One-site density matrix renormalization group and alternating minimum energy algorithm

Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT) / matrix product states (MPS) representation. Both methods empower the traditional alternating direction scheme with the auxiliary (e.g. gradient) information, which substantially improves the convergence in many difficult cases. Being conceptually close, these methods have different derivation, implementation, theoretical and practical properties. We emphasize the differences, and reproduce the numerical example to compare the performance of two algorithms.Comment: Submitted to the proceedings of ENUMATH 201

Optical absorption in the strong coupling limit of Eliashberg theory

We calculate the optical conductivity of superconductors in the strong-coupling limit. In this anomalous limit the typical energy scale is set by the coupling energy, and other energy scales such as the energy of the bosons mediating the attraction are negligibly small. We find a universal frequency dependence of the optical absorption which is dominated by bound states and differs significantly from the weak coupling results. A comparison with absorption spectra of superconductors with enhanced electron-phonon coupling shows that typical features of the strong-coupling limit are already present at intermediate coupling.Comment: 10 pages, revtex, 4 uuencoded figure

Viability of Noether symmetry of F(R) theory of gravity

Canonization of F(R) theory of gravity to explore Noether symmetry is performed treating R - 6(\frac{\ddot a}{a} + \frac{\dot a^2}{a^2} + \frac{k}{a^2}) = 0 as a constraint of the theory in Robertson-Walker space-time, which implies that R is taken as an auxiliary variable. Although it yields correct field equations, Noether symmetry does not allow linear term in the action, and as such does not produce a viable cosmological model. Here, we show that this technique of exploring Noether symmetry does not allow even a non-linear form of F(R), if the configuration space is enlarged by including a scalar field in addition, or taking anisotropic models into account. Surprisingly enough, it does not reproduce the symmetry that already exists in the literature (A. K. Sanyal, B. Modak, C. Rubano and E. Piedipalumbo, Gen.Relativ.Grav.37, 407 (2005), arXiv:astro-ph/0310610) for scalar tensor theory of gravity in the presence of R^2 term. Thus, R can not be treated as an auxiliary variable and hence Noether symmetry of arbitrary form of F(R) theory of gravity remains obscure. However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar-tensor theory (A. K. Sanyal, Phys.Lett.B624, 81 (2005), arXiv:hep-th/0504021 and Mod.Phys.Lett.A25, 2667 (2010), arXiv:0910.2385 [astro-ph.CO]). Here, we briefly expatiate the non-Noether conserved current and cite an example to reveal its importance in finding cosmological solution for such an action, taking F(R) \propto R^{3/2}.Comment: 16 pages, 1 figure. appears in Int J Theoretical Phys (2012

Comissioning of the linear accelerator-injector at the TNK facility

The industrial storage facility has been developed and manufactured at the Budker INP SB RAS. It contains an 80 MeV electron linear accelerator-injector and two electron storage rings: the lesser 450 MeV booster ring and the main 2.5 GeV storage ring. In 2002, the work on the accelerator assembling was begun. On December, 25 this year the accelerator was started up, and the current at the linear accelerator output was obtained. The linear accelerator schematic together with a description of the 6 meter long accelerating DAW structure which operates at 2.8 GHz, are presented in the paper. The first results of the accelerator start-up are as follows: the accelerated electron current of ~50 mA with the energy of ~55...60 MeV.Технологічний накопичувальний комплекс був спроектований і виготовлений у ІЯФ ім. Г.І. Будкера СВ РАН. Він містить у собі інжектор–лінійний прискорювач електронів з енергією до 80 МеВ і два накопичувачі електронів: малий накопичувач–бустер на енергію 450 МеВ і основний накопичувач на енергію 2.5 ГеВ. Приводяться функціональна схема лінійного прискорювача й опис конструкції прискорюючої структури із шайбами і діафрагмами довжиною 6 м, що працює на частоті 2.8 ГГц.Представлено перші результати запуску прискорювача: отриманий прискорений струм електронів ~50 мА з енергією ~(55...60) МеВ.Технологический накопительный комплекс был спроектирован и изготовлен в ИЯФ им. Г.И. Будкера СО РАН. Он включает в себя инжектор–линейный ускоритель электронов с энергией до 80 МэВ и два накопителя электронов: малый накопитель–бустер на энергию 450 МэВ и основной накопитель на энергию 2.5 ГэВ. Приводятся функциональная схема линейного ускорителя и описание конструкции ускоряющей структуры с шайбами и диафрагмами длиной 6 метров, работающей на частоте 2.8 ГГц. Представлены первые результаты запуска ускорителя: получен ускоренный ток электронов ~50 мA с энергией ~(55...60) МэВ

Measurement of the Nucleon Structure Function F2 in the Nuclear Medium and Evaluation of its Moments

We report on the measurement of inclusive electron scattering off a carbon target performed with CLAS at Jefferson Laboratory. A combination of three different beam energies 1.161, 2.261 and 4.461 GeV allowed us to reach an invariant mass of the final-state hadronic system W~2.4 GeV with four-momentum transfers Q2 ranging from 0.2 to 5 GeV2. These data, together with previous measurements of the inclusive electron scattering off proton and deuteron, which cover a similar continuous two-dimensional region of Q2 and Bjorken variable x, permit the study of nuclear modifications of the nucleon structure. By using these, as well as other world data, we evaluated the F2 structure function and its moments. Using an OPE-based twist expansion, we studied the Q2-evolution of the moments, obtaining a separation of the leading-twist and the total higher-twist terms. The carbon-to-deuteron ratio of the leading-twist contributions to the F2 moments exhibits the well known EMC effect, compatible with that discovered previously in x-space. The total higher-twist term in the carbon nucleus appears, although with large systematic uncertainites, to be smaller with respect to the deuteron case for n<7, suggesting partial parton deconfinement in nuclear matter. We speculate that the spatial extension of the nucleon is changed when it is immersed in the nuclear medium.Comment: 37 pages, 15 figure

Clinical topographical correlation upon brain tumors in children

The aim of the study was to explore the most characteristic clinical manifestations of brain tumors in children, depending on their localization, and to detect the earliest of them. Patients and methods. A total of 56 children (32 boys and 24 girls) with brain tumor, aged from 1.5 months to 15 years, were examined. The time elapsed between the onset of disease to the emergence of clinical symptoms was assessed. Neurological symptomatology was compared to the localization of a tumor diagnosed using neuroimaging techniques (computed tomography or magnetic resonance imaging) and during surgery. Surgery was performed in 18 children (in all of them, localization of the process was observed in the posterior cranial fossa, PCF). Results. The highest incidence of brain tumors was revealed in children aged 3–13 years; most patients became ill at the age between 3 and 6 years. Tumors of the PCF predominated in terms of their localization (67.9% of cases). Intracerebral tumors of the hemispheres or vermis were observed in most (63.2%) patients with tumors of the PCF. In 11 (61%) of the 18 operated children with subtentorial tumors, astrocytomas of various degrees of differentiation and medulloblastomas were detected using the histological examination. Tumors of the IV ventricle were ependymal. Tumors of the cerebral hemispheres (19.6%), of the pineal and chiasmosellar regions (8.9%) predominated among supratentorial tumors. The time between the emergence of initial symptoms of a disease and admission to hospital ranged from 1 month to 3 years. The most characteristic and earliest symptoms for tumors of the PCF and brain ventricles were headache, nausea and vomiting. For tumors of the cerebellar vermis and hemispheres, these symptoms included impairment of the coordination of movements and the muscle tone change. For brain stem tumors, these symptoms included dysfunction of the cranial nerves. For tumors of the cerebral hemispheres, these were seizures and motor and sensory disturbances in the limbs

Electron-phonon spectral function and two-band model in tunneling measurement on MgB2

In the present work we calculate for the first time the density of states of MgB2 for different tunneling directions by directly solving the two-band Eliashberg equations in the real-axis formulation starting from the first-principle calculation of the interband and intraband electron-phonon spectral functions. This complicated numeric procedure allows preserving the fine structures of the DOS in the phonon energy range. We show that the numeric inversion of the standard single-band Eliashberg equations when applied to the densities of states obtained by the two-band model may lead to artifacts in the extracted electron-phonon spectral function α2 F(ω). We also suggest that the small DOS structures produced by the two-band inter-action at energies between 20 and 100 meV can be observed only at very low temperature in junctions in perfect clean limit

Temperature dependence of the magnetic field penetration depth in YBa₂Cu₃O₇-b: effect of impurity scattering

Temperature dependence of the anisotropic magnetic field penetration depth of a two-band superconductor is calculated in the model of strong s-wave pairing interaction in one of the bands (S band) and induced superconductivity in the second band (N band). The results of the calculations are compared with experimental data on the (ab) plane and c axis penetration depth in YBa₂Cu₃O₇-b . It is shown that all recent measurements over the entire temperature range are consistent with the two-band model

Comparative Description of the Microwave Surface Impedance of Nb, BaKBiO, and YBaCuO

Measurements of microwave impedance versus temperature, $Z_{\rm s}(T)$, in Nb, Ba$_{0.6}$K$_{0.4}$BiO$_3$, and YBa$_2$Cu$_3$O$_{7-\delta}$ are given. The measurements were made by the “hot finger” cavity perturbation technique. The electromagnetic properties of Nb are in a good quantitative agreement with the isotropic s-wave BCS theory. This model can also describe the experimental $Z_{\rm s}(T)$ curves in Ba$_{0.6}$K$_{0.4}$BiO$_3$ crystals if the nonhomogeneous broadening of the superconducting transition is properly taken into account. The behavior of the microwave impedance of YBa$_2$Cu$_3$O$_{7-\delta}$ disagrees with the isotropic BCS theory. This suggests a strong anisotropy of the order parameter in this compound. Since the controversy between s- and d-wave descriptions of YBa$_2$Cu$_3$O$_{7-\delta}$ properties has not been resolved yet, we have checked a simpler strongly anisotropic s-wave model. Calculations by this model have been compared to measurements on YBa$_2$Cu$_3$O$_{7-\delta}$. With due account of the strong-coupling effects, two-band anisotropy, and impurity scattering in YBa$_2$Cu$_3$O$_{7-\delta}$, the agreement between the generalized BCS model and experimental data is surprisingly good