arXiv subjects

Eric J. Heller

Publications and source records attributed to Eric J. Heller.

At least 73 records · Page 4Linked to original sources

arXiv2007

Displacement Echoes: Classical Decay and Quantum Freeze

Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value because of quantum effects. Our analytical results are corroborated by numerical simulations.

quant-ph↗

arXiv2007

Statistical Properties of Many Particle Eigenfunctions

Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions appear which reflect the emergence of the canonical ensemble as the number of particles approaches infinity. This arises through a little known asymptotic limit of Bessel functions. Constraints due to symmetries, boundaries, and collisions between particles can be included.

quant-ph↗

arXiv2005

Multiple Scattering Theory for Two-dimensional Electron Gases in the Presence of Spin-Orbit Coupling

In order to model the phase-coherent scattering of electrons in two-dimensional electron gases in the presence of Rashba spin-orbit coupling, a general partial-wave expansion is developed for scattering from a cylindrically symmetric potential. The theory is applied to possible electron flow imaging experiments using a moveable scanning probe microscope tip. In such experiments, it is demonstrated theoretically that the Rashba spin-orbit coupling can give rise to spin interference effects, even for unpolarized electrons at nonzero temperature and no magnetic field.

cond-mat.mes-hall↗

arXiv2005

Quasiresonance

The concept of quasiresonance was introduced in connection with inelastic collisions between one atom and a vibro-rotationally excited diatomic molecule. In its original form, the collisions induce {\sl quasiresonant} transfer of energy between the internal degrees of freedom of the diatom: there is a surprisingly accurate low order rational value for the ratio of the changes in the vibrational and rotational classical actions, provided the vibrational and rotational frequencies of the diatom are approximately related by low order rational values, and the collision was longer that the rotational period of the molecule. In this paper we show that quasiresonance can be extended to many other processes and systems, and that it may be understood in terms of the adiabatic invariance theory and the method of averaging.

physics.class-ph↗

arXiv2005

Imaging a Single-Electron Quantum Dot

Images of a single-electron quantum dot were obtained in the Coulomb blockade regime at liquid He temperatures using a cooled scanning probe microscope (SPM). The charged SPM tip shifts the lowest energy level in the dot and creates a ring in the image corresponding to a peak in the Coulomb-blockade conductance. Fits to the lineshape of the ring determine the tip-induced shift of the electron energy state in the dot. SPM manipulation of electrons in quantum dots promises to be useful in understanding, building and manipulating circuits for quantum information processing.

cond-mat.mes-hall↗

arXiv2004

Fidelity Decay for Phase Space Displacements

In this letter we analyse the behavior of fidelity decay under a very specific kind of perturbation: phase space displacements. Under these perturbations, systems will decay following the Lyapunov regime only. Others universal regimes discussed in the literature are not presented in this case; instead, for small values of the perturbation we observe quantum freeze of the fidelity. We also show that it is possible to connect this result with the incoherent neutron scattering problem

nlin.CD↗

arXiv2003

Consolidating boundary methods for finding the eigenstates of billiards

The plane-wave decomposition method (PWDM), a widely used means of numerically finding eigenstates of the Helmholtz equation in billiard systems is described as a variant of the mathematically well-established boundary integral method (BIM). A new unified framework encompassing the two methods is discussed. Furthermore, a third numerical method, which we call the Gauge Freedom Method (GFM) is derived from the BIM equations. This opens the way to further improvements in eigenstate search techniques.

nlin.CD↗

arXiv2003

Semiclassical evaluation of quantum fidelity

We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform expression is accurate at times when there are 10^70 semiclassical contributions. Remarkably, it also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation (CPA) and show that within this approximation, the so-called ``diagonal approximation'' is automatic and does not require ensemble averaging.

quant-ph↗

arXiv2003

Semiclassical Theory of Coherence and Decoherence

A general semiclassical approach to quantum systems with system-bath interactions is developed. We study system decoherence in detail using a coherent state semiclassical wavepacket method which avoids singularity issues arising in the usual Green's function approach. We discuss the general conditions under which it is approximately correct to discuss quantum decoherence in terms of a ``dephasing'' picture and we derive semiclassical expressions for the phase and phase distribution. Remarkably, an effective system wavefunction emerges whose norm measures the decoherence and is equivalent to a density matrix formulation.

quant-ph↗

arXiv2003

Theory of Quantum Corrals and Quantum Mirages

Quantum corrals are two dimensional structures built atom by atom on an atomically clean metallic surface using a scanning tunneling microscope. These two dimensional structures ``corral'' electrons in the surface states of noble metals which lead to standing wave patterns in the electron density inside the quantum corral. We review the physics of quantum corrals and relate the signal of the scanning tunneling microscope to the scattering properties of substrate electrons from atomic impurities supported on the surface. The theory includes the effects of incoherent surface state electron scattering at the impurities and quantitively describes all of the current STM data on quantum corrals, including the recent quantum mirage experiments with Kondo effect. We discuss the physics underlying the recent mirage experiments and review some of the outstanding questions regarding Kondo effect from impurities in nanoscale structures on metallic surfaces. We also summarize recent work on variations of ``quantum'' corrals: optical corrals and acoustical corrals.

cond-mat.mes-hall↗

arXiv2002

Quantum Multiple Scattering: Eigenmode Expansion and Its Applications to Proximity Resonance

We show that for a general system of N s-wave point scatterers, there are always N eigenmodes. These eigenmodes or eigenchannels play the same role as spherical harmonics for a spherically symmetric target--they give a phase shift only. In other words, the T matrix of the system is of rank N and the eigenmodes are eigenvectors corresponding to non-0 eigenvalues of the T matrix. The eigenmode expansion approach can give insight to the total scattering cross section; the position, width, and superradiant or subradiant nature of resonance peaks; the unsymmetric Fano lineshape of sharp proximity resonance peaks based on the high energy tail of a broad band; and other properties. Off-resonant eigenmodes for identical proximate scatterers are approximately angular momentum eigenstates.

physics.atom-ph↗

arXiv2002

Uniform semiclassical wave function for coherent 2D electron flow

We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The formation of branches has been explained by classical arguments, but the SC simulations necessary to account for the coherence are made difficult by the proliferation of catastrophes in the phase space. In this paper, expansion in terms of "replacement manifolds" is used to find a uniform SC wave function for a cusp singularity. The method is then generalized and applied to calculate uniform wave functions for a quantum-map model of coherent flow through a 2DEG. Finally, the quantum-map approximation is dropped and the method is shown to work for a continuous-time model as well.

nlin.CD↗

arXiv2002

Comment on "Ehrenfest times for classically chaotic systems"

In a recent Phys. Rev. E Rapid Communication, the authors, Silvestrov and Beenakker, introduce a way to lengthen the Ehrenfest time, $τ$, for fully chaotic systems. We disagree with several statements made in their paper, and address the following points essential to their conclusions: 1) it is not true that all semiclassical approximations for chaotic systems fail at a so-called `logtime', $τ\propto - \ln (\hbar)$, differing only by a numerical coefficient; and 2) the limitation of the semiclassical approximation as expressed in the authors' Eq. (8) is not limited by their argument leading to Eq. (12).

nlin.CD↗

arXiv2001

A new class of semiclassical wave function uniformizations

We present a new semiclassical technique which 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.

nlin.CD↗

arXiv2001

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) = , also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.

nlin.CD↗

arXiv2000

Rate of energy absorption for a driven chaotic cavity

We consider the response of a chaotic cavity in d dimensions to periodic driving. We are motivated by older studies of one-body dissipation in nuclei, and also by anticipated mesoscopic applications. For calculating the rate of energy absorption due to time-dependent deformation of the confining potential, we introduce an improved version of the wall formula. Our formulation takes into account that a special class of deformations causes no heating in the zero-frequency limit. We also derive a mesoscopic version of the Drude formula, and explain that it can be regarded as a special example of our calculations. Specifically we consider a quantum dot driven by electro-motive force which is induced by a time-dependent homogeneous magnetic field.

nlin.CD↗

arXiv2000

The No-sticking Effect in Ultra-cold Collisions

We provide the theoretical basis for understanding the phenomenon in which an ultra cold atom incident on a possibly warm target will not stick, even in the large $n$ limit where $n$ is the number of internal degrees of freedom of the target. Our treatment is non-perturbative in which the full many-body problem is viewed as a scattering event purely within the context of scattering theory. The question of sticking is then simply and naturally identified with the formation of a long lived resonance. One crucial physical insight that emerges is that the many internal degrees of freedom serve to decohere the incident one body wavefunction, thus upsetting the delicate interference process necessary to form a resonance in the first place. This is the physical reason for not sticking.

physics.atom-ph↗

arXiv2000

Transition from reflection to sticking in ultracold atom-surface scattering

In paper I (physics/0010068) entitled "The No-sticking Effect in Ultra-cold Collisions", we showed that under very general circumstances, atoms approaching a surface will not stick as its incoming energy approaches zero. This is true of either warm or cold surfaces. Here we explore the transition region from non sticking to sticking as energy is increased. The key to understanding the transition region is the WKB approximation and the nature of its breakdown. Simple rules for understanding the rollover to higher energy, post-threshold behavior, including analytical formulae for some asymptotic forms of the attractive potential are presented. We discuss a practical example of atom-surface pair in various substrate geometries. We also discuss the case of low energy scattering from clusters.

physics.atom-ph↗