Topological Excitations of One-Dimensional Correlated Electron Systems

Properties of low-energy excitations in one-dimensional superconductors and density-wave systems are examined by the bosonization technique. In addition to the usual spin and charge quantum numbers, a new, independently measurable attribute is introduced to describe elementary, low-energy excitations. It can be defined as a number w which determines, in multiple of $\pi$, how many times the phase of the order parameter winds as an excitation is transposed from far left to far right. The winding number is zero for electrons and holes with conventional quantum numbers, but it acquires a nontrivial value w=1 for neutral spin-1/2 excitations and for spinless excitations with a unit electron charge. It may even be irrational, if the charge is irrational. Thus, these excitations are topological, and they can be viewed as composite particles made of spin or charge degrees of freedom and dressed by kinks in the order parameter.Comment: 5 pages. And we are not only splitting point

Students' experiences of teaching based on character strengths : longitudinal study on the experiences of boys of lower school age in positive pedagogy

Tavoitteet. Tutkimukseni tavoitteena on tutkia tuntevatko alakouluikäiset pojat omat luonteen-vahvuutensa, käyttävätkö he luonteenvahvuuksia oman oppimisensa tukena sekä vahvistaa-ko positiivinen pedagogiikka oppilaiden minäkäsitystä ja itsetuntoa tavoitteidensa mukaisesti. Positiivinen pedagogiikka on tällä hetkellä kasvatuksen ja opetuksen kentällä paljon pinnalla oleva opetuksen ja kasvatuksen suuntaus. Se on merkittävästi myös esillä perusopetuksen opetussuunnitelman perusteissa 2014, jossa korostetaan hyvinvoinnin ja vahvuuksien huo-mioimisen tärkeyttä. Opetusta ja pedagogiikkaan tehdään lasten oppimisen hyväksi, halusin tämän vuoksi tällä tutkimuksella tuoda esille lasten näkökulmaa positiivisesta pedagogiikasta ja sen toimivuudesta. Menetelmät. Tutkimus toteutettiin laadullisena pitkittäistutkimuksena sekä puolistrukturoituna teemahaastatteluna. Tutkimusta varten haastateltiin pääkaupunkiseutulaisen koulun erään luokan poikia 2. vuosiluokalla ja 4. vuosiluokalla. Ensimmäisellä haastattelukerralla haastatel-tiin seitsemää (n=7) luokan poikaa. Toisen haastattelukerran haastatteluihin osallistuivat luo-kan kaikki pojat (n=16). Analyysimenetelmänä tutkimuksessa käytettiin teemoittelua. Tulokset ja johtopäätökset. Tutkimuksen tutkimustulokset vahvistavat, että positiivinen peda-gogiikka on vahvistanut haastatteluihin osallistuneiden poikien omien luonteenvahvuuksien tuntemusta ja heidän minäkäsityksensä oli myös vahva. Pojat tunsivat luonteenvahvuudet yksittäisinä vahvuuksina, mutta eivät laajemmassa merkityksessä. Luonteenvahvuuksista myötätunto nousi erityisesti esille poikien vastauksista. Pojat kokivat positiivisen palautteen antamisen tärkeäksi ja he kertoivat viihtyvänsä koulussa. Minäkäsityksen ja itsetunnon vah-vuus näkyi positiivisena ajatteluna itsestä ja omista kyvyistä, omien vahvuuksien ja heik-kouksien tuntemisena sekä uskona omaan tulevaisuuteensa.Objectives. My study examines whether boys of primary school age are familiar with their own character strengths, whether they use their own character strengths to support their learning and whether positive pedagogy strengthens the mindset and self-esteem of these boys, as is its goal. Positive pedagogy is currently a very popular pedagogical trend in Finland. It is also well discussed in the Finnish basic education curriculum, which considers it important to take well-being and the strengths of character into account. Teaching and pedagogy are being carried out to teach children, which is why I wanted to study children in my study and to highlight their perspective in relation to a positive pedagogical and whether positive pedagogy works. Methods. This study is a qualitative long-term study and has been conducted as a half-structured theme interview. In the study, I interviewed one-class students from a school in the capital region twice. The first-time boys were in 2nd grade and the second time they were in 4th grade. The first time I interviewed seven (n=7) boys and the second time interviewed all the boys from the class (n=16). As an analysis method, I used themes. The results and conclusions. According to the results of my research, positive pedagogy has taught boys to know their own character strengths and made their self-concepts and self-esteem strong. Boys feel character strengths as individual character strengths, but they do not feel character strengths in a broad sense. These boys think it's important to give positive feedback and they like it at school. Compassion became an important strength of character in boys' answers. Self-concepts and self-esteem are strong for boys, because boys thought of themselves positively, they think they do many things well, and they believe that they have a good future ahead of them

Comment on ``Quasiparticle Spectra around a Single Vortex in a d-wave Superconductor''

In a recent Letter Morita, Kohmoto and Maki analyzed the structure of quasiparticle states near a single vortex in a d-wave superconductor using an approximate version of the Bogoliubov - de Gennes theory. Their principal result is the existence of a bound state within the core region at finite energy with full rotational symmetry, which they assert explains the recent scanning tunneling microscopy results on YBCO single crystals. Here we argue that the approximation used in this work is fundamentally inadequate for the description of a d-wave vortex and that the obtained circular symmetry of the local density of states is an unphysical artifact of this approximation.Comment: 1 page REVTeX, to appear in PR

Quantum Vibrational Impurity Embedded in a One-dimensional Chain

We perform a fully quantum mechanical numerical calculation for the problem of a single electron (or excitation) propagating in a N-site one-dimensional chain in the presence of a single Holstein impurity. We compute the long-time averaged probability for finding the electron on the impurity site as a function of the nonlinearity parameter, defined in terms of the electron-phonon coupling strength and the oscillator frequency. The results, in the intermediate nonlinearity parameter range, differ substantially from the ones obtained through the use of the discrete nonlinear Schroedinger equation, even in the high-frequency regime.Comment: 8 pages, 4 figure

The wave-vector power spectrum of the local tunnelling density of states: ripples in a d-wave sea

A weak scattering potential imposed on a $CuO_2$ layer of a cuprate superconductor modulates the local density of states $N(x,\omega)$. In recently reported experimental studies scanning-tunneling maps of $N(x,\omega)$ have been Fourier transformed to obtain a wave-vector power spectrum. Here, for the case of a weak scattering potential, we discuss the structure of this power spectrum and its relationship to the quasi-particle spectrum and the structure factor of the scattering potential. Examples of quasi-particle interferences in normal metals and $s$- and d-wave superconductors are discussed.Comment: 22 pages, 21 figures; enlarged discussion of the d-wave response, to be published in Physical Review

Effect of anisotropic impurity scattering on a density of states of a d-wave superconductor

We discuss the effect of an anisotropic impurity potential on the critical temperature, local density of states in the vicinity of a single impurity, and the quasiparticle density of states for a finite impurity concentration in a d-wave superconductor. Different scattering regimes are concerned.Comment: 3 pages, revtex4, 4 figure

Mirage phenomena in superconducting quantum corrals

We investigate the local density of states and the order parameter structure inside an elliptic quantum corral on surfaces of isotropic and anisotropic superconductors. The Bogoliubov-de Gennes equations are solved in the presence of non-magnetic and magnetic impurities. We observe and discuss a variety of mirage and anti-mirage phenomena, which specifically reflect the nature of the superconducting pairing state.Comment: 8 pages, 8 figure

Quantum interference between non-magnetic impurities in d_x2-y2-wave superconductors

We study quantum interference of electronic waves that are scattered by multiple non-magnetic impurities in a d_x2-y2-wave superconductor. We show that the number of resonance states in the density-of-states (DOS), as well as their frequency and spatial dependence change significantly as the distance between the impurities or their orientation relative to the crystal lattice is varied. Since the latter effect arises from the momentum dependence of the superconducting gap, we argue that quantum interference is a novel tool to identify the symmetry of unconventional superconductors.Comment: 4 pages, 4 figure