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E J Heller

Publications and source records attributed to E J Heller.

12 recordsLinked to original sources
PubMed2001

Replacement manifolds: a method to uniformize semiclassical wave functions.

We present a semiclassical technique that relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold structure gives poor or useless results semiclassically the replacement manifolds can yield remarkable accuracy. We give several working examples to illustrate the theory presented here.

Journal Article↗
PubMed2001

Scarring effects on tunneling in chaotic double-well potentials.

The connection between scarring and tunneling in chaotic double-well potentials is studied in detail through the distribution of level splittings. The mean level splitting is found to have oscillations as a function of energy, as expected if scarring plays a role in determining the size of the splittings, and the spacing between peaks is observed to be periodic of period 2 pi Planck's over 2 pi in action. Moreover, the size of the oscillations is directly correlated with the strength of scarring. These results are interpreted within the theoretical framework of Creagh and Whelan. The semiclassical limit and finite-Planck's over 2 pi effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.

Journal Article↗
PubMed2001

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 by 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 are also investigated, as a function of phase space location. Aside from the bouncing-ball region of phase space, excess localization 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 our results, the excess localization in individual eigenstates is interpreted as being primarily due to symmetry effects.

Journal Article↗
PubMed2001

Parametric evolution for a deformed cavity.

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum eigenstates of the system are /n(x)>. We describe how the parametric kernel P(n/m)=/ /(2), also known as the local density of states, evolves as a function of deltax=x-x(0). We illuminate the nonunitary nature of this parametric evolution, the emergence of nonperturbative features, the final nonuniversal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.

Journal Article↗
PubMed2001

Scattering theory of Kondo mirages and observation of single Kondo atom phase shift.

We explain the origin of the Kondo mirage seen in recent quantum corral scanning tunneling microscope experiments with a scattering theory of electrons on the surfaces of metals. Our theory, combined with experimental data, provides a direct observation of a single Kondo atom phase shift. The Kondo mirage observed at the empty focus of an elliptical quantum corral is shown to arise from multiple electron bounces off the corral wall adatoms. We demonstrate our theory with direct quantitive comparison to experimental data.

Journal Article↗
PubMed2001

Coherent branched flow in a two-dimensional electron gas.

Semiconductor nanostructures based on two-dimensional electron gases (2DEGs) could form the basis of future devices for sensing, information processing and quantum computation. Although electron transport in 2DEG nanostructures has been well studied, and many remarkable phenomena have already been discovered (for example, weak localization, quantum chaos, universal conductance fluctuations), fundamental aspects of the electron flow through these structures have so far not been clarified. However, it has recently become possible to image current directly through 2DEG devices using scanning probe microscope techniques. Here, we use such a technique to observe electron flow through a narrow constriction in a 2DEG-a quantum point contact. The images show that the electron flow from the point contact forms narrow, branching strands instead of smoothly spreading fans. Our theoretical study of this flow indicates that this branching of current flux is due to focusing of the electron paths by ripples in the background potential. The strands are decorated by interference fringes separated by half the Fermi wavelength, indicating the persistence of quantum mechanical phase coherence in the electron flow. These findings may have important implications for a better understanding of electron transport in 2DEGs and for the design of future nanostructure devices.

Journal Article↗
PubMed1999

Measuring scars of periodic orbits.

The phenomenon of periodic orbit scarring of eigenstates of classically chaotic systems is attracting increasing attention. Scarring is one of the most important "corrections" to the ideal random eigenstates suggested by random matrix theory. This paper discusses measures of scars and in so doing also tries to clarify the concepts and effects of eigenfunction scarring. We propose a universal scar measure which takes into account an entire periodic orbit and the linearized dynamics in its vicinity. This measure is tuned to pick out those structures which are induced in quantum eigenstates by unstable periodic orbits and their manifolds. It gives enhanced scarring strength as measured by eigenstate overlaps and inverse participation ratios, especially for longer orbits. We also discuss off-resonance scars which appear naturally on either side of an unstable periodic orbit.

Journal Article↗
PubMed1994

A novel synergistic stimulation of Swiss 3T3 cells by extracellular ATP and mitogens with opposite effects on cAMP levels.

In Swiss 3T3 mouse fibroblasts, the mitogenic effect of extracellular ATP depends on stimulation of adenylyl cyclase. Lysophosphatidic acid (LPA) and phosphatidic acid (PA) inhibited adenylyl cyclase but synergized with ATP in mitogenic stimulation. This unusual synergism of two mitogens with opposite effects on cAMP levels was further investigated. LPA and PA inhibited the elevation of cAMP caused by cholera toxin, prostaglandin E2, or forskolin, but not the rise induced by ATP. In fact, ATP overcame the inhibitory effects of LPA or PA on cAMP levels. Indeed, in the presence of ATP and either cholera toxin or prostaglandin E2, LPA became a stimulator of adenylyl cyclase. Stimulation of DNA synthesis and inhibition of cAMP accumulation by LPA were inhibited by pertussis toxin, but with different dose-response characteristics. In addition, a normal mitogenic response to LPA was obtained in transfected mutant cells with a defective regulatory subunit for protein kinase A and in cells whose regulation of cAMP levels was abnormal because of overproduction of cAMP phosphodiesterase. The data support the hypothesis that the mitogenic effect of LPA involves a PTX-sensitive Gi protein but not inhibition of adenylyl cyclase.

3T3 Cells↗