Gibanje dalekih tijela u svemiru

We give a brief survey of investigations of the structure of the Universe and of its expansion, for educational purposes. As we know it today, the size of the Universe is immense, enormous numbers of galaxies have been found in it, and in each galaxy enormous numbers of stars. The galaxies move from us at very high speeds, some of the more distant ones at speeds comparable to the velocity of light. Many theories have been developed to explain the vast amount of data that have been obtained by astronomical observations. We give a simplified theory of the cosmic expansion and present results of three models for the cosmic scale function R(t): the constant rate of expansion, the accelerated expansion and the constant Hubble parameter models.Dajemo kratak pregled istraživanja o građi Svemira i njegovom širenju u svrhu nastave. Kako danas znamo, Svemir je neshvatljivo velik, s ogromnim brojem galaksija, a svaka galaksija sadrži ogroman broj zvijezda. Galaksije se udaljuju od nas s vrlo velikim brzinama koje su usporedive brzini svjetlosti. Razvijene su mnoge teorije radi objašnjenja mnoštva podataka dobivenih u astronomskim opažanjima. Izlažemo jednostavnu teoriju širenja Svemira i opisujemo ishode računa za tri modela za funkciju svemirske ljestvice R(t): za stalnu brzinu i ubrzano (usporeno) širenje, te za stalan Hubbleov parametar

Gibanje dalekih tijela u svemiru

We give a brief survey of investigations of the structure of the Universe and of its expansion, for educational purposes. As we know it today, the size of the Universe is immense, enormous numbers of galaxies have been found in it, and in each galaxy enormous numbers of stars. The galaxies move from us at very high speeds, some of the more distant ones at speeds comparable to the velocity of light. Many theories have been developed to explain the vast amount of data that have been obtained by astronomical observations. We give a simplified theory of the cosmic expansion and present results of three models for the cosmic scale function R(t): the constant rate of expansion, the accelerated expansion and the constant Hubble parameter models.Dajemo kratak pregled istraživanja o građi Svemira i njegovom širenju u svrhu nastave. Kako danas znamo, Svemir je neshvatljivo velik, s ogromnim brojem galaksija, a svaka galaksija sadrži ogroman broj zvijezda. Galaksije se udaljuju od nas s vrlo velikim brzinama koje su usporedive brzini svjetlosti. Razvijene su mnoge teorije radi objašnjenja mnoštva podataka dobivenih u astronomskim opažanjima. Izlažemo jednostavnu teoriju širenja Svemira i opisujemo ishode računa za tri modela za funkciju svemirske ljestvice R(t): za stalnu brzinu i ubrzano (usporeno) širenje, te za stalan Hubbleov parametar

Opažanje gibanja brzih tijela iz jedne točke

We study the kinematical problem of observation of motion of objects that move at velocities comparable to the velocity of signals which are used to determine the velocity and distance of the objects. The main purpose of this work is to demonstrate the importance of time delay between the emission of signals and their reception at the observation point. The simplest cases are considered, i.e., rectilinear motion and assuming the observational point at the path of the moving object. Sound and light signals are considered to transmit the information on the motion. The results relating to the motion at constant velocity and for the acceleration due to a constant force are presented.Razmatramo kinematički problem opažanja gibanja tijela čije su brzine usporedive s brzinama signala koji se rabe za određivanje udaljenosti i brzine tih tijela. Osnovni je cilj ovog rada pokazivanje važnosti vremenskog kašnjenja od trenutka emisije do prijama signala u točki opažanja. Razmatraju se najjednostavniji slučajevi, tj. gibanje duž pravca i položaj opažača na putu promatranog tijela. Pretpostavlja se prijenos podataka o gibanju zvučnim i svjetlosnim signalima. Prikazuju se ishodi računa za gibanje stalnom brzinom i pod djelovanjem stalne sile

Opažanje gibanja brzih tijela iz jedne točke

We study the kinematical problem of observation of motion of objects that move at velocities comparable to the velocity of signals which are used to determine the velocity and distance of the objects. The main purpose of this work is to demonstrate the importance of time delay between the emission of signals and their reception at the observation point. The simplest cases are considered, i.e., rectilinear motion and assuming the observational point at the path of the moving object. Sound and light signals are considered to transmit the information on the motion. The results relating to the motion at constant velocity and for the acceleration due to a constant force are presented.Razmatramo kinematički problem opažanja gibanja tijela čije su brzine usporedive s brzinama signala koji se rabe za određivanje udaljenosti i brzine tih tijela. Osnovni je cilj ovog rada pokazivanje važnosti vremenskog kašnjenja od trenutka emisije do prijama signala u točki opažanja. Razmatraju se najjednostavniji slučajevi, tj. gibanje duž pravca i položaj opažača na putu promatranog tijela. Pretpostavlja se prijenos podataka o gibanju zvučnim i svjetlosnim signalima. Prikazuju se ishodi računa za gibanje stalnom brzinom i pod djelovanjem stalne sile

Resonant inelastic x-ray scattering probes the electron-phonon coupling in the spin-liquid kappa-(BEDT-TTF)2Cu2(CN)3

Resonant inelastic x-ray scattering at the N K edge reveals clearly resolved harmonics of the anion plane vibrations in the kappa-(BEDT-TTF)2Cu2(CN)3 spin-liquid insulator. Tuning the incoming light energy at the K edge of two distinct N sites permits to excite different sets of phonon modes. Cyanide CN stretching mode is selected at the edge of the ordered N sites which are more strongly connected to the BEDT-TTF molecules, while positionally disordered N sites show multi-mode excitation. Combining measurements with calculations on an anion plane cluster permits to estimate the sitedependent electron-phonon coupling of the modes related to nitrogen excitation

Polarization correlations in the two--photon decay of hydrogen--like ions

Polarization properties of the photons emitted in the two-photon decay of hydrogen-like ions are studied within the framework of the density matrix and second-order perturbation theory. In particular, we derive the polarization correlation function that gives the probability of the (two-photon) coincidence measurement performed by polarization-sensitive detectors. Detailed calculations of this function are performed for the $2s_{1/2} \to 1s_{1/2}$ transition in neutral hydrogen as well as Xe$^{53+}$ and U$^{91+}$ ions. The obtained results allow us to understand the influence of relativistic and non-dipole effects on the polarization correlations in the bound-bound two-photon transitions in heavy ions

Covariant and Heavy Quark Symmetric Quark Models

There exist relativistic quark models (potential or MIT-bag) which satisfy the heavy quark symmetry (HQS) relations among meson decay constants and form factors. Covariant construction of the momentum eigenstates, developed here, can correct for spurious center-of-mass motion contributions.Proton form factor and M1 transitions in quarkonia are calculated. Explicit expression for the Isgur-Wise function is found and model determined deviations from HQS are studied. All results depend on the model parameters only. No additional ad hoc assumptions are needed.Comment: 34 pages (2 figures not included but avaliable upon request), LATEX, (to be published in Phys.Rev.D

Spectrum and transition rates of the XX chain analyzed via Bethe ansatz

As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the Bethe ansatz solutions for the entire XX spectrum, which include states with real and complex magnon momenta. We discuss the relation between the spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions (Jordan-Wigner representation). We present determinantal expressions for transition rates of spin fluctuation operators between Bethe wave functions and reduce them to product expressions. We apply the new formulas to two-spinon transition rates for chains with up to N=4096 sites.Comment: 11 pages, 4 figure

Lepton Flavour Violating Leptonic/Semileptonic Decays of Charged Leptons in the Minimal Supersymmetric Standard Model

We consider the leptonic and semileptonic (SL) lepton flavour violating (LFV) decays of the charged leptons in the minimal supersymmetric standard model (MSSM). The formalism for evaluation of branching fractions for the SL LFV charged-lepton decays with one or two pseudoscalar mesons, or one vector meson in the final state, is given. Previous amplitudes for the SL LFV charged-lepton decays in MSSM are improved, for instance the $\gamma$-penguin amplitude is corrected to assure the gauge invariance. The decays are studied not only in the model-independent formulation of the theory in the frame of MSSM, but also within the frame of the minimal supersymmetric SO(10) model within which the parameters of the MSSM are determined. The latter model gives predictions for the neutrino-Dirac Yukawa coupling matrix, once free parameters in the model are appropriately fixed to accommodate the recent neutrino oscillation data. Using this unambiguous neutrino-Dirac Yukawa couplings, we calculate the LFV leptonic and SL decay processes assuming the minimal supergravity scenario. A very detailed numerical analysis is done to constrain the MSSM parameters. Numerical results for SL LFV processes are given, for instance for tau -> e (mu) pi0, tau -> e (mu) eta, tau -> e (mu) eta', tau -> e (mu) rho0, tau -> e (mu) phi, tau -> e (mu) omega, etc.Comment: 36 pages, 3 tables, 5 .eps figure