466 research outputs found
Universal approximation of multi-copy states and universal quantum lossless data compression
We have proven that there exists a quantum state approximating any multi-copy
state universally when we measure the error by means of the normalized relative
entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE
Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been
open for more than ten years. For a deeper analysis, we have solved the
mini-max problem concerning `approximation error' up to the second order.
Furthermore, we have applied this result to quantum lossless data compression,
and have constructed a universal quantum lossless data compression
An almost sure limit theorem for super-Brownian motion
We establish an almost sure scaling limit theorem for super-Brownian motion
on associated with the semi-linear equation , where and are positive constants. In
this case, the spectral theoretical assumptions that required in Chen et al
(2008) are not satisfied. An example is given to show that the main results
also hold for some sub-domains in .Comment: 14 page
On the stability of black hole event horizons
In this work we study a {\it gedanken} experiment constructed in order to
test the cosmic censorship hypothesis and the second law of black hole
thermo-dynamics. Matter with a negative gravitating energy is imagined added to
a near extremal -charged static black hole in Einstein-Maxwell theory.
The dynamics of a similar process is studied and the thermo-dynamical
properties of the resulting black hole structure is discussed. A new mechanism
which stabilizes black hole event horizons is shown to operate in such
processes.Comment: 16, grammatical errors corrected and two references adde
On the Hybrid Extension of CTL and CTL+
The paper studies the expressivity, relative succinctness and complexity of
satisfiability for hybrid extensions of the branching-time logics CTL and CTL+
by variables. Previous complexity results show that only fragments with one
variable do have elementary complexity. It is shown that H1CTL+ and H1CTL, the
hybrid extensions with one variable of CTL+ and CTL, respectively, are
expressively equivalent but H1CTL+ is exponentially more succinct than H1CTL.
On the other hand, HCTL+, the hybrid extension of CTL with arbitrarily many
variables does not capture CTL*, as it even cannot express the simple CTL*
property EGFp. The satisfiability problem for H1CTL+ is complete for triply
exponential time, this remains true for quite weak fragments and quite strong
extensions of the logic
A new determination of the orbit and masses of the Be binary system delta Scorpii
The binary star delta Sco (HD143275) underwent remarkable brightening in the
visible in 2000, and continues to be irregularly variable. The system was
observed with the Sydney University Stellar Interferometer (SUSI) in 1999,
2000, 2001, 2006 and 2007. The 1999 observations were consistent with
predictions based on the previously published orbital elements. The subsequent
observations can only be explained by assuming that an optically bright
emission region with an angular size of > 2 +/- 1 mas formed around the primary
in 2000. By 2006/2007 the size of this region grew to an estimated > 4 mas.
We have determined a consistent set of orbital elements by simultaneously
fitting all the published interferometric and spectroscopic data as well as the
SUSI data reported here. The resulting elements and the brightness ratio for
the system measured prior to the outburst in 2000 have been used to estimate
the masses of the components. We find Ma = 15 +/- 7 Msun and Mb = 8.0 +/- 3.6
Msun. The dynamical parallax is estimated to be 7.03 +/- 0.15 mas, which is in
good agreement with the revised HIPPARCOS parallax.Comment: 8 pages, 4 figs. Accepted for publication in MNRA
Regularity of a kind of marginal functions in Hilbert spaces
We study well-posedness of some mathematical programming problem depending on a parameter that generalizes in a certain sense the metric projection onto a closed nonconvex set. We are interested in regularity of the set of minimizers as well as of the value function, which can be seen, on one hand, as the viscosity solution to a Hamilton-Jacobi equation, while, on the other, as the minimal time in some related optimal time control problem. The regularity includes both the Fréchet differentiability of the value function and the Hölder continuity of its (Fréchet) gradient
Larkin-Ovchinnikov-Fulde-Ferrell state in quasi-one-dimensional superconductors
The properties of a quasi-one-dimensional (quasi-1D) superconductor with {\it
an open Fermi surface} are expected to be unusual in a magnetic field. On the
one hand, the quasi-1D structure of the Fermi surface strongly favors the
formation of a non-uniform state (Larkin-Ovchinnikov-Fulde-Ferrell (LOFF)
state) in the presence of a magnetic field acting on the electron spins. On the
other hand, a magnetic field acting on an open Fermi surface induces a
dimensional crossover by confining the electronic wave-functions wave-functions
along the chains of highest conductivity, which results in a divergence of the
orbital critical field and in a stabilization at low temperature of a cascade
of superconducting phases separated by first order transistions. In this paper,
we study the phase diagram as a function of the anisotropy. We discuss in
details the experimental situation in the quasi-1D organic conductors of the
Bechgaard salts family and argue that they appear as good candidates for the
observation of the LOFF state, provided that their anisotropy is large enough.
Recent experiments on the organic quasi-1D superconductor (TMTSF)ClO
are in agreement with the results obtained in this paper and could be
interpreted as a signature of a high-field superconducting phase. We also point
out the possibility to observe a LOFF state in some quasi-2D organic
superconductors.Comment: 24 pages+17 figures (upon request), RevTex, ORSAY-LPS-24109
Universal coding for classical-quantum channel
We construct a universal code for stationary and memoryless classical-quantum
channel as a quantum version of the universal coding by Csisz\'{a}r and
K\"{o}rner. Our code is constructed by the combination of irreducible
representation, the decoder introduced through quantum information spectrum,
and the packing lemma
Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
We present the general theory of clean, two-dimensional, quantum Heisenberg
antiferromagnets which are close to the zero-temperature quantum transition
between ground states with and without long-range N\'{e}el order. For
N\'{e}el-ordered states, `nearly-critical' means that the ground state
spin-stiffness, , satisfies , where is the
nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered
ground states have a energy-gap, , towards excitations with spin-1,
which satisfies . Under these circumstances, we show that the
wavevector/frequency-dependent uniform and staggered spin susceptibilities, and
the specific heat, are completely universal functions of just three
thermodynamic parameters. Explicit results for the universal scaling functions
are obtained by a expansion on the quantum non-linear sigma model,
and by Monte Carlo simulations. These calculations lead to a variety of
testable predictions for neutron scattering, NMR, and magnetization
measurements. Our results are in good agreement with a number of numerical
simulations and experiments on undoped and lightly-doped .Comment: 81 pages, REVTEX 3.0, smaller updated version, YCTP-xxx
- …