Spin wave contribution to the nuclear spin-lattice relaxation in triplet superconductors

We discuss collective spin wave excitations in triplet superconductors with an easy axis anisotropy for the order parameter. Using a microscopic model for interacting electrons we estimate the frequency of such excitations in Bechgaard salts and ruthenate superconductors to be one and twenty GHz respectively. We introduce an effective bosonic model to describe spin-wave excitations and calculate their contribution to the nuclear spin lattice relaxation rate. We find that in the experimentally relevant regime of temperatures, this mechanism leads to the power law scaling of 1/T_1 with temperature. For two and three dimensional systems the scaling exponents are three and five respectively. We discuss experimental manifestations of the spin wave mechanism of the nuclear spin lattice relaxation.Comment: 4 pages, 2 figure

Exact Methods in Analysis of Nonequilibrium Dynamics of Integrable Models: Application to the Study of Correlation Functions in Nonequilibrium 1D Bose Gas

In this paper we study nonequilibrium dynamics of one dimensional Bose gas from the general perspective of dynamics of integrable systems. After outlining and critically reviewing methods based on inverse scattering transform, intertwining operators, q-deformed objects, and extended dynamical conformal symmetry, we focus on the form-factor based approach. Motivated by possible applications in nonlinear quantum optics and experiments with ultracold atoms, we concentrate on the regime of strong repulsive interactions. We consider dynamical evolution starting from two initial states: a condensate of particles in a state with zero momentum and a condensate of particles in a gaussian wavepacket in real space. Combining the form-factor approach with the method of intertwining operator we develop a numerical procedure which allows explicit summation over intermediate states and analysis of the time evolution of non-local density-density correlation functions. In both cases we observe a tendency toward formation of crystal-like correlations at intermediate time scales.Physic

EFFECTS OF ANTHROPOGENIC IMPACT ON SEXUAL DIFFERENTIATION OF CERTAIN SPECIES OF THE GENUS SALIX

Plant organisms actively respond to changes in the natural components of their environment. A sensitive indicator of the adaptation of the plant organism to the environment is the state of the reproductive system. The article discusses the results of a study of the sex composition of populations and the quality of pollen grains of two species of the genus Salix. The peculiarities of the sexual sphere Salix fragilis and Salix dasyclados revealed during the work show the feminizing effect on the sexual structure of the populations of these types of anthropogenic factors. During the increase of stress conditions the level of vitality and fertilizing ability of pollen grains decreases. The results of the study confirm the possibility of using these plants as bioindicators of the environment

THE SEX SYSTEM OF THE POPULATION OF SAGITTARIA SAITTIFOLIA AS AN INDICATOR OF THE ECOLOGICAL STATUS OF A RIVER

The ecological state of small rivers that define the water regime of the territory, as well as the water supply of larger rivers, the quality of their waters is a matter of a serious concern. The ecosystems of watercourses in urban areas exposed to pollution by industrial and domestic wastes are under the maximum anthropogenic load. Bioindicative methods, which let to assess directly the status of aquatic ecosystems and their individual components, occupy an important place in the system of ecological monitoring of water bodies. Plants respond to toxicants in an aquatic habitat by the abnormality of biosynthesis of chlorophyll, carotenoids and other pigments, change of mineral balance, phytohormones, which leads to a change in their reproductive differentiation. In this regard, water quality assessment was carried out on the basis of chemical analysis and bioindication concerning Sagittaria sagittifolia populations in the upper and middle stream ways of the river Tyosha flowing through the Nizhny Novgorod region. The article presents the results of some organoleptic and chemical parameters such as pH level of overall hardness, concentration of nitrates and nitrites, ions of ammonium, phosphates, mercury, concentration of oxygen and carbon dioxide in the water. It was detected that there were exceeding quantities of ammonium ions, nitrite ions, phosphates in the water of all ranges of the river Tyosha, and also high content of iron in the downstreams of the river. The findings suggest that the reproductive structure of arrowhead inflorescences can serve as a bio-indicator of the degree of water pollution. The harder the environmental conditions of the plant habitat in the water body, the more intensive is a shift in the ratio of flowers to the feminine side. It has been shown that due to the deterioration of environmental conditions, the number of compound inflorescences of the arrowhead and the numbers of whorls in them decrease and, on the other hand, there is an increase in the percentage of plants with simple typical inflorescences. A credible shift in the reproductive ratio of arrowhead inflorescences to the female side is spotted on the downstream river station near Lukoyanov and industrial community Shatky, where the complex of environmental factors for its growth is the least favorable. It was established that anthropogenic pollution of the river has a negative effect on the reproductive sphere of Sagittaria sagittifolia, causing a reduction in pollen fertility, which is confirmed by the chemical analysis of water. On the basis of the studies the assessment of the ecological status of the water in the Tyosha river was given

Spin-Wave Contribution to the Nuclear Spin-Lattice Relaxation in Triplet Superconductors

We discuss collective spin-wave excitations in triplet superconductors with an easy axis anisotropy for the order parameter. Using a microscopic model for interacting electrons, we estimate the frequency of such excitations in Bechgaard salts and ruthenate superconductors to be 1 and 20 GHz, respectively. We introduce an effective bosonic model to describe spin-wave excitations and calculate their contribution to the nuclear spin-lattice relaxation rate. We find that, in the experimentally relevant regime of temperatures, this mechanism leads to the power law scaling of 1=T 1 with temperature. For two-and threedimensional systems, the scaling exponents are 3 and 5, respectively. We discuss experimental manifestations of the spin-wave mechanism of the nuclear spin-lattice relaxation. A common feature of the NMR experiments in certain families of triplet superconductors (TSC) is the power law temperature dependence of the nuclear spin-lattice relaxation rate (NRR). Bechgaard salts Our starting point is the Moriya relation Here A describes the strength of hyperfine interactions between nuclear spins and conduction electrons, g N is a gyromagnetic ratio of the nucleus, g eff is an effective gyromagnetic ratio of conducting electrons, B is a Bohr magneton, and 00 ?H q; ! N is the imaginary part of the transverse (i.e., perpendicular to the magnetic field) electron spin susceptibility taken at the nuclear Larmor frequency ! N . In the case of a perfect spin SU(2) symmetry, linearly dispersing SW excitations exist down to arbitrarily small energies. In real materials, there is always spin anisotropy which gives rise to a finite gap for spin excitations, ! 0 . Below, we estimate the value of ! 0 to be tens of millidegrees Kelvin for Bechgaard salts and hundreds of millidegrees Kelvin for the ruthenates. This is much larger than the nuclear Larmor frequency ! N but smaller than the typical temperature used in experiments. When ! 0 is much larger than ! N , creation and annihilation of individual SWs does not affect 00 ! N . However, there is a contribution due to the scattering of thermally excited SW excitations. Let E be the density of states for SW excitations and nE expE=k B T ÿ 1 ÿ1 be the Bose distribution function. From the second order perturbation theory, we have 00 zz ! N R EE ! N nE ÿ nE ! N dE. The characteristic energy scale in this integral is set by the temperature T. Since T ! 0 , we can assume linear dispersion of SW excitations and take E E dÿ1 , where d is the number of spatial dimensions. Using ! N T, we have 00 zz ! N ! N R E 2dÿ2 ÿ@n=@EdE T 2dÿ2 . Combining this result with the Moriya relation (1), we obtain 1=T 1 T 2dÿ1 . Thi

SO(4) Theory of Competition between Triplet Superconductivity and Antiferromagnetism in Bechgaard Salts

Motivated by recent experiments with Bechgaard salts, we investigate the competition between antiferromagnetism and triplet superconductivity in quasi one-dimensional electron systems. We unify the two orders in an SO(4) symmetric framework, and demonstrate the existence of such symmetry in one-dimensional Luttinger liquids. SO(4) symmetry, which strongly constrains the phase diagram, can explain coexistence regions between antiferromagnetic, superconducting, and normal phases, as observed in (TMTSF)$_2$PF$_6$. We predict a sharp neutron scattering resonance in superconducting samples.Comment: 5 pages, 3 figures; Added discussion of applicability of SO(4) symmetry for strongly anisotropic Fermi liquids; Added reference

Finite size effect of harmonic measure estimation in a DLA model: Variable size of probe particles

A finite size effect in the probing of the harmonic measure in simulation of diffusion-limited aggregation (DLA) growth is investigated. We introduce a variable size of probe particles, to estimate harmonic measure and extract the fractal dimension of DLA clusters taking two limits, of vanishingly small probe particle size and of infinitely large size of a DLA cluster. We generate 1000 DLA clusters consisting of 50 million particles each, using an off-lattice killing-free algorithm developed in the early work. The introduced method leads to unprecedented accuracy in the estimation of the fractal dimension. We discuss the variation of the probability distribution function with the size of probing particles

Reflection of a Lieb-Liniger wave packet from the hard-wall potential

Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet comprised of N particles, can be found by solving an $N$-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta.Comment: revised version, improved notation, Fig. 5 adde

On the Aizenman exponent in critical percolation

The probabilities of clusters spanning a hypercube of dimensions two to seven along one axis of a percolation system under criticality were investigated numerically. We used a modified Hoshen--Kopelman algorithm combined with Grassberger's "go with the winner" strategy for the site percolation. We carried out a finite-size analysis of the data and found that the probabilities confirm Aizenman's proposal of the multiplicity exponent for dimensions three to five. A crossover to the mean-field behavior around the upper critical dimension is also discussed.Comment: 5 pages, 4 figures, 4 table

Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium

Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties usually relevant in solid-state many-body systems. In this paper we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ-model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. This reveals which aspects of non-equilibrium dynamics can as in equilibrium be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.Comment: 28 page