1,007 research outputs found
Chaotic dephasing in a double-slit scattering experiment
We design a computational experiment in which a quantum particle tunnels into
a billiard of variable shape and scatters out of it through a double-slit
opening on the billiard's base. The interference patterns produced by the
scattered probability currents for a range of energies are investigated in
relation to the billiard's geometry which is connected to its classical
integrability. Four billiards with hierarchical integrability levels are
considered: integrable, pseudo-integrable, weak-mixing and strongly chaotic. In
agreement with the earlier result by Casati and Prosen [1], we find the
billiard's integrability to have a crucial influence on the properties of the
interference patterns. In the integrable case most experiment outcomes are
found to be consistent with the constructive interference occurring in the
usual double-slit experiment. In contrast to this, non-integrable billiards
typically display asymmetric interference patterns of smaller visibility
characterized by weakly correlated wave function values at the two slits. Our
findings indicate an intrinsic connection between the classical integrability
and the quantum dephasing, responsible for the destruction of interference
Quantum transport in semiconductor quantum dot superlattices: electron-phonon resonances and polaron effects
Electron transport in periodic quantum dot arrays in the presence of
interactions with phonons was investigated using the formalism of
nonequilibrium Green's functions. The self-consistent Born approximation was
used to model the self-energies. Its validity was checked by comparison with
the results obtained by direct diagonalization of the Hamiltonian of
interacting electrons and longitudinal optical phonons. The nature of charge
transport at electron -- phonon resonances was investigated in detail and
contributions from scattering and coherent tunnelling to the current were
identified. It was found that at larger values of the structure period the main
peak in the current -- field characteristics exhibits a doublet structure which
was shown to be a transport signature of polaron effects. At smaller values of
the period, electron -- phonon resonances cause multiple peaks in the
characteristics. A phenomenological model for treatment of nonuniformities of a
realistic quantum dot ensemble was also introduced to estimate the influence of
nonuniformities on current -- field characteristics
Fluctuations and Entanglement spectrum in quantum Hall states
The measurement of quantum entanglement in many-body systems remains
challenging. One experimentally relevant fact about quantum entanglement is
that in systems whose degrees of freedom map to free fermions with conserved
total particle number, exact relations hold relating the Full Counting
Statistics associated with the bipartite charge fluctuations and the sequence
of R\' enyi entropies. We draw a correspondence between the bipartite charge
fluctuations and the entanglement spectrum, mediated by the R\' enyi entropies.
In the case of the integer quantum Hall effect, we show that it is possible to
reproduce the generic features of the entanglement spectrum from a measurement
of the second charge cumulant only. Additionally, asking whether it is possible
to extend the free fermion result to the fractional quantum Hall
case, we provide numerical evidence that the answer is negative in general. We
further address the problem of quantum Hall edge states described by a
Luttinger liquid, and derive expressions for the spectral functions of the real
space entanglement spectrum at a quantum point contact realized in a quantum
Hall sample.Comment: Final Version. Invited Article, for Special Issue of JSTAT on
"Quantum Entanglement in Condensed Matter Physics
Learning Mixtures of Gaussians in High Dimensions
Efficiently learning mixture of Gaussians is a fundamental problem in
statistics and learning theory. Given samples coming from a random one out of k
Gaussian distributions in Rn, the learning problem asks to estimate the means
and the covariance matrices of these Gaussians. This learning problem arises in
many areas ranging from the natural sciences to the social sciences, and has
also found many machine learning applications. Unfortunately, learning mixture
of Gaussians is an information theoretically hard problem: in order to learn
the parameters up to a reasonable accuracy, the number of samples required is
exponential in the number of Gaussian components in the worst case. In this
work, we show that provided we are in high enough dimensions, the class of
Gaussian mixtures is learnable in its most general form under a smoothed
analysis framework, where the parameters are randomly perturbed from an
adversarial starting point. In particular, given samples from a mixture of
Gaussians with randomly perturbed parameters, when n > {\Omega}(k^2), we give
an algorithm that learns the parameters with polynomial running time and using
polynomial number of samples. The central algorithmic ideas consist of new ways
to decompose the moment tensor of the Gaussian mixture by exploiting its
structural properties. The symmetries of this tensor are derived from the
combinatorial structure of higher order moments of Gaussian distributions
(sometimes referred to as Isserlis' theorem or Wick's theorem). We also develop
new tools for bounding smallest singular values of structured random matrices,
which could be useful in other smoothed analysis settings
Understanding the Solar Sources of In Situ Observations
The solar wind can, to a good approximation be described as a twoâcomponent flow with fast, tenuous, quiescent flow emanating from coronal holes, and slow, dense and variable flow associated with the boundary between open and closed magnetic fields. In spite of its simplicity, this picture naturally produces a range of complex heliospheric phenomena, including the presence, location, and orientation of corotating interaction regions and their associated shocks. In this study, we apply a twoâstep mapping technique, incorporating a magnetohydrodynamic model of the solar corona, to bring in situ observations from Ulysses, WIND, and ACE back to the solar surface in an effort to determine some intrinsic properties of the quasiâsteady solar wind. In particular, we find that a âlayerâ of âŒ35,000 km exists between the Coronal Hole Boundary (CHB) and the fast solar wind, where the wind is slow and variable. We also derive a velocity gradient within large polar coronal holes (that were present during Ulyssesâ rapid latitude scan) as a function of distance from the CHB. We find that v = 713 km/s + 3.2 d, where d is the angular distance from the CHB boundary in degrees. © 2003 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87654/2/79_1.pd
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