10,489 research outputs found
On the intersection of free subgroups in free products of groups
Let (G_i | i in I) be a family of groups, let F be a free group, and let G =
F *(*I G_i), the free product of F and all the G_i. Let FF denote the set of
all finitely generated subgroups H of G which have the property that, for each
g in G and each i in I, H \cap G_i^{g} = {1}. By the Kurosh Subgroup Theorem,
every element of FF is a free group. For each free group H, the reduced rank of
H is defined as r(H) = max{rank(H) -1, 0} in \naturals \cup {\infty} \subseteq
[0,\infty]. To avoid the vacuous case, we make the additional assumption that
FF contains a non-cyclic group, and we define sigma := sup{r(H\cap
K)/(r(H)r(K)) : H, K in FF and r(H)r(K) \ne 0}, sigma in [1,\infty]. We are
interested in precise bounds for sigma. In the special case where I is empty,
Hanna Neumann proved that sigma in [1,2], and conjectured that sigma = 1;
almost fifty years later, this interval has not been reduced. With the
understanding that \infty/(\infty -2) = 1, we define theta := max{|L|/(|L|-2) :
L is a subgroup of G and |L| > 2}, theta in [1,3]. Generalizing Hanna Neumann's
theorem, we prove that sigma in [theta, 2 theta], and, moreover, sigma = 2
theta if G has 2-torsion. Since sigma is finite, FF is closed under finite
intersections. Generalizing Hanna Neumann's conjecture, we conjecture that
sigma = theta whenever G does not have 2-torsion.Comment: 28 pages, no figure
Magnetoconductance switching in an array of oval quantum dots
Employing oval shaped quantum billiards connected by quantum wires as the
building blocks of a linear quantum dot array, we calculate the ballistic
magnetoconductance in the linear response regime. Optimizing the geometry of
the billiards, we aim at a maximal finite- over zero-field ratio of the
magnetoconductance. This switching effect arises from a relative phase change
of scattering states in the oval quantum dot through the applied magnetic
field, which lifts a suppression of the transmission characteristic for a
certain range of geometry parameters. It is shown that a sustainable switching
ratio is reached for a very low field strength, which is multiplied by
connecting only a second dot to the single one. The impact of disorder is
addressed in the form of remote impurity scattering, which poses a temperature
dependent lower bound for the switching ratio, showing that this effect should
be readily observable in experiments.Comment: 11 pages, 8 figure
Classical, quantum and total correlations
We discuss the problem of separating consistently the total correlations in a
bipartite quantum state into a quantum and a purely classical part. A measure
of classical correlations is proposed and its properties are explored.Comment: 10 pages, 3 figure
L-Convex Polyominoes are Recognizable in Real Time by 2D Cellular Automata
A polyomino is said to be L-convex if any two of its cells are connected by a
4-connected inner path that changes direction at most once. The 2-dimensional
language representing such polyominoes has been recently proved to be
recognizable by tiling systems by S. Brocchi, A. Frosini, R. Pinzani and S.
Rinaldi. In an attempt to compare recognition power of tiling systems and
cellular automata, we have proved that this language can be recognized by
2-dimensional cellular automata working on the von Neumann neighborhood in real
time.
Although the construction uses a characterization of L-convex polyominoes
that is similar to the one used for tiling systems, the real time constraint
which has no equivalent in terms of tilings requires the use of techniques that
are specific to cellular automata
Berry phase, topology, and diabolicity in quantum nano-magnets
A topological theory of the diabolical points (degeneracies) of quantum
magnets is presented. Diabolical points are characterized by their diabolicity
index, for which topological sum rules are derived. The paradox of the the
missing diabolical points for Fe8 molecular magnets is clarified. A new method
is also developed to provide a simple interpretation, in terms of destructive
interferences due to the Berry phase, of the complete set of diabolical points
found in biaxial systems such as Fe8.Comment: 4 pages, 3 figure
Is Communication Complexity Physical?
Recently, Brassard et. al. conjectured that the fact that the maximal
possible correlations between two non-local parties are the quantum-mechanical
ones is linked to a reasonable restriction on communication complexity. We
provide further support for the conjecture in the multipartite case. We show
that any multipartite communication complexity problem could be reduced to
triviality, had Nature been more non-local than quantum-mechanics by a quite
small gap for any number of parties. Intriguingly, the multipartite
nonlocal-box that we use to show the result corresponds to the generalized Bell
inequality that manifests maximal violation in respect to a local
hidden-variable theory
Universal Uncertainty Principle in the Measurement Operator Formalism
Heisenberg's uncertainty principle has been understood to set a limitation on
measurements; however, the long-standing mathematical formulation established
by Heisenberg, Kennard, and Robertson does not allow such an interpretation.
Recently, a new relation was found to give a universally valid relation between
noise and disturbance in general quantum measurements, and it has become clear
that the new relation plays a role of the first principle to derive various
quantum limits on measurement and information processing in a unified
treatment. This paper examines the above development on the noise-disturbance
uncertainty principle in the model-independent approach based on the
measurement operator formalism, which is widely accepted to describe a class of
generalized measurements in the field of quantum information. We obtain
explicit formulas for the noise and disturbance of measurements given by the
measurement operators, and show that projective measurements do not satisfy the
Heisenberg-type noise-disturbance relation that is typical in the gamma-ray
microscope thought experiments. We also show that the disturbance on a Pauli
operator of a projective measurement of another Pauli operator constantly
equals the square root of 2, and examine how this measurement violates the
Heisenberg-type relation but satisfies the new noise-disturbance relation.Comment: 11 pages. Based on the author's invited talk at the 9th International
Conference on Squeezed States and Uncertainty Relations (ICSSUR'2005),
Besancon, France, May 2-6, 200
A photoelectron spectroscopy study of the electronic structure evolution in CuInSe2-related compounds at changing copper content
Evolution of the valence-band structure at gradually increasing copper content has been analysed by x-ray photoelectron spectroscopy (XPS) in In2Se3, CuIn5Se8, CuIn3Se5, and CuInSe2 single crystals. A comparison of these spectra with calculated total and angular-momentum resolved density-of-states (DOS) revealed the main trends of this evolution. The formation of the theoretically predicted gap between the bonding and non-bonding states has been observed in both experimental XPS spectra and theoretical DOS
Search for weak M1 transitions in Ca with inelastic proton scattering
The spinflip M1 resonance in the doubly magic nucleus Ca, dominated by
a single transition, serves as a reference case for the quenching of
spin-isospin modes in nuclei. The aim of the present work is a search for weak
M1 transitions in Ca with a high-resolution (p,p') experiment at 295 MeV
and forward angles including 0 degree and a comparison to results from a
similar study using backward-angle electron scattering at low momentum
transfers in order to estimate their contribution to the total B(M1) strength.
M1 cross sections of individual peaks in the spectra are deduced with a
multipole decomposition analysis. The corresponding reduced B(M1) transition
strengths are extracted following the approach outlined in J. Birkhan et al.,
Phys. Rev. C 93, 041302(R) (2016). In total, 29 peaks containing a M1
contribution are found in the excitation energy region 7 - 13 MeV. The
resulting B(M1) strength distribution compares well to the electron scattering
results considering different factors limiting the sensitivity in both
experiments and the enhanced importance of mechanisms breaking the
proportionality of nuclear cross sections and electromagnetic matrix elements
for weak transitions as studied here. The total strength of 1.19(6)
deduced assuming a non-quenched isoscalar part of the (p,p') cross sections
agrees with the (e,e') result of 1.21(13) . A binwise analysis above
10 MeV provides an upper limit of 1.62(23) . The present results
confirm that weak transitions contribute about 25% to the total B(M1) strength
in Ca and the quenching factors of GT and spin-M1 strength are
comparable in fp-shell nuclei. Thus, the role of of meson exchange currents
seems to be neglible, in contrast to sd-shell nuclei.Comment: 11 pages, 9 figures, revised analysis with oxygen contamination
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