321 research outputs found
Weak localization in disordered systems at the ballistic limit
The weak localization (WL) contribution to the two-level correlation function
is calculated for two-dimensional disordered conductors. Our analysis extends
to the nondiffusive (ballistic) regime, where the elastic mean path is of order
of the size of the system. In this regime the structure factor (the Fourier
transform of the two-point correlator) exhibits a singular behavior consisting
of dips superimposed on a smooth positive background. The strongest dips appear
at periods of the periodic orbits of the underlying clean system. Somewhat
weaker singularities appear at times which are sums of periods of two such
orbits. The results elucidate various aspects of the weak localization physics
of ballistic chaotic systems.Comment: 13 pages, 13 figure
Effects of Spin-Orbit Interactions on Tunneling via Discrete Energy Levels in Metal Nanoparticles
The presence of spin-orbit scattering within an aluminum nanoparticle affects
measurements of the discrete energy levels within the particle by (1) reducing
the effective g-factor below the free-electron value of 2, (2) causing avoided
crossings as a function of magnetic field between predominantly-spin-up and
predominantly-spin-down levels, and (3) introducing magnetic-field-dependent
changes in the amount of current transported by the tunneling resonances. All
three effects can be understood in a unified fashion by considering a simple
Hamiltonian. Spin-orbit scattering from 4% gold impurities in superconducting
aluminum nanoparticles produces no dramatic effect on the superconducting gap
at zero magnetic field, but we argue that it does modify the nature of the
superconducting transition in a magnetic field.Comment: 10 pages, 5 figures. Submitted to Phys. Rev.
Wavefunctions, Green's functions and expectation values in terms of spectral determinants
We derive semiclassical approximations for wavefunctions, Green's functions
and expectation values for classically chaotic quantum systems. Our method
consists of applying singular and regular perturbations to quantum
Hamiltonians. The wavefunctions, Green's functions and expectation values of
the unperturbed Hamiltonian are expressed in terms of the spectral determinant
of the perturbed Hamiltonian. Semiclassical resummation methods for spectral
determinants are applied and yield approximations in terms of a finite number
of classical trajectories. The final formulas have a simple form. In contrast
to Poincare surface of section methods, the resummation is done in terms of the
periods of the trajectories.Comment: 18 pages, no figure
Ehrenfest times for classically chaotic systems
We describe the quantum mechanical spreading of a Gaussian wave packet by
means of the semiclassical WKB approximation of Berry and Balazs. We find that
the time scale on which this approximation breaks down in a chaotic
system is larger than the Ehrenfest times considered previously. In one
dimension \tau=\fr{7}{6}\lambda^{-1}\ln(A/\hbar), with the Lyapunov
exponent and a typical classical action.Comment: 4 page
Structures of Malcev Bialgebras on a simple non-Lie Malcev algebra
Lie bialgebras were introduced by Drinfeld in studying the solutions to the
classical Yang-Baxter equation. The definition of a bialgebra in the sense of
Drinfeld (D-bialgebra), related with any variety of algebras, was given by
Zhelyabin. In this work, we consider Malcev bialgebras. We describe all
structures of a Malcev bialgebra on a simple non-Lie Malcev algebra
Quasiclassical Random Matrix Theory
We directly combine ideas of the quasiclassical approximation with random
matrix theory and apply them to the study of the spectrum, in particular to the
two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN
unitary matrix, is considered to be a random matrix. Rather than rejecting all
knowledge of the system, except for its symmetry, [as with Dyson's circular
unitary ensemble], we choose an ensemble which incorporates the knowledge of
the shortest periodic orbits, the prime quasiclassical information bearing on
the spectrum. The results largely agree with expectations but contain novel
features differing from other recent theories.Comment: 4 pages, RevTex, submitted to Phys. Rev. Lett., permanent e-mail
[email protected]
Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory
The Bohigas--Giannoni--Schmit conjecture stating that the statistical
spectral properties of systems which are chaotic in their classical limit
coincide with random matrix theory is proved. For this purpose a new
semiclassical field theory for individual chaotic systems is constructed in the
framework of the non--linear -model. The low lying modes are shown to
be associated with the Perron--Frobenius spectrum of the underlying
irreversible classical dynamics. It is shown that the existence of a gap in the
Perron-Frobenius spectrum results in a RMT behavior. Moreover, our formalism
offers a way of calculating system specific corrections beyond RMT.Comment: 4 pages, revtex, no figure
Quantum breaking time near classical equilibrium points
By using numerical and semiclassical methods, we evaluate the quantum
breaking, or Ehrenfest time for a wave packet localized around classical
equilibrium points of autonomous one-dimensional systems with polynomial
potentials. We find that the Ehrenfest time diverges logarithmically with the
inverse of the Planck constant whenever the equilibrium point is exponentially
unstable. For stable equilibrium points, we have a power law divergence with
exponent determined by the degree of the potential near the equilibrium point.Comment: 4 pages, 5 figure
Spectral form factor in a random matrix theory
In the theory of disordered systems the spectral form factor , the
Fourier transform of the two-level correlation function with respect to the
difference of energies, is linear for and constant for
. Near zero and near its exhibits oscillations which have
been discussed in several recent papers. In the problems of mesoscopic
fluctuations and quantum chaos a comparison is often made with random matrix
theory. It turns out that, even in the simplest Gaussian unitary ensemble,
these oscilllations have not yet been studied there. For random matrices, the
two-level correlation function exhibits several
well-known universal properties in the large N limit. Its Fourier transform is
linear as a consequence of the short distance universality of
. However the cross-over near zero and
requires to study these correlations for finite N. For this purpose we use an
exact contour-integral representation of the two-level correlation function
which allows us to characterize these cross-over oscillatory properties. The
method is also extended to the time-dependent case.Comment: 36P, (+5 figures not included
Coulomb singularity effects in tunnelling spectroscopy of individual impurities
Non-equilibrium Coulomb effects in resonant tunnelling processes through deep
impurity states are analyzed. It is shown that Coulomb vertex corrections to
the tunnelling transfer amplitude lead to a power-law singularity in current-
voltage characteristicsComment: 7 pages, 2 figure
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