PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring

We study the properties of an N-site tight-binding ring with parity and time-reversal (PT) symmetric, Hermitian, site-dependent tunneling and a pair of non-Hermitian, PT-symmetric, loss and gain impurities $\pm i\gamma$. The properties of such lattices with open boundary conditions have been intensely explored over the past two years. We numerically investigate the PT-symmetric phase in a ring with a position-dependent tunneling function $t_\alpha(k)=[k(N-k)]^{\alpha/2}$ that, in an open lattice, leads to a strengthened PT-symmetric phase, and study the evolution of the PT-symmetric phase from the open chain to a ring. We show that, generally, periodic boundary conditions weaken the PT-symmetric phase, although for experimentally relevant lattice sizes $N \sim 50$, it remains easily accessible. We show that the chirality, quantified by the (magnitude of the) average transverse momentum of a wave packet, shows a maximum at the PT-symmetric threshold. Our results show that although the wavepacket intensity increases monotonically across the PT-breaking threshold, the average momentum decays monotonically on both sides of the threshold.Comment: 11 pages, 5 figures, preprin

PT-Symmetric Electronics

We show both theoretically and experimentally that a pair of inductively coupled active LRC circuits (dimer), one with amplification and another with an equivalent amount of attenuation, display all the features which characterize a wide class of non-Hermitian systems which commute with the joint parity-time PT operator: typical normal modes, temporal evolution, and scattering processes. Utilizing a Liouvilian formulation, we can define an underlying PT-symmetric Hamiltonian, which provides important insight for understanding the behavior of the system. When the PT-dimer is coupled to transmission lines, the resulting scattering signal reveals novel features which reflect the PT-symmetry of the scattering target. Specifically we show that the device can show two different behaviors simultaneously, an amplifier or an absorber, depending on the direction and phase relation of the interrogating waves. Having an exact theory, and due to its relative experimental simplicity, PT-symmetric electronics offers new insights into the properties of PT-symmetric systems which are at the forefront of the research in mathematical physics and related fields.Comment: 17 pages, 7 figure

An exactly solvable quantum-lattice model with a tunable degree of nonlocality

An array of N subsequent Laguerre polynomials is interpreted as an eigenvector of a non-Hermitian tridiagonal Hamiltonian $H$ with real spectrum or, better said, of an exactly solvable N-site-lattice cryptohermitian Hamiltonian whose spectrum is known as equal to the set of zeros of the N-th Laguerre polynomial. The two key problems (viz., the one of the ambiguity and the one of the closed-form construction of all of the eligible inner products which make $H$ Hermitian in the respective {\em ad hoc} Hilbert spaces) are discussed. Then, for illustration, the first four simplest, $k-$parametric definitions of inner products with $k=0,k=1,k=2$ and $k=3$ are explicitly displayed. In mathematical terms these alternative inner products may be perceived as alternative Hermitian conjugations of the initial N-plet of Laguerre polynomials. In physical terms the parameter $k$ may be interpreted as a measure of the "smearing of the lattice coordinates" in the model.Comment: 35 p

Structure formation in active networks

Structure formation and constant reorganization of the actin cytoskeleton are key requirements for the function of living cells. Here we show that a minimal reconstituted system consisting of actin filaments, crosslinking molecules and molecular-motor filaments exhibits a generic mechanism of structure formation, characterized by a broad distribution of cluster sizes. We demonstrate that the growth of the structures depends on the intricate balance between crosslinker-induced stabilization and simultaneous destabilization by molecular motors, a mechanism analogous to nucleation and growth in passive systems. We also show that the intricate interplay between force generation, coarsening and connectivity is responsible for the highly dynamic process of structure formation in this heterogeneous active gel, and that these competing mechanisms result in anomalous transport, reminiscent of intracellular dynamics

Molecular motors robustly drive active gels to a critically connected state

Living systems often exhibit internal driving: active, molecular processes drive nonequilibrium phenomena such as metabolism or migration. Active gels constitute a fascinating class of internally driven matter, where molecular motors exert localized stresses inside polymer networks. There is evidence that network crosslinking is required to allow motors to induce macroscopic contraction. Yet a quantitative understanding of how network connectivity enables contraction is lacking. Here we show experimentally that myosin motors contract crosslinked actin polymer networks to clusters with a scale-free size distribution. This critical behavior occurs over an unexpectedly broad range of crosslink concentrations. To understand this robustness, we develop a quantitative model of contractile networks that takes into account network restructuring: motors reduce connectivity by forcing crosslinks to unbind. Paradoxically, to coordinate global contractions, motor activity should be low. Otherwise, motors drive initially well-connected networks to a critical state where ruptures form across the entire network.Comment: Main text: 21 pages, 5 figures. Supplementary Information: 13 pages, 8 figure

Defect solitons supported by nonlocal PT symmetric superlattices

The existence and stability of defect solitons supported by parity-time (PT) symmetric superlattices with nonlocal nonlinearity are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive or zero defects, but can not exist in the presence of negative defects with strong nonlocality. In the first gap, out-of-phase solitons are stable for positive or zero defects, whereas in-phase solitons are stable for negative defects. The dependence of soliton stabilities on modulation depth of the PT potentials is studied. It is interesting that solitons can exist stably for positive and zero defects when the PT potentials are above the phase transition points.Comment: 12 figures, 6 pages, Accepted by EP

Light interception principally drives the understory response to boxelder invasion in riparian forests

Since several decades, American boxelder (Acer negundo) is replacing white willow (Salix alba) riparian forests along southern European rivers. This study aims to evaluate the consequences of boxelder invasion on understory community in riparian areas. We determined the understory species richness, composition and biomass in boxelder and white willow stands located in three riparian forests, representative of three rivers with distinct hydrological regimes. We investigated correlation of these variables to soil moisture and particle size, main soil nutrient stocks, potential nitrification and denitrification, tree canopy cover and photosynthetic active radiation (PAR) at the ground level. A greenhouse experiment was then conducted to identify the causal factors responsible for changes in the understory. The effect of soil type, PAR level and water level on the growth and the biomass production of Urtica dioica were examined. A lower plant species richness and biomass, and a modification of community composition were observed for boxelder understory in all sites, regardless of their environmental characteristics. The strongest modification that follows boxelder invasion was the decline in U. dioica, the dominant species of the white willow forest understory. These differences were mainly correlated with a lower incident PAR under boxelder canopy. The greenhouse experiment identified PAR level as the main factor responsible for the changes in U. dioica stem number and biomass. Our results indicate that adult boxelder acts as an ecosystem engineer that decreases light availability. The opportunistic invasion by boxelder leads to important understory changes, which could alter riparian ecosystem functioning

The clinical course of low back pain: a meta-analysis comparing outcomes in randomised clinical trials (RCTs) and observational studies.

BACKGROUND: Evidence suggests that the course of low back pain (LBP) symptoms in randomised clinical trials (RCTs) follows a pattern of large improvement regardless of the type of treatment. A similar pattern was independently observed in observational studies. However, there is an assumption that the clinical course of symptoms is particularly influenced in RCTs by mere participation in the trials. To test this assumption, the aim of our study was to compare the course of LBP in RCTs and observational studies. METHODS: Source of studies CENTRAL database for RCTs and MEDLINE, CINAHL, EMBASE and hand search of systematic reviews for cohort studies. Studies include individuals aged 18 or over, and concern non-specific LBP. Trials had to concern primary care treatments. Data were extracted on pain intensity. Meta-regression analysis was used to compare the pooled within-group change in pain in RCTs with that in cohort studies calculated as the standardised mean change (SMC). RESULTS: 70 RCTs and 19 cohort studies were included, out of 1134 and 653 identified respectively. LBP symptoms followed a similar course in RCTs and cohort studies: a rapid improvement in the first 6 weeks followed by a smaller further improvement until 52 weeks. There was no statistically significant difference in pooled SMC between RCTs and cohort studies at any time point:- 6 weeks: RCTs: SMC 1.0 (95% CI 0.9 to 1.0) and cohorts 1.2 (0.7to 1.7); 13 weeks: RCTs 1.2 (1.1 to 1.3) and cohorts 1.0 (0.8 to 1.3); 27 weeks: RCTs 1.1 (1.0 to 1.2) and cohorts 1.2 (0.8 to 1.7); 52 weeks: RCTs 0.9 (0.8 to 1.0) and cohorts 1.1 (0.8 to 1.6). CONCLUSIONS: The clinical course of LBP symptoms followed a pattern that was similar in RCTs and cohort observational studies. In addition to a shared 'natural history', enrolment of LBP patients in clinical studies is likely to provoke responses that reflect the nonspecific effects of seeking and receiving care, independent of the study design

Ferromagnetism in Co7(TeO3)4Br6: A byproduct of complex antiferromagnetic order and single-ion anisotropy

Pronounced anisotropy of magnetic properties and complex magnetic order of a new oxi-halide compound Co7(TeO3)4Br6 has been investigated by powder and single crystal neutron diffraction, magnetization and ac susceptibility techniques. Anisotropy of susceptibility extends far into the paramagnetic temperature range. A principal source of anisotropy are anisotropic properties of the involved octahedrally coordinated single Co(2+) ions, as confirmed by angular-overlap-model calculations presented in this work. Incommensurate antiferromagnetic order sets in at TN=34 K. Propagation vector is strongly temperature dependent reaching k1=(0.9458(6), 0, 0.6026(5)) at 30 K. A transition to a ferrimagnetic structure with k2=0 takes place at TC=27 K. Magnetically ordered phase is characterized by very unusual anisotropy as well: while M-H scans along b-axis reveals spectacularly rectangular but otherwise standard ferromagnetic hysteresis loops, M-H studies along other two principal axes are perfectly reversible, revealing very sharp spin flop (or spin flip) transitions, like in a standard antiferromagnet (or metamagnet). Altogether, the observed magnetic phenomenology is interpreted as an evidence of competing magnetic interactions permeating the system, first of all of the single ion anisotropy energy and the exchange interactions. Different coordinations of the Co(2+)-ions involved in the low-symmetry C2/c structure of Co7(TeO3)4Br6 render the exchange-interaction network very complex by itself. Temperature dependent changes in the magnetic structure, together with an abrupt emergence of a ferromagnetic component, are ascribed to continual spin reorientations described by a multi-component, but yet unknown, spin Hamiltonian.Comment: 12 pages, 13 figures; submitted to PR