Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space coordinates, in Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincar\'e-Weyl generators or $\mathfrak{gl}(n)$ generators, are constructed and R-matrix is discussed. Classification of linear realizations leading to vector-like deformed phase spaces is given. There are 3 types of spaces: $i)$ commutative spaces, $ii)$ $\kappa$-Minkowski spaces and $iii)$ $\kappa$-Snyder spaces. Corresponding star products are $i)$ associative and commutative (but non-local), $ii)$ associative and non-commutative and $iii)$ non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.Comment: 20 pages, version accepted for publication in EPJ

Solutions of coupled BPS equations for two-family Calogero and matrix models

We consider a large N, two-family Calogero and matrix model in the Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the solutions to the coupled Bogomol'nyi-Prasad-Sommerfeld equations are given by the static soliton configurations. We find all solutions close to constant and construct exact one-parameter solutions in the strong-weak dual case. Full classification of these solutions is presented.Comment: latex, 15 pages, no figure

Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach

We consider new Abelian twists of Poincare algebra describing non-symmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as generating quantum Poincare-Hopf algebra providing quantum Poincare symmetries, and by considering the quantization which provides Hopf algebroid describing the class of quantum relativistic phase spaces with built-in quantum Poincare covariance. If we assume that Lorentz generators are orbital i.e.do not describe spin degrees of freedom, one can embed the considered generalized phase spaces into the ones describing the quantum-deformed Heisenberg algebras.Comment: 15 pages,no figures; v2 with completed references, which appeared in PL

Twist for Snyder space

We construct the twist operator for the Snyder space. Our starting point is a non-associative star product related to a Hermitian realisation of the noncommutative coordinates originally introduced by Snyder. The corresponding coproduct of momenta is non-coassociative. The twist is constructed using a general definition of the star product in terms of a bi-differential operator in the Hopf algebroid approach. The result is given by a closed analytical expression. We prove that this twist reproduces the correct coproducts of the momenta and the Lorentz generators. The twisted Poincar\'{e} symmetry is described by a non-associative Hopf algebra, while the twisted Lorentz symmetry is described by the undeformed Hopf algebra. This new twist might be important in the construction of different types of field theories on Snyder space.Comment: 15 pages, references added, matches published versio

Defects and nanostructures in metal oxides suitable for organic solar cells

Da bi tanki film metalnog oksida ušao u upotrebu kao prozirni i vodljivi sloj za solarne ćelije, način njegovog formiranja mora garantirati vrhunske performanse ostvarene na jednostavan način i sa perspektivom jednostavnog povećavanja proizvodne skale. Hipoteza rada je da se ovo može postići preciznim podešavanjem procesa formiranja i jednostavnim postupcima naknadne obrade. Posebnost organskih solarnih ćelija je mala difuziona dužina fotogeneriranih nosilaca naboja (kratko vrijeme života) i dominantan udio ekscitonske generacije. Zbog toga je nužan preduvjet zadovoljavajuće efikasnosti velika površina ćelije, veliki optički procijep, te posljedično mogućnost relativno jednostavnog podešavanja izlaznog rada dekoriranjem površine metalnim česticama. Da bi se to postiglo, u radu je naglasak dan na nanostrukture koje definiraju morfologiju površine, te na defekte koji određuju procese rekombinacije i transporta nosilaca naboja. Posebna pažnja je posvećena slojevima ZnO i SnO2. Struktura im je bila varirana uvjetima rasta a ispitivana je mogućnost naknadne obrade filmova termičkim tretmanom u reaktivnoj atmosferi. U prvom koraku se određivala korelacija nanostrukturnih i optičkih svojstava sa parametrima depozicije. Istraživane su tri tehnike depozicije: pulsna laserska depozicija (PLD), magnetronsko rasprašenje (MS), i kemijska depozicija iz plinovite faze (CVD). Dobivenim filmovima je određivana struktura na nivou kristalne rešetke i na nanometarskoj skali, korištenjem raspršenja rendgenskih zraka za vrlo male upadne kuteve i male kuteve raspršenja (Grazing Incidence Small Angle X-ray Scattering), te velike kutove raspršenja (GIWAXS). U analizi raspršenih rendgenskih zraka su osim standardnih metoda uvedena određena poboljšanja u prilagodbi spektara dobivenih GISAXS tehnikom koja dozvoljavaju ocijenu distribucije čestica po veličini. Osim korelacije s uvjetima rasta, provedeni eksperimenti su potvrdili usku povezanost optičkih svojstava i strukture, a posebno korelaciju između luminiscentnih svojstava i točkastih defekata. Depozicija filmova PLD tehnikom dozvoljava istraživanje rasta filmova u različitim atmosferama, nezavisno od procesa emisije čestica. Da bi se istražio utjecaj reaktivne atmosfere kisika na svojstva tankih slojeva ZnO dopiranih Al, uzorci su deponirani u vakuumu i u atmosferi kisika. Mijenjajući tlak plina između 10 i 70 Pa, te povećavajući reaktivnost kisika uvođenjem pobuđenih čestica iz RF plazme kisika, dobiveni su razni strukturni oblici. Strukturna analiza je pokazala da povećanje tlaka kisika rezultira povećanjem hrapavosti površine uzorka, smanjenjem njegove gustoće i promjenom raspodjele veličina nanošupljina u volumenu. Pokazano je da se dodavanjem aktivnih čestica kisika (atomarni kisik, O, i pobuđene molekule kisika, O2*) može manipulirati koncentracijom i vrstom točkastih defekata u filmu i na njegovoj površini. Ovaj rezultat otvara cijelo polje novih mogućnosti formiranja slojeva uz reaktivnu atmosferu i kod drugih tehnika (npr. kod magnetronske depozicije). Na uzorcima ZnO:Al tankih filmova dobivenim DC magnetronskim rasprašenjem istraživan je utjecaj grijanja u vodikovoj atmosferi na strukturna i optička svojstava. Nakon depozicije, uzorci su zagrijavani tijekom jednog sata u vodikovoj atmosferi na temperaturama od 200, 300 i 400 °C. Strukturna ispitivanja su pokazala da ovakvim tretmanom dolazi do smanjenja naprezanja u materijalu, da se volumen kristalne rešetke smanjuje i da veličina kristala raste. Mjerenjem optičkih svojstava, pokazano je da se grijanjem povećava optički procijep i anuliraju defekti vezani za intersticijske atome. Ovakav termički tretman smanjuje broj točkastih defekata i može promijeniti vodljivost sloja za gotovo 9 redova veličine. Povećanje vodljivosti je posljedica povećanja mobilnosti i koncentracije slobodnih nosilaca naboja zbog smanjenja broja defekata i aktivacije dopanada koji djeluju kao plitki donori. Pri tome su najvjerojatniji proces difuzije intersticijskih atoma, uz anihilaciju vakancija i pasivizacija defekata na granicama zrna. Uzorci SnO2 filmova su pripravljeni CVD tehnikom uz variranje temperature podloge na koju se nanosila otopina SnCl4 sprejanjem pri atmosferskom tlaku. Pokazano je da relativno male promjene u temperaturi podloge od 590 °C na 610 °C imaju za posljedicu značajne promjene u orijentaciji kristala filma u odnosu na podlogu, koja utječe na električna i optička svojstva pa tako i na efikasnost solarne ćelije koja se deponira na njima. Također je pokazano da nivo dopiranja sloja fluorom, osim na transportna svojstva zbog povećanja slobodnih nosilaca naboja, utječe i na veličinu i orijentaciju kristala u filmu.In order to use a metal oxide thin film as a transparent conductive layer for solar cells, the method of formation has to guarantee high performance, realized in a simple way and with a perspective of simply increasing the production scale. The hypothesis of this Thesis is that this can be done by fine-tuning the process of formation and simple postdeposition treatment. Emphasis is given to nanostructures that define the morphology of the surface, which determines the active surface of the cell and the fraction of the diffuse component of the input light, and on the defects that determine the processes of recombination and transport of the charge carriers. Special attention was given to the layers of ZnO and SnO2. Their structure was varied with growth conditions and the possibility of postdeposition treatment of films by heat treatment in reactive atmosphere. In the first step, the correlation of nanostructural and optical properties with the deposition parameters was determined. Three deposition techniques have been investigated: pulsed laser deposition, PLD, magnetron sputtering, MS, and chemical vapor deposition, CVD. For the obtained films, structure on the the crystal lattice scale and on the nanometer scale was determined, using Grazing Incidence Small Angle X-ray Scattering, GISAXS and Grazing Incidence Wide Angle Scattering, GIWAXS. In the analysis of X-ray scattering, in addition to standard methods, some improvements in fitting of the ispectra obtained by GISAXS technique was introduced, that allows an estimation of the distribution of particles sizes. In addition to the correlation with the growth conditions, conducted experiments confirmed the close connection between optical and structural properties, especially the correlation between luminescent properties and point defects. It was shown that, introducing the RF excitation in the oxygen atmosphere during PLD deposition can reduce the number of point defects in the ZnO:Al films considerably. The deposition of films by the PLD technique allows the study of the growth of films in different atmospheres, independently of the process of particle emissions. To investigate the influence of the reactive oxygen atmosphere on the properties of the ZnO thin films doped with Al, the samples were deposited in vacuum and in an oxygen atmosphere. By changing the gas pressure between 10 and 70 Pa, and increasing the reactivity of oxygen by introducing excited particles from the oxygen plasma, various structural forms were obtained. Structural analysis has shown that an increase in oxygen pressure results in an increase of surface roughness of the sample, by reducing its density, and by changing the size distribution of nanovoids in the volume. It was shown that by adding active species of oxygen, one can manipulate with the concentration and the type of point defects in the film and on its surface. This result opens up new possibilities of forming layers in reactive atmosphere in other techniques as well (eg. magnetron deposition). In particular, with the RF discharge and pressure lower than 70Pa, the total concentration of defects is significantly decreased. On ZnO:Al thin films, obtained by DC magnetron sputtering, the effect of thermal treatment in a hydrogen atmosphere on the structural and optical properties was examined. After deposition, the samples were heated for one hour in a hydrogen atmosphere at temperatures of 200, 300 and 400 °C. Structural investigation demonstrated that heat treatment reduces the stress in the material, the volume of the crystal lattice decreases and the crystal size grows. By measuring the optical properties, it was shown that heating increases the optical gap and nullify defects related to interstitial atoms. This kind of heat treatment reduces the number of point defects and may change the conductivity of the layer for almost 9 orders of magnitude. The increase in conductivity is a result of increased mobility and concentration of free charge carriers due to the reduced number of defects and the activation of the dopands that act as shallow donors. In doing so, the most probable process is diffusion of interstitial atoms with the annihilation of vacancies and the passivation of defects at the grain boundaries. Samples of SnO2 films were prepared by atmospheric pressure CVD technique, by spraying SnCl4 solution on glass substrate heated on various temperatures. It has been shown that relatively small changes in the substrate temperature from 590 °C to 610 °C result in significant changes in the crystal orientation that affects the electrical and optical properties and thus the efficiency of solar cells, which are deposited on them. Furthermore, it was shown that the level of doping with fluorine, in addition to the lowering of resistivity due to the increase of free charge carriers, influences the size and orientation of the crystals in the film

Remarks on simple interpolation between Jordanian twists

In this paper, we propose a simple generalization of the locally r-symmetric Jordanian twist, resulting in the one-parameter family of Jordanian twists. All the proposed twists differ by the coboundary twists and produce the same Jordanian deformation of the corresponding Lie algebra. They all provide the $\kappa$-Minkowski spacetime commutation relations. Constructions from noncommutative coordinates to the star product and coproduct, and from the star product to the coproduct and the twist are presented. The corresponding twist in the Hopf algebroid approach is given. Our results are presented symbolically by a diagram relating all of the possible constructions.Comment: 12 page