18,076 research outputs found
Spherical Hartree-Fock calculations with linear momentum projection before the variation.Part II: Spectral functions and spectroscopic factors
The hole--spectral functions and from these the spectroscopic factors have
been calculated in an Galilei--invariant way for the ground state wave
functions resulting from spherical Hartree--Fock calculations with projection
onto zero total linear momentum before the variation for the nuclei 4He, 12C,
16O, 28Si, 32S and 40Ca. The results are compared to those of the conventional
approach which uses the ground states resulting from usual spherical
Hartree--Fock calculations subtracting the kinetic energy of the center of mass
motion before the variation and to the results obtained analytically with
oscillator occupations.Comment: 16 pages, 22 postscript figure
Spherical Hartree-Fock calculations with linear momentum projection before the variation.Part I: Energies, form factors, charge densities and mathematical sum rules
Spherical Hartree--Fock calculations with projection onto zero total linear
momentum before the variation are performed for the nuclei 4He, 12C, 16O, 28Si,
32S and 40Ca using a density--independent effective nucleon--nucleon
interaction. The results are compared to those of usual spherical Hartree--Fock
calculations subtracting the kinetic energy of the center of mass motion either
before or after the variation and to the results obtained analytically with
oscillator occupations. Total energies, hole--energies, elastic charge form
factors and charge densities and the mathematical Coulomb sum rules are
discussed.Comment: 16 pages, 13 postscript figure
Contextual advantage for state discrimination
Finding quantitative aspects of quantum phenomena which cannot be explained
by any classical model has foundational importance for understanding the
boundary between classical and quantum theory. It also has practical
significance for identifying information processing tasks for which those
phenomena provide a quantum advantage. Using the framework of generalized
noncontextuality as our notion of classicality, we find one such nonclassical
feature within the phenomenology of quantum minimum error state discrimination.
Namely, we identify quantitative limits on the success probability for minimum
error state discrimination in any experiment described by a noncontextual
ontological model. These constraints constitute noncontextuality inequalities
that are violated by quantum theory, and this violation implies a quantum
advantage for state discrimination relative to noncontextual models.
Furthermore, our noncontextuality inequalities are robust to noise and are
operationally formulated, so that any experimental violation of the
inequalities is a witness of contextuality, independently of the validity of
quantum theory. Along the way, we introduce new methods for analyzing
noncontextuality scenarios, and demonstrate a tight connection between our
minimum error state discrimination scenario and a Bell scenario.Comment: 18 pages, 9 figure
Glass transition of hard spheres in high dimensions
We have investigated analytically and numerically the liquid-glass transition
of hard spheres for dimensions in the framework of mode-coupling
theory. The numerical results for the critical collective and self
nonergodicity parameters and exhibit
non-Gaussian -dependence even up to . and
differ for , but become identical on a scale
, which is proven analytically. The critical packing fraction
is above the corresponding Kauzmann packing
fraction derived by a small cage expansion. Its quadratic
pre-exponential factor is different from the linear one found earlier. The
numerical values for the exponent parameter and therefore the critical
exponents and depend on , even for the largest values of .Comment: 11 pages, 8 figures, Phys. Rev. E (in print
On the arithmetic of Krull monoids with infinite cyclic class group
Let be a Krull monoid with infinite cyclic class group and let denote the set of classes containing prime divisors. We study under
which conditions on some of the main finiteness properties of
factorization theory--such as local tameness, the finiteness and rationality of
the elasticity, the structure theorem for sets of lengths, the finiteness of
the catenary degree, and the existence of monotone and of near monotone chains
of factorizations--hold in . In many cases, we derive explicit
characterizations
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