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 $m\times n$-mode bipartitions of continuous variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as $(m+n)$-mode Gaussian states invariant under local mode permutations on the $m$-mode and $n$-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of $m+n-2$ uncorrelated single-mode states. The entanglement between the $m$-mode and the $n$-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 $(m + n)$-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

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 $H$. We examine the particular case when the Hessian $H^{\prime\prime}(X_{t})$ evaluated at the corresponding solution $X_{t}$ 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}

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

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

Extreme Covariant Quantum Observables in the Case of an Abelian Symmetry Group and a Transitive Value Space

We represent quantum observables as POVMs (normalized positive operator valued measures) and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group $G$. The value space of such observables is a transitive $G$-space. We characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables. The results are applied to position, position difference and time observables.Comment: 23 page