904 research outputs found
Chiral surfaces self-assembling in one-component systems with isotropic interactions
We show that chiral symmetry can be broken spontaneously in one-component
systems with isotropic interactions, i.e. many-particle systems having maximal
a priori symmetry. This is achieved by designing isotropic potentials that lead
to self-assembly of chiral surfaces. We demonstrate the principle on a simple
chiral lattice and on a more complex lattice with chiral super-cells. In
addition we show that the complex lattice has interesting melting behavior with
multiple morphologically distinct phases that we argue can be qualitatively
predicted from the design of the interaction.Comment: 4 pages, 4 figure
Unitarily localizable entanglement of Gaussian states
We consider generic -mode bipartitions of continuous variable
systems, and study the associated bisymmetric multimode Gaussian states. They
are defined as -mode Gaussian states invariant under local mode
permutations on the -mode and -mode subsystems. We prove that such states
are equivalent, under local unitary transformations, to the tensor product of a
two-mode state and of uncorrelated single-mode states. The entanglement
between the -mode and the -mode blocks can then be completely
concentrated on a single pair of modes by means of local unitary operations
alone. This result allows to prove that the PPT (positivity of the partial
transpose) condition is necessary and sufficient for the separability of -mode bisymmetric Gaussian states. We determine exactly their negativity and
identify a subset of bisymmetric states whose multimode entanglement of
formation can be computed analytically. We consider explicit examples of pure
and mixed bisymmetric states and study their entanglement scaling with the
number of modes.Comment: 10 pages, 2 figure
Whey protein does not enhance the adaptations to elbow flexor resistance training
Purpose: It is unclear whether protein supplementation augments the gains in muscle strength and size observed following resistance training (RT), as limitations to previous studies include small cohorts, imprecise measures of muscle size and strength, and no control of prior exercise or habitual protein intake (HPI). We aimed to determine whether whey protein supplementation affected RT-induced changes in elbow flexor muscle strength and size. Methods: We pair-matched 33 previously untrained, healthy young men for their HPI and strength response to 3-wk RT without nutritional supplementation (followed by 6-wk no training), and then randomly assigned them to protein (PRO; n = 17) or placebo (PLA; n = 16) groups. Participants subsequently performed elbow flexor RT 3 d/wk for 12-wk and consumed PRO or PLA immediately before and after each training session. We assessed elbow flexor muscle strength [unilateral 1-RM and isometric maximum voluntary force (MVF)] and size [total volume and maximum anatomical cross-sectional area (ACSAmax) determined with MRI] before and after the 12-wk RT. Results: PRO and PLA demonstrated similar increases in muscle volume (PRO, 17.0 ± 7.1% vs. PLA, 14.9 ± 4.6%; P = 0.32), ACSAmax (PRO, 16.2 ± 7.1% vs. PLA, 15.6 ± 4.4%; P = 0.80), 1-RM (PRO, 41.8 ± 21.2% vs. PLA, 41.4 ± 19.9%; P = 0.97) and MVF (PRO, 12.0 ± 9.9% vs. PLA, 14.5 ± 8.3%; P = 0.43). Conclusion: In the context of this study, protein supplementation did not augment elbow flexor muscle strength and size changes that occurred after 12-wk RT. Key words: Protein supplementation – strength training – muscle hypertrophy – muscle architecture – training respons
Tsirelson's problem and Kirchberg's conjecture
Tsirelson's problem asks whether the set of nonlocal quantum correlations
with a tensor product structure for the Hilbert space coincides with the one
where only commutativity between observables located at different sites is
assumed. Here it is shown that Kirchberg's QWEP conjecture on tensor products
of C*-algebras would imply a positive answer to this question for all bipartite
scenarios. This remains true also if one considers not only spatial
correlations, but also spatiotemporal correlations, where each party is allowed
to apply their measurements in temporal succession; we provide an example of a
state together with observables such that ordinary spatial correlations are
local, while the spatiotemporal correlations reveal nonlocality. Moreover, we
find an extended version of Tsirelson's problem which, for each nontrivial Bell
scenario, is equivalent to the QWEP conjecture. This extended version can be
conveniently formulated in terms of steering the system of a third party.
Finally, a comprehensive mathematical appendix offers background material on
complete positivity, tensor products of C*-algebras, group C*-algebras, and
some simple reformulations of the QWEP conjecture.Comment: 57 pages, to appear in Rev. Math. Phy
Localization of quantum wave packets
We study the semiclassical propagation of squeezed Gau{\ss}ian states. We do
so by considering the propagation theorem introduced by Combescure and Robert
\cite{CR97} approximating the evolution generated by the Weyl-quantization of
symbols . We examine the particular case when the Hessian
evaluated at the corresponding solution of
Hamilton's equations of motion is periodic in time. Under this assumption, we
show that the width of the wave packet can remain small up to the Ehrenfest
time. We also determine conditions for ``classical revivals'' in that case.
More generally, we may define recurrences of the initial width. Some of these
results include the case of unbounded classical motion. In the classically
unstable case we recover an exponential spreading of the wave packet as in
\cite{CR97}
Sequential measurements of conjugate observables
We present a unified treatment of sequential measurements of two conjugate
observables. Our approach is to derive a mathematical structure theorem for all
the relevant covariant instruments. As a consequence of this result, we show
that every Weyl-Heisenberg covariant observable can be implemented as a
sequential measurement of two conjugate observables. This method is applicable
both in finite and infinite dimensional Hilbert spaces, therefore covering
sequential spin component measurements as well as position-momentum sequential
measurements.Comment: 25 page
Modified Partition Functions, Consistent Anomalies and Consistent Schwinger Terms
A gauge invariant partition function is defined for gauge theories which
leads to the standard quantization. It is shown that the descent equations and
consequently the consistent anomalies and Schwinger terms can be extracted from
this modified partition function naturally.Comment: 25 page
On a certain class of semigroups of operators
We define an interesting class of semigroups of operators in Banach spaces,
namely, the randomly generated semigroups. This class contains as a remarkable
subclass a special type of quantum dynamical semigroups introduced by
Kossakowski in the early 1970s. Each randomly generated semigroup is
associated, in a natural way, with a pair formed by a representation or an
antirepresentation of a locally compact group in a Banach space and by a
convolution semigroup of probability measures on this group. Examples of
randomly generated semigroups having important applications in physics are
briefly illustrated.Comment: 11 page
Designing isotropic interactions for self-assembly of complex lattices
We present a direct method for solving the inverse problem of designing
isotropic potentials that cause self-assembly into target lattices. Each
potential is constructed by matching its energy spectrum to the reciprocal
representation of the lattice to guarantee that the desired structure is a
ground state. We use the method to self-assemble complex lattices not
previously achieved with isotropic potentials, such as a snub square tiling and
the kagome lattice. The latter is especially interesting because it provides
the crucial geometric frustration in several proposed spin liquids.Comment: 4 pages, 3 figure
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