More is the Same; Phase Transitions and Mean Field Theories

This paper looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter", "mean field theory", and "variational method". In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor, "steam", come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in a some statistical variable of the system. The discontinuous property is called the order parameter. Each phase transitions has its own order parameter that range over a tremendous variety of physical properties. These properties include the density of a liquid gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when that jump approaches zero. This note is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of this phenomenon.Comment: 25 pages, 6 figure

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

What can local authorities do to improve the social care-related quality of life of older adults living at home? Evidence from the Adult Social Care Survey

Local authorities spend considerable resources on social care at home for older adults. Given the expected growth in the population of older adults and budget cuts on local government, it is important to find efficient ways of maintaining and improving the quality of life of older adults. The ageing in place literature suggests that policies in other functions of local authorities may have a significant role to play. This study aims to examine the associations between social care-related quality of life (SCRQoL) in older adults and three potential policy targets for local authorities: (i) accessibility of information and advice, (ii) design of the home and (iii) accessibility of the local area. We used cross-sectional data from the English national Adult Social Care Survey (ASCS) 2010/2011 on service users aged 65 years and older and living at home (N=29,935). To examine the association between SCRQoL, as measured by the ASCOT, and three single-item questions about accessibility of information, design of the home and accessibility of the local area, we estimate linear and quantile regression models. After adjusting for physical and mental health factors and other confounders our findings indicate that SCRQoL is significantly lower for older adults who find it more difficult to find information and advice, for those who report that their home design is inappropriate for their needs and for those who find it more difficult to get around their local area. In addition, these three variables are as strongly associated with SCRQoL as physical and mental health factors. We conclude that in seeking to find ways to maintain and improve the quality of life of social care users living at home, local authorities could look more broadly across their responsibilities. Further research is required to explore the cost-effectiveness of these options compared to standard social care services

Models of cognition and affect in perceptions of well-being

How do people arrive at assessments of their own life quality? A series of models was developed to provide an interpretation of the way the factors of cognition and affect operate along with evaluations of specific life concerns (domains) in the perception of well-being. Following previous research, cognition was defined operationally as a factor which accounts for the covariance among a set of assessments of life-as-a-whole after affect, as measured by Bradburn's scales, is partialled out and after allowance is made for the presence of correlated measurement errors. It was found that loadings on the cognitive factor, and hence the interpretation of this factor, changed little despite quite large changes in the models. Moreover, in all major comparisons, models that contained the cognitive factor fitted the data better than models that did not. Models that included affect as the only variable intervening between the domains and the life-as-a-whole factor led to results that were intuitively difficult to accept. In the preferred model both affect and cognition were positioned as intervening variables. In this model it was found that the domain evaluations had no direct impact on life-as-a-whole assessments — the contribution of the domains was indirect by way of their association with cognition and affect. It was hypothesised that associated with each domain was a domain-specific element of affect and a domain-specific element of cognition. The linear additive relation found by previous researchers between domain evaluations and life-as-a-whole assessments would then be explainable as a statistical result arising from the summing of the domain-specific elements of affect and cognition.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43703/1/11205_2004_Article_BF00292640.pd

Bose-Einstein condensates in a one-dimensional double square well: Analytical solutions of the Nonlinear Schr\"odinger equation and tunneling splittings

We present a representative set of analytic stationary state solutions of the Nonlinear Schr\"odinger equation for a symmetric double square well potential for both attractive and repulsive nonlinearity. In addition to the usual symmetry preserving even and odd states, nonlinearity introduces quite exotic symmetry breaking solutions - among them are trains of solitons with different number and sizes of density lumps in the two wells. We use the symmetry breaking localized solutions to form macroscopic quantum superpositions states and explore a simple model for the exponentially small tunneling splitting.Comment: 11 pages, 11 figures, revised version, typos and references correcte

Model-independent search for CP violation in D0→K−K+π−π+ and D0→π−π+π+π− decays

A search for CP violation in the phase-space structures of D0 and View the MathML source decays to the final states K−K+π−π+ and π−π+π+π− is presented. The search is carried out with a data set corresponding to an integrated luminosity of 1.0 fb−1 collected in 2011 by the LHCb experiment in pp collisions at a centre-of-mass energy of 7 TeV. For the K−K+π−π+ final state, the four-body phase space is divided into 32 bins, each bin with approximately 1800 decays. The p-value under the hypothesis of no CP violation is 9.1%, and in no bin is a CP asymmetry greater than 6.5% observed. The phase space of the π−π+π+π− final state is partitioned into 128 bins, each bin with approximately 2500 decays. The p-value under the hypothesis of no CP violation is 41%, and in no bin is a CP asymmetry greater than 5.5% observed. All results are consistent with the hypothesis of no CP violation at the current sensitivity

Search for the lepton-flavor-violating decays Bs0→e±μ∓ and B0→e±μ∓

A search for the lepton-flavor-violating decays Bs0→e±μ∓ and B0→e±μ∓ is performed with a data sample, corresponding to an integrated luminosity of 1.0  fb-1 of pp collisions at √s=7  TeV, collected by the LHCb experiment. The observed number of Bs0→e±μ∓ and B0→e±μ∓ candidates is consistent with background expectations. Upper limits on the branching fractions of both decays are determined to be B(Bs0→e±μ∓)101  TeV/c2 and MLQ(B0→e±μ∓)>126  TeV/c2 at 95% C.L., and are a factor of 2 higher than the previous bounds

Branching fraction and CP asymmetry of the decays B+→K0Sπ+ and B+→K0SK+

An analysis of B+ → K0 Sπ+ and B+ → K0 S K+ decays is performed with the LHCb experiment. The pp collision data used correspond to integrated luminosities of 1 fb−1 and 2 fb−1 collected at centre-ofmass energies of √ s = 7 TeV and √ s = 8 TeV, respectively. The ratio of branching fractions and the direct CP asymmetries are measured to be B(B+ → K0 S K+ )/B(B+ → K0 Sπ+ ) = 0.064 ± 0.009 (stat.) ± 0.004 (syst.), ACP(B+ → K0 Sπ+ ) = −0.022 ± 0.025 (stat.) ± 0.010 (syst.) and ACP(B+ → K0 S K+ ) = −0.21 ± 0.14 (stat.) ± 0.01 (syst.). The data sample taken at √ s = 7 TeV is used to search for B+ c → K0 S K+ decays and results in the upper limit ( fc · B(B+ c → K0 S K+ ))/( fu · B(B+ → K0 Sπ+ )) < 5.8 × 10−2 at 90% confidence level, where fc and fu denote the hadronisation fractions of a ¯b quark into a B+ c or a B+ meson, respectively

Evolution of the Neckeraceae (Bryophyta): resolving the backbone phylogeny

Earlier phylogenetic studies, including species belonging to the Neckeraceae, have indicated that this pleurocarpous moss family shares a strongly supported sister group relationship with the Lembophyllaceae, but the family delimitation of the former needs adjustment. To test the monophyly of the Neckeraceae, as well as to redefine the family circumscription and to pinpoint its phylogenetic position in a larger context, a phylogenetic study based on molecular data was carried out. Sequence data were compiled, combining data from all three genomes: nuclear ITS1 and 2, plastid trnS-rps4-trnT-trnL-trnF and rpl16, and mitochondrial nad5 intron. The Neckeraceae have sometimes been divided into the two families, Neckeraceae and Thamnobryaceae, a division rejected here. Both parsimony and Bayesian analyses of molecular data revealed that the family concept of the Neckeraceae needs several further adjustments, such as the exclusion of some individual species and smaller genera as well as the inclusion of the Leptodontaceae. Within the family three well-supported clades (A, B and C) can be distinguished. Members of clade A are mainly non-Asiatic and nontropical. Most species have a weak costa and immersed capsules with reduced peristomes (mainly Neckera spp.) and the teeth at the leaf margins are usually unicellular. Clade B members are also mainly non-Asiatic. They are typically fairly robust, distinctly stipilate, having a single, at least relatively strong costa, long setae (capsules exserted), and the peristomes are well developed or only somewhat reduced. Members of clade C are essentially Asiatic and tropical. The species of this clade usually have a strong costa and a long seta, the seta often being mammillose in its upper part. The peristome types in this clade are mixed, since both reduced and unreduced types are found. Several neckeraceous genera that were recognised on a morphological basis are polyphyletic (e.g. Neckera, Homalia, Thamnobryum, Porotrichum). Ancestral state reconstructions revealed that currently used diagnostic traits, such as the leaf asymmetry and costa strength are highly homoplastic. Similarly, the reconstructions revealed that the 'reduced' sporophyte features have evolved independently in each of the three clades.Earlier phylogenetic studies, including species belonging to the Neckeraceae, have indicated that this pleurocarpous moss family shares a strongly supported sister group relationship with the Lembophyllaceae, but the family delimitation of the former needs adjustment. To test the monophyly of the Neckeraceae, as well as to redefine the family circumscription and to pinpoint its phylogenetic position in a larger context, a phylogenetic study based on molecular data was carried out. Sequence data were compiled, combining data from all three genomes: nuclear ITS1 and 2, plastid trnS-rps4-trnT-trnL-trnF and rpl16, and mitochondrial nad5 intron. The Neckeraceae have sometimes been divided into the two families, Neckeraceae and Thamnobryaceae, a division rejected here. Both parsimony and Bayesian analyses of molecular data revealed that the family concept of the Neckeraceae needs several further adjustments, such as the exclusion of some individual species and smaller genera as well as the inclusion of the Leptodontaceae. Within the family three well-supported clades (A, B and C) can be distinguished. Members of clade A are mainly non-Asiatic and nontropical. Most species have a weak costa and immersed capsules with reduced peristomes (mainly Neckera spp.) and the teeth at the leaf margins are usually unicellular. Clade B members are also mainly non-Asiatic. They are typically fairly robust, distinctly stipilate, having a single, at least relatively strong costa, long setae (capsules exserted), and the peristomes are well developed or only somewhat reduced. Members of clade C are essentially Asiatic and tropical. The species of this clade usually have a strong costa and a long seta, the seta often being mammillose in its upper part. The peristome types in this clade are mixed, since both reduced and unreduced types are found. Several neckeraceous genera that were recognised on a morphological basis are polyphyletic (e.g. Neckera, Homalia, Thamnobryum, Porotrichum). Ancestral state reconstructions revealed that currently used diagnostic traits, such as the leaf asymmetry and costa strength are highly homoplastic. Similarly, the reconstructions revealed that the 'reduced' sporophyte features have evolved independently in each of the three clades.Earlier phylogenetic studies, including species belonging to the Neckeraceae, have indicated that this pleurocarpous moss family shares a strongly supported sister group relationship with the Lembophyllaceae, but the family delimitation of the former needs adjustment. To test the monophyly of the Neckeraceae, as well as to redefine the family circumscription and to pinpoint its phylogenetic position in a larger context, a phylogenetic study based on molecular data was carried out. Sequence data were compiled, combining data from all three genomes: nuclear ITS1 and 2, plastid trnS-rps4-trnT-trnL-trnF and rpl16, and mitochondrial nad5 intron. The Neckeraceae have sometimes been divided into the two families, Neckeraceae and Thamnobryaceae, a division rejected here. Both parsimony and Bayesian analyses of molecular data revealed that the family concept of the Neckeraceae needs several further adjustments, such as the exclusion of some individual species and smaller genera as well as the inclusion of the Leptodontaceae. Within the family three well-supported clades (A, B and C) can be distinguished. Members of clade A are mainly non-Asiatic and nontropical. Most species have a weak costa and immersed capsules with reduced peristomes (mainly Neckera spp.) and the teeth at the leaf margins are usually unicellular. Clade B members are also mainly non-Asiatic. They are typically fairly robust, distinctly stipilate, having a single, at least relatively strong costa, long setae (capsules exserted), and the peristomes are well developed or only somewhat reduced. Members of clade C are essentially Asiatic and tropical. The species of this clade usually have a strong costa and a long seta, the seta often being mammillose in its upper part. The peristome types in this clade are mixed, since both reduced and unreduced types are found. Several neckeraceous genera that were recognised on a morphological basis are polyphyletic (e.g. Neckera, Homalia, Thamnobryum, Porotrichum). Ancestral state reconstructions revealed that currently used diagnostic traits, such as the leaf asymmetry and costa strength are highly homoplastic. Similarly, the reconstructions revealed that the 'reduced' sporophyte features have evolved independently in each of the three clades.Peer reviewe