Biomedical subjects

EJ Heller

Publications and source records attributed to EJ Heller.

At least 19 recordsLinked to original sources

PubMed2000

Imaging coherent electron flow from a quantum point contact

Scanning a charged tip above the two-dimensional electron gas inside a gallium arsenide/aluminum gallium arsenide nanostructure allows the coherent electron flow from the lowest quantized modes of a quantum point contact at liquid helium temperatures to be imaged. As the width of the quantum point contact is increased, its electrical conductance increases in quantized steps of 2 e(2)/h, where e is the electron charge and h is Planck's constant. The angular dependence of the electron flow on each step agrees with theory, and fringes separated by half the electron wavelength are observed. Placing the tip so that it interrupts the flow from particular modes of the quantum point contact causes a reduction in the conductance of those particular conduction channels below 2 e(2)/h without affecting other channels.

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PubMed2000

Deformations and dilations of chaotic billiards: dissipation rate, and quasiorthogonality of the boundary wave functions

We consider chaotic billiards in d dimensions, and study the matrix elements M(nm) corresponding to general deformations of the boundary. We analyze the dependence of |M(nm)|(2) on omega = (E(n)-E(m))/Planck's over 2pi using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency omega. We show that, for dilations and translations of the boundary, |M(nm)|(2) vanishes like omega(4) as omega-->0, for rotations such as omega(2), whereas for generic deformations it goes to a constant. Such special cases lead to quasiorthogonality of the eigenstates on the boundary.

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PubMed2000

Unification of perturbation theory, random matrix theory, and semiclassical considerations in the study of parametrically dependent eigenstates

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where x is a constant parameter. Specifically, we discuss a gas particle inside a cavity, where x controls a deformation of the boundary or the position of a "piston." The quantum eigenstates of the system are |n(x)>. We describe how the parametric kernel P(nmid R:m) = | |(2) evolves as a function of deltax = x-x(0). We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.

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PubMed2000

Quantum transport through cantori

We study the effect of classical cantori in quantum mechanics, extending previous results by several groups. We find that cantori form exponential barriers to quantum transport not only when Planck's constant exceeds the flux through the cantorus but also when it is smaller than the flux. The mechanism of localization in the two cases is different, and we describe the switch from dynamical localization to a mechanism we call "retunneling" as Planck's constant increases. We investigate the Planck's over 2pi dependence of the exponential decay for retunneling and find that the Planck's over 2pi(-0.66) coefficient found previously at criticality appears to hold also away from criticality provided piPlanck's over 2pi is large enough compared to the flux. Numerical evidence as well as an analytic argument are given. Our final contribution to this subject is a phase space view of cantori in quantum mechanics. We illustrate our results using the whisker map.

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PubMed2000

Short-time effects on eigenstate structure in sinai billiards and related systems

There is much latitude between the requirements of Schnirelman's theorem regarding the ergodicity of individual high-energy eigenstates of classically chaotic systems on the one hand, and the extreme requirements of random matrix theory on the other. It seems likely that some eigenstate statistics and long-time transport behavior bear nonrandom imprints of the underlying classical dynamics while simultaneously obeying Schnirelman's theorem. Indeed this was shown earlier in the case of systems that approach classical ergodicity slowly, and is also realized in the scarring of eigenstates, even in the Planck's over 2pi-->0 limit, along unstable periodic orbits and their manifolds. Here we demonstrate the nonrandom character of eigenstates of Sinai-like systems. We show that mixing between channels in Sinai systems is dramatically deficient compared to random matrix theory predictions. The deficit increases as |ln Planck's over 2pi| for Planck's over 2pi-->0, and is due to the vicinity of the measure zero set of orbits that never collide with the Sinai obstruction. Coarse graining to macroscopic scales recovers the Schnirelman result. Three systems are investigated here: a Sinai-type billiard, a quantum map that possesses the essential properties of the Sinai billiard, and a unitary map corresponding to a quasirandom Hamiltonian. Various wave function and long-time transport statistics are defined, theoretically investigated, and compared to numerical data.

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PubMed2000

Influence of diffraction on the spectrum and wave functions of an open system

In this paper, we demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off a sharp edge of the system are found to have a strong influence on the transmission spectrum of the system, especially in the regime where there are no stable classical orbits. On resonance, the wave functions are influenced by both classical and diffractive orbits. Off resonance, the wave functions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented

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PubMed1996