Semiclassical Propagation of Wavepackets with Real and Complex Trajectories

We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield three different semiclassical formulae involving different real trajectories. One of these formulae is Heller's thawed gaussian approximation. The other approximations are non-gaussian and may involve several trajectories determined by mixed initial-final conditions. These different formulae are tested for the cases of scattering by a hard wall, scattering by an attractive gaussian potential, and bound motion in a quartic oscillator. The formula with complex trajectories gives good results in all cases. The non-gaussian approximations with real trajectories work well in some cases, whereas the thawed gaussian works only in very simple situations.Comment: revised text, 24 pages, 6 figure

Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators

We discuss some basic tools for an analysis of one-dimensionalquantum systems defined on a cyclic coordinate space. The basic features of the generalized coherent states, the complexifier coherent states are reviewed. These states are then used to define the corresponding (quasi)densities in phase space. The properties of these generalized Husimi distributions are discussed, in particular their zeros.Furthermore, the use of the complexifier coherent states for a semiclassical analysis is demonstrated by deriving a semiclassical coherent state propagator in phase space.Comment: 29 page

Weak-Localization in Chaotic Versus Non-Chaotic Cavities: A Striking Difference in the Line Shape

We report experimental evidence that chaotic and non-chaotic scattering through ballistic cavities display distinct signatures in quantum transport. In the case of non-chaotic cavities, we observe a linear decrease in the average resistance with magnetic field which contrasts markedly with a Lorentzian behavior for a chaotic cavity. This difference in line-shape of the weak-localization peak is related to the differing distribution of areas enclosed by electron trajectories. In addition, periodic oscillations are observed which are probably associated with the Aharonov-Bohm effect through a periodic orbit within the cavities.Comment: 4 pages revtex + 4 figures on request; amc.hub.94.

Reflection Symmetric Ballistic Microstructures: Quantum Transport Properties

We show that reflection symmetry has a strong influence on quantum transport properties. Using a random S-matrix theory approach, we derive the weak-localization correction, the magnitude of the conductance fluctuations, and the distribution of the conductance for three classes of reflection symmetry relevant for experimental ballistic microstructures. The S-matrix ensembles used fall within the general classification scheme introduced by Dyson, but because the conductance couples blocks of the S-matrix of different parity, the resulting conductance properties are highly non-trivial.Comment: 4 pages, includes 3 postscript figs, uses revte

How Phase-Breaking Affects Quantum Transport Through Chaotic Cavities

We investigate the effects of phase-breaking events on electronic transport through ballistic chaotic cavities. We simulate phase-breaking by a fictitious lead connecting the cavity to a phase-randomizing reservoir and introduce a statistical description for the total scattering matrix, including the additional lead. For strong phase-breaking, the average and variance of the conductance are calculated analytically. Combining these results with those in the absence of phase-breaking, we propose an interpolation formula, show that it is an excellent description of random-matrix numerical calculations, and obtain good agreement with several recent experiments.Comment: 4 pages, revtex, 3 figures: uuencoded tar-compressed postscrip

Decoherence by Correlated Noise and Quantum Error Correction

We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.Comment: 4 pages, 1 figure, Phys. Rev. Lett. in pres

On the Inequivalence of Weak-Localization and Coherent Backscattering

We define a current-conserving approximation for the local conductivity tensor of a disordered system which includes the effects of weak localization. Using this approximation we show that the weak localization effect in conductance is not obtained simply from the diagram corresponding to the coherent back-scattering peak observed in optical experiments. Other diagrams contribute to the effect at the same order and decrease its value. These diagrams appear to have no semiclassical analogues, a fact which may have implications for the semiclassical theory of chaotic systems. The effects of discrete symmetries on weak localization in disordered conductors is evaluated and and compared to results from chaotic scatterers.Comment: 24 pages revtex + 12 figures on request; hub.94.

Signatures of Classical Periodic Orbits on a Smooth Quantum System

Gutzwiller's trace formula and Bogomolny's formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a large spatial and energy range.Comment: 12 pages, uuencoded postscript file (1526 kb

Interaction-Induced Strong Localization in Quantum Dots

We argue that Coulomb blockade phenomena are a useful probe of the cross-over to strong correlation in quantum dots. Through calculations at low density using variational and diffusion quantum Monte Carlo (up to r_s ~ 55), we find that the addition energy shows a clear progression from features associated with shell structure to those caused by commensurability of a Wigner crystal. This cross-over (which occurs near r_s ~ 20 for spin-polarized electrons) is, then, a signature of interaction-driven localization. As the addition energy is directly measurable in Coulomb blockade conductance experiments, this provides a direct probe of localization in the low density electron gas.Comment: 4 pages, published version, revised discussio