673 research outputs found
Localization in an Inhomogeneous Quantum Wire
We study interaction-induced localization of electrons in an inhomogeneous
quasi-one-dimensional system--a wire with two regions, one at low density and
the other high. Quantum Monte Carlo techniques are used to treat the strong
Coulomb interactions in the low density region, where localization of electrons
occurs. The nature of the transition from high to low density depends on the
density gradient--if it is steep, a barrier develops between the two regions,
causing Coulomb blockade effects. Ferromagnetic spin polarization does not
appear for any parameters studied. The picture emerging here is in good
agreement with measurements of tunneling between two wires.Comment: 4 pages; 2 new figures, substantial revisions and clarification
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.
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
Incipient Wigner Localization in Circular Quantum Dots
We study the development of electron-electron correlations in circular
quantum dots as the density is decreased. We consider a wide range of both
electron number, N<=20, and electron gas parameter, r_s<18, using the diffusion
quantum Monte Carlo technique. Features associated with correlation appear to
develop very differently in quantum dots than in bulk. The main reason is that
translational symmetry is necessarily broken in a dot, leading to density
modulation and inhomogeneity. Electron-electron interactions act to enhance
this modulation ultimately leading to localization. This process appears to be
completely smooth and occurs over a wide range of density. Thus there is a
broad regime of ``incipient'' Wigner crystallization in these quantum dots. Our
specific conclusions are: (i) The density develops sharp rings while the pair
density shows both radial and angular inhomogeneity. (ii) The spin of the
ground state is consistent with Hund's (first) rule throughout our entire range
of r_s for all 4<N<20. (iii) The addition energy curve first becomes smoother
as interactions strengthen -- the mesoscopic fluctuations are damped by
correlation -- and then starts to show features characteristic of the classical
addition energy. (iv) Localization effects are stronger for a smaller number of
electrons. (v) Finally, the gap to certain spin excitations becomes small at
the strong interaction (large r_s) side of our regime.Comment: 14 pages, 12 figure
Chaos and Interacting Electrons in Ballistic Quantum Dots
We show that the classical dynamics of independent particles can determine
the quantum properties of interacting electrons in the ballistic regime. This
connection is established using diagrammatic perturbation theory and
semiclassical finite-temperature Green functions. Specifically, the orbital
magnetism is greatly enhanced over the Landau susceptibility by the combined
effects of interactions and finite size. The presence of families of periodic
orbits in regular systems makes their susceptibility parametrically larger than
that of chaotic systems, a difference which emerges from correlation terms.Comment: 4 pages, revtex, includes 3 postscript fig
Semiclassical Approach to Orbital Magnetism of Interacting Diffusive Quantum Systems
We study interaction effects on the orbital magnetism of diffusive mesoscopic
quantum systems. By combining many-body perturbation theory with semiclassical
techniques, we show that the interaction contribution to the ensemble averaged
quantum thermodynamic potential can be reduced to an essentially classical
operator. We compute the magnetic response of disordered rings and dots for
diffusive classical dynamics. Our semiclassical approach reproduces the results
of previous diagrammatic quantum calculations.Comment: 8 pages, revtex, includes 1 postscript fi
Semiclassical Approximations Based On Complex Trajectories.
The semiclassical limit of the coherent state propagator involves complex classical trajectories of the Hamiltonian H(u,v) = satisfying u(0) = z' and v(T) = z*. In this work we study mostly the case z' = z. The propagator is then the return probability amplitude of a wave packet. We show that a plot of the exact return probability brings out the quantal images of the classical periodic orbits. Then we compare the exact return probability with its semiclassical approximation for a soft chaotic system with two degrees of freedom. We find two situations where classical trajectories satisfying the correct boundary conditions must be excluded from the semiclassical formula. The first occurs when the contribution of the trajectory to the propagator becomes exponentially large as Planck's over 2 pi goes to zero. The second occurs when the contributing trajectories undergo bifurcations. Close to the bifurcation the semiclassical formula diverges. More interestingly, in the example studied, after the bifurcation, where more than one trajectory satisfying the boundary conditions exist, only one of them in fact contributes to the semiclassical formula, a phenomenon closely related to Stokes lines. When the contributions of these trajectories are filtered out, the semiclassical results show excellent agreement with the exact calculations.6906620
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
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
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
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