705 research outputs found
Macroscopic objects in quantum mechanics: A combinatorial approach
Why we do not see large macroscopic objects in entangled states? There are
two ways to approach this question. The first is dynamic: the coupling of a
large object to its environment cause any entanglement to decrease
considerably. The second approach, which is discussed in this paper, puts the
stress on the difficulty to observe a large scale entanglement. As the number
of particles n grows we need an ever more precise knowledge of the state, and
an ever more carefully designed experiment, in order to recognize entanglement.
To develop this point we consider a family of observables, called witnesses,
which are designed to detect entanglement. A witness W distinguishes all the
separable (unentangled) states from some entangled states. If we normalize the
witness W to satisfy |tr(W\rho)| \leq 1 for all separable states \rho, then the
efficiency of W depends on the size of its maximal eigenvalue in absolute
value; that is, its operator norm ||W||. It is known that there are witnesses
on the space of n qbits for which ||W|| is exponential in n. However, we
conjecture that for a large majority of n-qbit witnesses ||W|| \leq O(\sqrt{n
logn}). Thus, in a non ideal measurement, which includes errors, the largest
eigenvalue of a typical witness lies below the threshold of detection. We prove
this conjecture for the family of extremal witnesses introduced by Werner and
Wolf (Phys. Rev. A 64, 032112 (2001)).Comment: RevTeX, 14 pages, some additions to the published version: A second
conjecture added, discussion expanded, and references adde
Approximated maximum likelihood estimation in multifractal random walks
We present an approximated maximum likelihood method for the multifractal
random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The
likelihood is computed using a Laplace approximation and a truncation in the
dependency structure for the latent volatility. The procedure is implemented as
a package in the R computer language. Its performance is tested on synthetic
data and compared to an inference approach based on the generalized method of
moments. The method is applied to estimate parameters for various financial
stock indices.Comment: 8 pages, 3 figures, 2 table
Elastic and Raman scattering of 9.0 and 11.4 MeV photons from Au, Dy and In
Monoenergetic photons between 8.8 and 11.4 MeV were scattered elastically and
in elastically (Raman) from natural targets of Au, Dy and In.15 new cross
sections were measured. Evidence is presented for a slight deformation in the
197Au nucleus, generally believed to be spherical. It is predicted, on the
basis of these measurements, that the Giant Dipole Resonance of Dy is very
similar to that of 160Gd. A narrow isolated resonance at 9.0 MeV is observed in
In.Comment: 31 pages, 11 figure
The Past and Future History of Regulus
We show how the recent discovery of a likely close white dwarf companion to
the well known star Regulus, one of the brightest stars in the sky, leads to
considerable insight into the prior evolutionary history of this star,
including the cause of its current rapid rotation. We infer a relatively narrow
range for the initial masses of the progenitor system: M_{10} = 2.3 +/- 0.2
M_sun and M_{20} = 1.7 +/- 0.2 M_sun, where M_{10} and M_{20} are the initial
masses of the progenitors of the white dwarf and Regulus, respectively. In this
scenario, the age of the Regulus system would exceed 1 Gyr. We also show that
Regulus, with a current orbital period of 40 days, has an interesting future
ahead of it. This includes (i) a common envelope phase, and, quite possibly,
(ii) an sdB phase, followed by (iii) an AM CVn phase with orbital periods < 1
hr. Binary evolution calculations are presented in support of this scenario. We
also discuss alternative possibilities, emphasizing the present uncertainties
in binary evolution theory. Thus, this one particular star system illustrates
many different aspects of binary stellar evolution.Comment: PDFLaTeX, 9 pages with 8 figure
Spectrum and diffusion for a class of tight-binding models on hypercubes
We propose a class of exactly solvable anisotropic tight-binding models on an
infinite-dimensional hypercube. The energy spectrum is analytically computed
and is shown to be fractal and/or absolutely continuous according to the value
hopping parameters. In both cases, the spectral and diffusion exponents are
derived. The main result is that, even if the spectrum is absolutely
continuous, the diffusion exponent for the wave packet may be anything between
0 and 1 depending upon the class of models.Comment: 5 pages Late
Lognormal scale invariant random measures
In this article, we consider the continuous analog of the celebrated
Mandelbrot star equation with lognormal weights. Mandelbrot introduced this
equation to characterize the law of multiplicative cascades. We show existence
and uniqueness of measures satisfying the aforementioned continuous equation;
these measures fall under the scope of the Gaussian multiplicative chaos theory
developed by J.P. Kahane in 1985 (or possibly extensions of this theory). As a
by product, we also obtain an explicit characterization of the covariance
structure of these measures. We also prove that qualitative properties such as
long-range independence or isotropy can be read off the equation.Comment: 31 pages; Probability Theory and Related Fields (2012) electronic
versio
Exact and explicit probability densities for one-sided Levy stable distributions
We study functions g_{\alpha}(x) which are one-sided, heavy-tailed Levy
stable probability distributions of index \alpha, 0< \alpha <1, of fundamental
importance in random systems, for anomalous diffusion and fractional kinetics.
We furnish exact and explicit expression for g_{\alpha}(x), 0 \leq x < \infty,
satisfying \int_{0}^{\infty} exp(-p x) g_{\alpha}(x) dx = exp(-p^{\alpha}),
p>0, for all \alpha = l/k < 1, with k and l positive integers. We reproduce all
the known results given by k\leq 4 and present many new exact solutions for k >
4, all expressed in terms of known functions. This will allow a 'fine-tuning'
of \alpha in order to adapt g_{\alpha}(x) to a given experimental situation.Comment: 4 pages, 3 figures and 1 tabl
Exact asymptotics of the freezing transition of a logarithmically correlated random energy model
We consider a logarithmically correlated random energy model, namely a model
for directed polymers on a Cayley tree, which was introduced by Derrida and
Spohn. We prove asymptotic properties of a generating function of the partition
function of the model by studying a discrete time analogy of the KPP-equation -
thus translating Bramson's work on the KPP-equation into a discrete time case.
We also discuss connections to extreme value statistics of a branching random
walk and a rescaled multiplicative cascade measure beyond the critical point
- …