Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange

We study the one-dimensional quantum Heisenberg ferromagnet with exchange couplings exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations on the random coupling landscape. By using renormalization group, integration of the equations of motion and exact diagonalization, we compute the spin-wave localization length and the mean-square displacement of the wave-packet. We find that, associated with the emergence of extended spin-waves in the low-energy region for $\alpha > 1$, the wave-packet mean-square displacement changes from a long-time super-diffusive behavior for $\alpha <1$ to a long-time ballistic behavior for $\alpha > 1$. At the vicinity of $\alpha =1$, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as $E_c\propto (\alpha -1)^{1/3}$.Comment: PRB to appea

Delocalization in harmonic chains with long-range correlated random masses

We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations on the random masses landscape. Using a transfer matrix method and exact diagonalization, we compute the localization length and participation ratio of eigenmodes within the band of allowed energies. We find extended vibrational modes in the low-energy region for $\alpha > 1$. In order to study the time evolution of an initially localized energy input, we calculate the second moment $M_2(t)$ of the energy spatial distribution. We show that $M_2(t)$, besides being dependent of the specific initial excitation and exhibiting an anomalous diffusion for weakly correlated disorder, assumes a ballistic spread in the regime $\alpha>1$ due to the presence of extended vibrational modes.Comment: 6 pages, 9 figure

Voronoi-Delaunay analysis of normal modes in a simple model glass

We combine a conventional harmonic analysis of vibrations in a one-atomic model glass of soft spheres with a Voronoi-Delaunay geometrical analysis of the structure. ``Structure potentials'' (tetragonality, sphericity or perfectness) are introduced to describe the shape of the local atomic configurations (Delaunay simplices) as function of the atomic coordinates. Apart from the highest and lowest frequencies the amplitude weighted ``structure potential'' varies only little with frequency. The movement of atoms in soft modes causes transitions between different ``perfect'' realizations of local structure. As for the potential energy a dynamic matrix can be defined for the ``structure potential''. Its expectation value with respect to the vibrational modes increases nearly linearly with frequency and shows a clear indication of the boson peak. The structure eigenvectors of this dynamical matrix are strongly correlated to the vibrational ones. Four subgroups of modes can be distinguished

Network models for localisation problems belonging to the chiral symmetry classes

We consider localisation problems belonging to the chiral symmetry classes, in which sublattice symmetry is responsible for singular behaviour at a band centre. We formulate models which have the relevant symmetries and which are generalisations of the network model introduced previously in the context of the integer quantum Hall plateau transition. We show that the generalisations required can be re-expressed as corresponding to the introduction of absorption and amplification into either the original network model, or the variants of it that represent disordered superconductors. In addition, we demonstrate that by imposing appropriate constraints on disorder, a lattice version of the Dirac equation with a random vector potential can be obtained, as well as new types of critical behaviour. These models represent a convenient starting point for analytic discussions and computational studies, and we investigate in detail a two-dimensional example without time-reversal invariance. It exhibits both localised and critical phases, and band-centre singularities in the critical phase approach more closely in small systems the expected asymptotic form than in other known realisations of the symmetry class.Comment: 14 pages, 15 figures, Submitted to Physical Review

Морфологічні особливості видів Anemone blanda Schott et Kotschy i A. caucasica Willd. ex Rupr., інтродукованих у НБС ім. М.М. Гришка НАН України

The results of introduction of eleven Anemone species (Ranunculaceae) from the natural populations in the Caucasus, Central Asia and Far East into the experimental plot of the National Botanical Gardens of the NAS of Ukraine are adduced. The results of introduction of two species (A. blanda Schott et Kotschy and A. caucasica Willd. ex Rupr.) are successful. On the basis of multiannual comparative morphological investigations of vegetative organs, flowers and fruit of plants of these taxa in natural populations and in conditions of introduction its independence as species is evidenced. Add diagnostic features are detected.Наведено результати інтродукції 11 видів Anemone (Ranunculaceae Juss.) з природних популяції Кавказу, Центральної Азії та Далекого Сходу на експериментальну ділянку Національного ботанічного саду НАН України. Вдалою виявилася інтродукція лише двох видів – A. blanda і A. caucasica, які мають спірний таксономічний статус. На основі багаторічних порівняльно-морфологічних досліджень вегетативних органів, а також квіток і плодів рослин цих таксонів у природних популяціях та в умовах інтродукції підтверджено їхню видову самостійність, а також виявлено додаткові діагностичні ознаки

Сучасний погляд на таксономію роду Anemone L. sensu stricto (Ranunculaceae Juss.). Частина 2

A key for definition of species, series, subsections, sections and subgenera of genera Anemone L. on the basis of the comparative analysis about of 70 characters of fruits, flowers, leaves, aboveground and underground shoots and roots is presented.Наведено ключ для визначення видів, рядів, підсекцій, секцій та підродів роду Anemone L. на підставі аналізу близько 70 ознак плодів, квіток, листків, надземних та підземних пагонів, а також кореневих систем

Сучасний погляд на таксономію роду Anemone L. sensu stricto (Ranunculaceae Juss.). Частина 3

As a result of the critical analysis of the taxonomy of the genus Anemone L. during a lot of years, we accepted this genus as includes 16 subgenera, 18 sections, 5 subsections, 27 series and 118 species. Within the genus Anemone we firstly proposed 7 genus, 1 subgenus, 2 section, and 13 series, and we re-examined the status of about 30 species and intraspecific taxa. We presented here the annotated conspect of the genus Anemone.У результаті критичного перегляду таксономії роду Anemone L. ми визнаємо його структуру з 16 підродів, 18 секцій, 5 підсекцій, 27 рядів та 118 видів, у тому числі нами підтверджено 8 родів, які існували в сучасній системі Tamura (1991), 7 родів запропоновано як нові комбінації, описано один підрід, 2 секції і 13 рядів. Крім того, ми переглянули статус майже 30 видів і внутрішньовидових таксонів. Представлено анотований конспект роду Anemone

Сучасний погляд на таксономію роду Anemone L. sensu stricto (Ranunculaceae Juss.). Частина I

Here we re-examined the literature on the genus Anemone L. taxonomy as the largest and most complicated within the family Ranunculaceae Juss. because its state, species content and intergeneric structure (dividing on sections and other taxa) were debatable during a lot of years. As a result of our critical examination of the characters being in use for Anemone taxonomy (approximately 25 ones) and the own analyse of ca. 70 characters of fruits, flowers, leaves, aboveground and underground shoots and roots, we selected the characters the most essential for the taxonomy of the genus Anemone which we revised in the next parts of our manuscript.Нами здійснено аналіз літератури по таксономії роду Anemone L., одного з найбільших у родині Ranunculaceae Juss., тому що його статус, видовий склад, поділ на секції та інші внутрішньородові таксони були й залишаються дискусійними протягом багатьох років. В результаті критичного перегляду морфологічних ознак, що використовувалися для таксономії Anemone (близько 25 ознак), а також на основі власного аналізу близько 70 ознак плодів, квіток, листків, надземних та підземних пагонів і кореневих систем ми виділили ознаки, найбільш значущі для таксономії роду Anemone, яка буде представлена в кількох публікаціях

Modern view on the taxonomy of the genus Anemone L. sensu stricto (Ranunculaceae Juss.). Part 2

A key for definition of species, series, subsections, sections and subgenera of genera Anemone L. on the basis of the comparative analysis about of 70 characters of fruits, flowers, leaves, aboveground and underground shoots and roots is presented