827 research outputs found
Risk aversion for nonsmooth utility functions
This paper generalizes the notion of risk aversion for functions which are not necessarily differentiable nor strictly concave. Using an approach based on superdifferentials, we define the notion of a risk aversion measure, from which the classical absolute as well as relative risk aversion follows as a RadonâNikodym derivative if it exists. Using this notion, we are able to compare risk aversions for nonsmooth utility functions, and to extend a classical result of Pratt to the case of nonsmooth utility functions. We prove how relative risk aversion is connected to a super-power property of the function. Furthermore, we show how boundedness of the relative risk aversion translates to the corresponding property of the conjugate function. We propose also a weaker ordering of the risk aversion, referred to as essential bounds for the risk aversion, which requires only that bounds of the (absolute or relative) risk aversion hold up to a certain tolerance
Quantum Copying: Beyond the No-Cloning Theorem
We analyze to what extent it is possible to copy arbitrary states of a
two-level quantum system. We show that there exists a "universal quantum
copying machine", which approximately copies quantum mechanical states in such
a way that the quality of its output does not depend on the input. We also
examine a machine which combines a unitary transformation with a selective
measurement to produce good copies of states in a neighborhood of a particular
state. We discuss the problem of measurement of the output states.Comment: RevTex, 26 pages, to appear in Physical Review
Cloud microphysical effects of turbulent mixing and entrainment
Turbulent mixing and entrainment at the boundary of a cloud is studied by
means of direct numerical simulations that couple the Eulerian description of
the turbulent velocity and water vapor fields with a Lagrangian ensemble of
cloud water droplets that can grow and shrink by condensation and evaporation,
respectively. The focus is on detailed analysis of the relaxation process of
the droplet ensemble during the entrainment of subsaturated air, in particular
the dependence on turbulence time scales, droplet number density, initial
droplet radius and particle inertia. We find that the droplet evolution during
the entrainment process is captured best by a phase relaxation time that is
based on the droplet number density with respect to the entire simulation
domain and the initial droplet radius. Even under conditions favoring
homogeneous mixing, the probability density function of supersaturation at
droplet locations exhibits initially strong negative skewness, consistent with
droplets near the cloud boundary being suddenly mixed into clear air, but
rapidly approaches a narrower, symmetric shape. The droplet size distribution,
which is initialized as perfectly monodisperse, broadens and also becomes
somewhat negatively skewed. Particle inertia and gravitational settling lead to
a more rapid initial evaporation, but ultimately only to slight depletion of
both tails of the droplet size distribution. The Reynolds number dependence of
the mixing process remained weak over the parameter range studied, most
probably due to the fact that the inhomogeneous mixing regime could not be
fully accessed when phase relaxation times based on global number density are
considered.Comment: 17 pages, 10 Postscript figures (figures 3,4,6,7,8 and 10 are in
reduced quality), to appear in Theoretical Computational Fluid Dynamic
Robustness of Decoherence-Free Subspaces for Quantum Computation
It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)]
that within the framework of the semigroup Markovian master equation,
decoherence-free (DF) subspaces exist which are stable to first order in time
to a perturbation. Here this result is extended to the non-Markovian regime and
generalized. In particular, it is shown that within both the semigroup and the
non-Markovian operator sum representation, DF subspaces are stable to all
orders in time to a symmetry-breaking perturbation. DF subspaces are thus ideal
for quantum memory applications. For quantum computation, however, the
stability result does not extend beyond the first order. Thus, to perform
robust quantum computation in DF subspaces, they must be supplemented with
quantum error correcting codes.Comment: 16 pages, no figures. Several changes, including a clarification of
the derivation of the Lindblad equation from the operator sum representation.
To appear in Phys. Rev
Empirical Determination of Bang-Bang Operations
Strong and fast "bang-bang" (BB) pulses have been recently proposed as a
means for reducing decoherence in a quantum system. So far theoretical analysis
of the BB technique relied on model Hamiltonians. Here we introduce a method
for empirically determining the set of required BB pulses, that relies on
quantum process tomography. In this manner an experimenter may tailor his or
her BB pulses to the quantum system at hand, without having to assume a model
Hamiltonian.Comment: 14 pages, 2 eps figures, ReVTeX4 two-colum
Quantum gates with neutral atoms: Controlling collisional interactions in time dependent traps
We theoretically study specific schemes for performing a fundamental
two-qubit quantum gate via controlled atomic collisions by switching
microscopic potentials. In particular we calculate the fidelity of a gate
operation for a configuration where a potential barrier between two atoms is
instantaneously removed and restored after a certain time. Possible
implementations could be based on microtraps created by magnetic and electric
fields, or potentials induced by laser light.Comment: 10 pages, 3 figure
Quantum inference of states and processes
The maximum-likelihood principle unifies inference of quantum states and
processes from experimental noisy data. Particularly, a generic quantum process
may be estimated simultaneously with unknown quantum probe states provided that
measurements on probe and transformed probe states are available. Drawbacks of
various approximate treatments are considered.Comment: 7 pages, 4 figure
Predictive powers of chiral perturbation theory in Compton scattering off protons
We study low-energy nucleon Compton scattering in the framework of baryon
chiral perturbation theory (BPT) with pion, nucleon, and (1232)
degrees of freedom, up to and including the next-to-next-to-leading order
(NNLO). We include the effects of order , and , with
MeV the -resonance excitation energy. These are
all "predictive" powers in the sense that no unknown low-energy constants enter
until at least one order higher (i.e, ). Estimating the theoretical
uncertainty on the basis of natural size for effects, we find that
uncertainty of such a NNLO result is comparable to the uncertainty of the
present experimental data for low-energy Compton scattering. We find an
excellent agreement with the experimental cross section data up to at least the
pion-production threshold. Nevertheless, for the proton's magnetic
polarizability we obtain a value of fm, in
significant disagreement with the current PDG value. Unlike the previous
PT studies of Compton scattering, we perform the calculations in a
manifestly Lorentz-covariant fashion, refraining from the heavy-baryon (HB)
expansion. The difference between the lowest order HBPT and BPT
results for polarizabilities is found to be appreciable. We discuss the chiral
behavior of proton polarizabilities in both HBPT and BPT with the
hope to confront it with lattice QCD calculations in a near future. In studying
some of the polarized observables, we identify the regime where their naive
low-energy expansion begins to break down, thus addressing the forthcoming
precision measurements at the HIGS facility.Comment: 24 pages, 9 figures, RevTeX4, revised version published in EPJ
An epitaxial model for heterogeneous nucleation on potent substrates
© The Minerals, Metals & Materials Society and ASM International 2012In this article, we present an epitaxial model for heterogeneous nucleation on potent substrates. It is proposed that heterogeneous nucleation of the solid phase (S) on a potent substrate (N) occurs by epitaxial growth of a pseudomorphic solid (PS) layer on the substrate surface under a critical undercooling (ÎT ). The PS layer with a coherent PS/N interface mimics the atomic arrangement of the substrate, giving rise to a linear increase of misfit strain energy with layer thickness. At a critical thickness (h ), elastic strain energy reaches a critical level, at which point, misfit dislocations are created to release the elastic strain energy in the PS layer. This converts the strained PS layer to a strainless solid (S), and changes the initial coherent PS/N interface into a semicoherent S/N interface. Beyond this critical thickness, further growth will be strainless, and solidification enters the growth stage. It is shown analytically that the lattice misfit (f) between the solid and the substrate has a strong influence on both h and ÎT ; h decreases; and ÎT increases with increasing lattice misfit. This epitaxial nucleation model will be used to explain qualitatively the generally accepted experimental findings on grain refinement in the literature and to analyze the general approaches to effective grain refinement.EPSRC Centre for Innovative Manufacturing in Liquid Metal Engineerin
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