Entanglement Induced Fluctuations of Cold Bosons

We show that due to entanglement, quantum fluctuations may differ significantly from statistical fluctuations. We calculate quantum fluctuations of the particle number and of the energy in a sub-volume of a system of bosons in a pure state, and briefly discuss the possibility of measuring them. We find that energy fluctuations have a non-extensive nature.Comment: Replaced with published version. Added calculations, explanations and clarifications, results unchange

Probing polymer chain constraint and synergistic effects in nylon 6-clay nanocomposites and nylon 6-silica flake sub-micro composites with nanomechanics

In this study, we report that a synergistic effect exists in the surface mechanical properties of nylon 6–clay nanocomposites (NC) that can be shown by nanomechanical testing. The hardness, elastic modulus, and nanoindentation creep behavior of nylon 6 and its nanocomposites with different filler loading produced by melt compounding were contrasted to those of model nylon 6 sub-microcomposites (SMC) reinforced by sub-micro-thick silica flakes in which constraint cannot occur due to the difference in filler geometry. Polymer chain constraint was assessed by the analysis of nanoindentation creep data. Time-dependent creep decreased with increasing the filler loading in the NC consistent with the clay platelets exerting a constraint effect on the polymer chains which increases with filler loading. In contrast, there was no evidence of any reduced time-dependent creep for the SMC samples, consistent with a lack of constraint expected due to much lower aspect ratio of the silica flake

Scanning SQUID Susceptometry of a paramagnetic superconductor

Scanning SQUID susceptometry images the local magnetization and susceptibility of a sample. By accurately modeling the SQUID signal we can determine the physical properties such as the penetration depth and permeability of superconducting samples. We calculate the scanning SQUID susceptometry signal for a superconducting slab of arbitrary thickness with isotropic London penetration depth, on a non-superconducting substrate, where both slab and substrate can have a paramagnetic response that is linear in the applied field. We derive analytical approximations to our general expression in a number of limits. Using our results, we fit experimental susceptibility data as a function of the sample-sensor spacing for three samples: 1) delta-doped SrTiO3, which has a predominantly diamagnetic response, 2) a thin film of LaNiO3, which has a predominantly paramagnetic response, and 3) a two-dimensional electron layer (2-DEL) at a SrTiO3/AlAlO3 interface, which exhibits both types of response. These formulas will allow the determination of the concentrations of paramagnetic spins and superconducting carriers from fits to scanning SQUID susceptibility measurements.Comment: 11 pages, 13 figure

The statistical strength of experiments to reject local realism with photon pairs and inefficient detectors

Because of the fundamental importance of Bell's theorem, a loophole-free demonstration of a violation of local realism (LR) is highly desirable. Here, we study violations of LR involving photon pairs. We quantify the experimental evidence against LR by using measures of statistical strength related to the Kullback-Leibler (KL) divergence, as suggested by van Dam et al. [W. van Dam, R. Gill and P. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)]. Specifically, we analyze a test of LR with entangled states created from two independent polarized photons passing through a polarizing beam splitter. We numerically study the detection efficiency required to achieve a specified statistical strength for the rejection of LR depending on whether photon counters or detectors are used. Based on our results, we find that a test of LR free of the detection loophole requires photon counters with efficiencies of at least 89.71%, or photon detectors with efficiencies of at least 91.11%. For comparison, we also perform this analysis with ideal unbalanced Bell states, which are known to allow rejection of LR with detector efficiencies above 2/3.Comment: 18 pages, 3 figures, minor changes (add more references, replace the old plots, etc.)

State-dependent rotations of spins by weak measurements

IIt is shown that a weak measurement of a quantum system produces a new state of the quantum system which depends on the prior state, as well as the (uncontrollable) measured position of the pointer variable of the weak measurement apparatus. The result imposes a constraint on hidden-variable theories which assign a different state to a quantum system than standard quantum mechanics. The constraint means that a crypto-nonlocal hidden-variable theory can be ruled out in a more direct way than previously.Comment: 10 pages, 2 figures. Substantially revised to concentrate on weak measurement transformation of states and application to crypto-nonlocal hidden-variable theor

Irreducible MultiQutrit Correlations in Greenberger-Horne-Zeilinger Type States

Following the idea of the continuity approach in [D. L. Zhou, Phys. Rev. Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multi-party correlations in two families of $n$-qutrit Greenberger-Horne-Zeilinger type states. For the pure states in one of the families, the irreducible 2-party, $n$-party and $(n-m)$-party ($0< m < n-2$) correlations are nonzero, which is different from the $n$-qubit case. We also derive the correlation distributions in the $n$-qutrit maximal slice state, which can be uniquely determined by its $(n-1)$-qutrit reduced density matrices among pure states. It is proved that there is no irreducible $n$-qutrit correlation in the maximal slice state. This enlightens us to give a discussion about how to characterize the pure states with irreducible $n$-party correlation in arbitrarily high-dimensional systems by the way of the continuity approach.Comment: 5p, no fi

Unified criteria for multipartite quantum nonlocality

Wiseman and co-workers (Phys. Rev. Lett. 98, 140402, 2007) proposed a distinction between the nonlocality classes of Bell's nonlocality, steering and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.Comment: V2: corrected image display; V3: substantial changes including new proofs, arguments, and result

The Identity Correspondence Problem and its Applications

In this paper we study several closely related fundamental problems for words and matrices. First, we introduce the Identity Correspondence Problem (ICP): whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. We prove that ICP is undecidable by a reduction of Post's Correspondence Problem via several new encoding techniques. In the second part of the paper we use ICP to answer a long standing open problem concerning matrix semigroups: "Is it decidable for a finitely generated semigroup S of square integral matrices whether or not the identity matrix belongs to S?". We show that the problem is undecidable starting from dimension four even when the number of matrices in the generator is 48. From this fact, we can immediately derive that the fundamental problem of whether a finite set of matrices generates a group is also undecidable. We also answer several question for matrices over different number fields. Apart from the application to matrix problems, we believe that the Identity Correspondence Problem will also be useful in identifying new areas of undecidable problems in abstract algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the published journal version of this article, see footnote 3 on page 1

Light to Mass Variations with Environment

Large and well defined variations exist between the distribution of mass and the light of stars on extragalactic scales. Mass concentrations in the range 10^12 - 10^13 M_sun manifest the most light per unit mass. Group halos in this range are typically the hosts of spiral and irregular galaxies with ongoing star formation. On average M/L_B ~ 90 M_sun/L_sun in these groups . More massive halos have less light per unit mass. Within a given mass range, halos that are dynamically old as measured by crossing times and galaxy morphologies have distinctly less light per unit mass. At the other end of the mass spectrum, below 10^12 M_sun, there is a cutoff in the manifestation of light. Group halos in the range 10^11 - 10^12 M_sun can host dwarf galaxies but with such low luminosities that M/L_B values can range from several hundred to several thousand. It is suspected that there must be completely dark halos at lower masses. Given the form of the halo mass function, it is the low relative luminosities of the high mass halos that has the greatest cosmological implications. Of order half the clustered mass may reside in halos with greater than 10^14 M_sun. By contrast, only 5-10% of clustered mass would lie in entities with less than 10^12 M_sun.Comment: 15 pages, 9 figures, 2 tables, Accepted Astrophysical Journal 619, 000, 2005 (Jan 1