2A1-A2B2 conical intersection

We use the effective Hamiltonian that we recently fitted against the first 306 experimentally observed vibronic transitions of NO2 [J. Chem. Phys. 119, 5923 (2003)] to investigate the time domain nonadiabatic dynamics of this molecule on the coupled X2A1 and A2B2 electronic states, using both quantum mechanical and quasiclassical techniques. From the quantum mechanical point of view, we show that the transfer of population to the electronic ground state originating from a wave packet launched on the excited state occurs in a stepwise fashion. The evolution of wave packets launched on the electronic ground state is instead more complex because the crossing seam is located close to the bottom of the electronic excited state. We next use the mapping formalism, which replaces the discrete electronic degrees of freedom by continuous ones, to obtain a classical description of the coupled electronic states. We propagate gaussian swarms of trajectories to show that this approach can be used to calculate the populations in each electronic state. We finally propose a very simple trajectory surface hopping model, which assumes that trajectories have a constant probability to jump onto the other state in a particular region of the phase space and a null hopping probability outside from this region. Quasiclassical calculations show that this model enables a precise estimation of complex quantities, like for example the projection of the instantaneous probability density on given planes.Comment: accepted for publication in J. Chem. Phy

Removal of luminal content protects the small intestine during hemorrhagic shock but is not sufficient to prevent lung injury.

The small intestine plays a key role in the pathogenesis of multiple organ failure following circulatory shock. Current results show that reduced perfusion of the small intestine compromises the mucosal epithelial barrier, and the intestinal contents (including pancreatic digestive enzymes and partially digested food) can enter the intestinal wall and transport through the circulation or mesenteric lymph to other organs such as the lung. The extent to which the luminal contents of the small intestine mediate tissue damage in the intestine and lung is poorly understood in shock. Therefore, rats were assigned to three groups: No-hemorrhagic shock (HS) control and HS with or without a flushed intestine. HS was induced by reducing the mean arterial pressure (30 mmHg; 90 min) followed by return of shed blood and observation (3 h). The small intestine and lung were analyzed for hemorrhage, neutrophil accumulation, and cellular membrane protein degradation. After HS, animals with luminal contents had increased neutrophil accumulation, bleeding, and destruction of E-cadherin in the intestine. Serine protease activity was elevated in mesenteric lymph fluid collected from a separate group of animals subjected to intestinal ischemia/reperfusion. Serine protease activity was elevated in the plasma after HS but was detected in lungs only in animals with nonflushed lumens. Despite removal of the luminal contents, lung injury occurred in both groups as determined by elevated neutrophil accumulation, permeability, and lung protein destruction. In conclusion, luminal contents significantly increase intestinal damage during experimental HS, suggesting transport of luminal contents across the intestinal wall should be minimized

Matter Wave Scattering and Guiding by Atomic Arrays

We investigate the possibility that linear arrays of atoms can guide matter waves, much as fiber optics guide light. We model the atomic line as a quasi-1D array of s wave point scatterers embedded in 2D. Our theoretical study reveals how matter wave guiding arises from the interplay of scattering phenomena with bands and conduction along the array. We discuss the conditions under which a straight or curved array of atoms can guide a beam focused at one end of the array.Comment: Submitted to Phys. Rev.