Rational approximation rate for the Müntz system {xλn} with λn↘0

AbstractThe present paper establishes, by employing some new ideas, a nontrivial result of quantitative rational approximation rate for the Müntz system {xλ n} in case λn↘0 as n → ∞

Nonequilibrium Evolution of Correlation Functions: A Canonical Approach

We study nonequilibrium evolution in a self-interacting quantum field theory invariant under space translation only by using a canonical approach based on the recently developed Liouville-von Neumann formalism. The method is first used to obtain the correlation functions both in and beyond the Hartree approximation, for the quantum mechanical analog of the $\phi^{4}$ model. The technique involves representing the Hamiltonian in a Fock basis of annihilation and creation operators. By separating it into a solvable Gaussian part involving quadratic terms and a perturbation of quartic terms, it is possible to find the improved vacuum state to any desired order. The correlation functions for the field theory are then investigated in the Hartree approximation and those beyond the Hartree approximation are obtained by finding the improved vacuum state corrected up to ${\cal O}(\lambda^2)$. These correlation functions take into account next-to-leading and next-to-next-to-leading order effects in the coupling constant. We also use the Heisenberg formalism to obtain the time evolution equations for the equal-time, connected correlation functions beyond the leading order. These equations are derived by including the connected 4-point functions in the hierarchy. The resulting coupled set of equations form a part of infinite hierarchy of coupled equations relating the various connected n-point functions. The connection with other approaches based on the path integral formalism is established and the physical implications of the set of equations are discussed with particular emphasis on thermalization.Comment: Revtex, 32 pages; substantial new material dealing with non-equilibrium evolution beyond Hartree approx. based on the LvN formalism, has been adde

The VEPP-5 injection complex modulator revision and operational experience

For the VEPP-5 injection complex klystrons (5045, SLAC Lab., USA) power supply the four modulators producing a pulse voltage of 23.5 kV, a current of 6.3 kA, a pulse-top-duration of 3.7 µs are used. The modulator scheme designed over ten years ago has proved its reliability and let us to find out and study the weak spots of the modulators. The output voltage stability and pulse-to-pulse time jitter improvements are made. The results of the thyratrons TGI1-2500/50 and TGI1-5000/50A long-term exploitation in the VEPP-5 injection complex modulators are presented. The test results of the thyratron TGI1-2500/50 operating in the mode of more then twice pulse current overload at the nominal mode of modulator operation are also presented.Для живлення клістронів 5045 (виробництво SLAC) інжекційного комплексу ВЕПП-5 використовуються модулятори, що формують імпульси напругою 23,5 кВ, струмом 6,3 кА, тривалістю 3,7 мкс у кількості 4 штук. Конструкція модуляторів, розроблена близько 10 років тому, довела свою надійність і, разом з тим, дозволила вивчити і виявити слабкі місця модуляторів. Проведена робота з підвищення стабільності напруги на клістроні, зменшенню часового розкиду від імпульсу до імпульсу. Приводяться результати тривалої експлуатації тиратронів ТГІ1-2500/50 і ТГІ1-5000/50 у модуляторах для живлення клістронів 5045. Викладено результати ресурсних іспитів тиратрона ТГІ1-2500/50 при більш ніж подвійному перевантаженню по амплітуді струму в номінальному режимі роботи модулятора.Для питания клистронов 5045 (производство SLAC) инжекционного комплекса ВЭПП-5 используются модуляторы, формирующие импульсы напряжением 23,5 кВ, током 6,3 кА, длительностью 3,7 мкс в количестве 4 штук. Конструкция модуляторов, разработанная около 10 лет назад, доказала свою надежность и, вместе с тем, позволила изучить и выявить слабые места модуляторов. Проведена работа по повышению стабильности напряжения на клистроне, уменьшению временного разброса от импульса к импульсу. Приводятся результаты длительной эксплуатации тиратронов ТГИ1-2500/50 и ТГИ1-5000/50 в модуляторах для питания клистронов 5045. Изложены результаты ресурсных испытаний тиратрона ТГИ1-2500/50 при более чем двойной перегрузке по амплитуде тока в номинальном режиме работы модулятора

Transverse phase-locking in fully frustrated Josephson junction arrays: a new type of fractional giant steps

We study, analytically and numerically, phase locking of driven vortex lattices in fully-frustrated Josephson junction arrays at zero temperature. We consider the case when an ac current is applied {\it perpendicular} to a dc current. We observe phase locking, steps in the current-voltage characteristics, with a dependence on external ac-drive amplitude and frequency qualitatively different from the Shapiro steps, observed when the ac and dc currents are applied in parallel. Further, the critical current increases with increasing transverse ac-drive amplitude, while it decreases for longitudinal ac-drive. The critical current and the phase-locked current step width, increase quadratically with (small) amplitudes of the ac-drive. For larger amplitudes of the transverse ac-signal, we find windows where the critical current is hysteretic, and windows where phase locking is suppressed due to dynamical instabilities. We characterize the dynamical states around the phase-locking interference condition in the $IV$ curve with voltage noise, Lyapunov exponents and Poincar\'e sections. We find that zero temperature phase-locking behavior in large fully frustrated arrays is well described by an effective four plaquette model.Comment: 12 pages, 11 figure

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page

Measurement of the azimuthal anisotropy of Y(1S) and Y(2S) mesons in PbPb collisions at √S^{S}NN = 5.02 TeV

The second-order Fourier coefficients (υ$_{2}$) characterizing the azimuthal distributions of Υ(1S) and Υ(2S) mesons produced in PbPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are studied. The Υmesons are reconstructed in their dimuon decay channel, as measured by the CMS detector. The collected data set corresponds to an integrated luminosity of 1.7 nb$^{-1}$. The scalar product method is used to extract the υ$_{2}$ coefficients of the azimuthal distributions. Results are reported for the rapidity range |y| < 2.4, in the transverse momentum interval 0 < p$_{T}$ < 50 GeV/c, and in three centrality ranges of 10–30%, 30–50% and 50–90%. In contrast to the J/ψ mesons, the measured υ$_{2}$ values for the Υ mesons are found to be consistent with zero