2,601 research outputs found
The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium
We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy
per particle for a dilute gas in equilibrium. For an equilibrium system, the KS
entropy, h_KS is the sum of all of the positive Lyapunov exponents
characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is
the number of particles in the gas. This quantity has a density expansion of
the form h_KS/N = a\nu[-\ln{\tilde{n}} + b + O(\tilde{n})], where \nu is the
single-particle collision frequency and \tilde{n} is the reduced number density
of the gas. The theoretical values for the coefficients a and b are compared
with the results of computer simulations, with excellent agreement for a, and
less than satisfactory agreement for b. Possible reasons for this difference in
b are discussed.Comment: 15 pages, 2 figures, submitted to Phys. Rev.
Polaronic state and nanometer-scale phase separation in colossal magnetoresistive manganites
High resolution topographic images obtained by scanning tunneling microscope
in the insulating state of Pr0.68Pb0.32MnO3 single crystals showed regular
stripe-like or zigzag patterns on a width scale of 0.4 - 0.5 nm confirming a
high temperature polaronic state. Spectroscopic studies revealed inhomogeneous
maps of zero-bias conductance with small patches of metallic clusters on length
scale of 2 - 3 nm only within a narrow temperature range close to the
metal-insulator transition. The results give a direct observation of polarons
in the insulating state, phase separation of nanometer-scale metallic clusters
in the paramagnetic metallic state, and a homogeneous ferromagnetic state
Complete quantum teleportation using nuclear magnetic resonance
Quantum mechanics provides spectacular new information processing abilities
(Bennett 1995, Preskill 1998). One of the most unexpected is a procedure called
quantum teleportation (Bennett et al 1993) that allows the quantum state of a
system to be transported from one location to another, without moving through
the intervening space. Partial implementations of teleportation (Bouwmeester et
al 1997, Boschi et al 1998) over macroscopic distances have been achieved using
optical systems, but omit the final stage of the teleportation procedure. Here
we report an experimental implementation of the full quantum teleportation
operation over inter-atomic distances using liquid state nuclear magnetic
resonance (NMR). The inclusion of the final stage enables for the first time a
teleportation implementation which may be used as a subroutine in larger
quantum computations, or for quantum communication. Our experiment also
demonstrates the use of quantum process tomography, a procedure to completely
characterize the dynamics of a quantum system. Finally, we demonstrate a
controlled exploitation of decoherence as a tool to assist in the performance
of an experiment.Comment: 15 pages, 2 figures. Minor differences between this and the published
versio
Energy Dependence of the NN t-matrix in the Optical Potential for Elastic Nucleon-Nucleus Scattering
The influence of the energy dependence of the free NN t-matrix on the optical
potential of nucleon-nucleus elastic scattering is investigated within the
context of a full-folding model based on the impulse approximation. The
treatment of the pole structure of the NN t-matrix, which has to be taken into
account when integrating to negative energies is described in detail. We
calculate proton-nucleus elastic scattering observables for O,
Ca, and Pb between 65 and 200 MeV laboratory energy and study
the effect of the energy dependence of the NN t-matrix. We compare this result
with experiment and with calculations where the center-of-mass energy of the NN
t-matrix is fixed at half the projectile energy. It is found that around 200
MeV the fixed energy approximation is a very good representation of the full
calculation, however deviations occur when going to lower energies (65 MeV).Comment: 11 pages (revtex), 6 postscript figure
Full-Folding Optical Potentials for Elastic Nucleon-Nucleus Scattering based on Realistic Densities
Optical model potentials for elastic nucleon nucleus scattering are
calculated for a number of target nuclides from a full-folding integral of two
different realistic target density matrices together with full off-shell
nucleon-nucleon t-matrices derived from two different Bonn meson exchange
models. Elastic proton and neutron scattering observables calculated from these
full-folding optical potentials are compared to those obtained from `optimum
factorized' approximations in the energy regime between 65 and 400 MeV
projectile energy. The optimum factorized form is found to provide a good
approximation to elastic scattering observables obtained from the full-folding
optical potentials, although the potentials differ somewhat in the structure of
their nonlocality.Comment: 21 pages, LaTeX, 17 postscript figure
Microscopic Models for Ultrarelativistic Heavy Ion Collisions
In this paper, the concepts of microscopic transport theory are introduced
and the features and shortcomings of the most commonly used ansatzes are
discussed. In particular, the Ultrarelativistic Quantum Molecular Dynamics
(UrQMD) transport model is described in great detail. Based on the same
principles as QMD and RQMD, it incorporates a vastly extended collision term
with full baryon-antibaryon symmetry, 55 baryon and 32 meson species. Isospin
is explicitly treated for all hadrons. The range of applicability stretches
from GeV/nucleon, allowing for
a consistent calculation of excitation functions from the intermediate energy
domain up to ultrarelativistic energies. The main physics topics under
discussion are stopping, particle production and collective flow.Comment: 129 pages, pagestyle changed using US letter (8.5x11 in) format. The
whole paper (13 Mb ps file) could also be obtained from
ftp://ftp.th.physik.uni-frankfurt.de/pub/urqmd/ppnp2.ps.g
The Significance of the -Numerical Range and the Local -Numerical Range in Quantum Control and Quantum Information
This paper shows how C-numerical-range related new strucures may arise from
practical problems in quantum control--and vice versa, how an understanding of
these structures helps to tackle hot topics in quantum information.
We start out with an overview on the role of C-numerical ranges in current
research problems in quantum theory: the quantum mechanical task of maximising
the projection of a point on the unitary orbit of an initial state onto a
target state C relates to the C-numerical radius of A via maximising the trace
function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one
may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii)
in restricting the dynamics to {\em local} operations on each qubit, i.e. to
the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2).
Interestingly, the latter then leads to a novel entity, the {\em local}
C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither
star-shaped nor simply connected in contrast to the conventional C-numerical
range. This is shown in the accompanying paper (math-ph/0702005).
We present novel applications of the C-numerical range in quantum control
assisted by gradient flows on the local unitary group: (1) they serve as
powerful tools for deciding whether a quantum interaction can be inverted in
time (in a sense generalising Hahn's famous spin echo); (2) they allow for
optimising witnesses of quantum entanglement. We conclude by relating the
relative C-numerical range to problems of constrained quantum optimisation, for
which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200
Designing spin-1 lattice models using polar molecules
We describe how to design a large class of always on spin-1 interactions
between polar molecules trapped in an optical lattice. The spin degrees of
freedom correspond to the hyperfine levels of a ro-vibrational ground state
molecule. Interactions are induced using a microwave field to mix ground states
in one hyperfine manifold with the spin entangled dipole-dipole coupled excited
states. Using multiple fields anistropic models in one, two, or three
dimensions, can be built with tunable spatial range. An illustrative example in
one dimension is the generalized Haldane model, which at a specific parameter
has a gapped valence bond solid ground state. The interaction strengths are
large compared to decoherence rates and should allow for probing the rich phase
structure of strongly correlated systems, including dimerized and gapped
phases.Comment: 24 pages, 5 figure
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