50 research outputs found
Rational approximation rate for the MĂŒntz system {xλn} with λnâ0
AbstractThe present paper establishes, by employing some new ideas, a nontrivial result of quantitative rational approximation rate for the MĂŒntz system {xλ n} in case λnâ0 as n â â
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 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 . 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 ”s 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.ĐĐ»Ń Đ¶ĐžĐČĐ»Đ”ĐœĐœŃ ĐșĐ»ŃŃŃŃĐŸĐœŃĐČ 5045 (ĐČĐžŃĐŸĐ±ĐœĐžŃŃĐČĐŸ SLAC) ŃĐœĐ¶Đ”ĐșŃŃĐčĐœĐŸĐłĐŸ ĐșĐŸĐŒĐżĐ»Đ”ĐșŃŃ ĐĐĐĐ-5 ĐČĐžĐșĐŸŃĐžŃŃĐŸĐČŃŃŃŃŃŃ
ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃĐž, ŃĐŸ ŃĐŸŃĐŒŃŃŃŃ ŃĐŒĐżŃĐ»ŃŃĐž ĐœĐ°ĐżŃŃĐłĐŸŃ 23,5 ĐșĐ, ŃŃŃŃĐŒĐŸĐŒ 6,3 ĐșĐ, ŃŃĐžĐČĐ°Đ»ŃŃŃŃ 3,7 ĐŒĐșŃ Ń ĐșŃĐ»ŃĐșĐŸŃŃŃ 4
ŃŃŃĐș. ĐĐŸĐœŃŃŃŃĐșŃŃŃ ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃŃĐČ, ŃĐŸĐ·ŃĐŸĐ±Đ»Đ”ĐœĐ° блОзŃĐșĐŸ 10 ŃĐŸĐșŃĐČ ŃĐŸĐŒŃ, ĐŽĐŸĐČДла ŃĐČĐŸŃ ĐœĐ°ĐŽŃĐčĐœŃŃŃŃ Ń, ŃĐ°Đ·ĐŸĐŒ Đ· ŃĐžĐŒ,
ĐŽĐŸĐ·ĐČĐŸĐ»ĐžĐ»Đ° ĐČĐžĐČŃĐžŃĐž Ń ĐČĐžŃĐČĐžŃĐž ŃлабĐșŃ ĐŒŃŃŃŃ ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃŃĐČ. ĐŃĐŸĐČĐ”ĐŽĐ”ĐœĐ° ŃĐŸĐ±ĐŸŃĐ° Đ· ĐżŃĐŽĐČĐžŃĐ”ĐœĐœŃ ŃŃабŃĐ»ŃĐœĐŸŃŃŃ ĐœĐ°ĐżŃŃгО
ĐœĐ° ĐșĐ»ŃŃŃŃĐŸĐœŃ, Đ·ĐŒĐ”ĐœŃĐ”ĐœĐœŃ ŃĐ°ŃĐŸĐČĐŸĐłĐŸ ŃĐŸĐ·ĐșĐžĐŽŃ ĐČŃĐŽ ŃĐŒĐżŃĐ»ŃŃŃ ĐŽĐŸ ŃĐŒĐżŃĐ»ŃŃŃ. ĐŃĐžĐČĐŸĐŽŃŃŃŃŃ ŃДзŃĐ»ŃŃĐ°ŃĐž ŃŃĐžĐČĐ°Đ»ĐŸŃ
Đ”ĐșŃплŃĐ°ŃĐ°ŃŃŃ ŃĐžŃĐ°ŃŃĐŸĐœŃĐČ ĐąĐĐ1-2500/50 Ń ĐąĐĐ1-5000/50 Ń ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃĐ°Ń
ĐŽĐ»Ń Đ¶ĐžĐČĐ»Đ”ĐœĐœŃ ĐșĐ»ŃŃŃŃĐŸĐœŃĐČ 5045.
ĐĐžĐșĐ»Đ°ĐŽĐ”ĐœĐŸ ŃДзŃĐ»ŃŃĐ°ŃĐž ŃĐ”ŃŃŃŃĐœĐžŃ
ŃŃпОŃŃĐČ ŃĐžŃĐ°ŃŃĐŸĐœĐ° ĐąĐĐ1-2500/50 ĐżŃĐž бŃĐ»ŃŃ ĐœŃж ĐżĐŸĐŽĐČŃĐčĐœĐŸĐŒŃ
пДŃĐ”ĐČĐ°ĐœŃĐ°Đ¶Đ”ĐœĐœŃ ĐżĐŸ Đ°ĐŒĐżĐ»ŃŃŃĐŽŃ ŃŃŃŃĐŒŃ ĐČ ĐœĐŸĐŒŃĐœĐ°Đ»ŃĐœĐŸĐŒŃ ŃĐ”Đ¶ĐžĐŒŃ ŃĐŸĐ±ĐŸŃĐž ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃĐ°.ĐĐ»Ń ĐżĐžŃĐ°ĐœĐžŃ ĐșлОŃŃŃĐŸĐœĐŸĐČ 5045 (ĐżŃĐŸĐžĐ·ĐČĐŸĐŽŃŃĐČĐŸ SLAC) ĐžĐœĐ¶Đ”ĐșŃĐžĐŸĐœĐœĐŸĐłĐŸ ĐșĐŸĐŒĐżĐ»Đ”ĐșŃĐ° ĐĐĐĐ-5 ĐžŃĐżĐŸĐ»ŃĐ·ŃŃŃŃŃ
ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃŃ, ŃĐŸŃĐŒĐžŃŃŃŃОД ĐžĐŒĐżŃĐ»ŃŃŃ ĐœĐ°ĐżŃŃĐ¶Đ”ĐœĐžĐ”ĐŒ 23,5 ĐșĐ, ŃĐŸĐșĐŸĐŒ 6,3 ĐșĐ, ЎлОŃДлŃĐœĐŸŃŃŃŃ 3,7 ĐŒĐșŃ ĐČ ĐșĐŸĐ»ĐžŃĐ”ŃŃĐČĐ” 4 ŃŃŃĐș. ĐĐŸĐœŃŃŃŃĐșŃĐžŃ ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃĐŸĐČ, ŃĐ°Đ·ŃĐ°Đ±ĐŸŃĐ°ĐœĐœĐ°Ń ĐŸĐșĐŸĐ»ĐŸ 10 Đ»Đ”Ń ĐœĐ°Đ·Đ°ĐŽ, ĐŽĐŸĐșазала ŃĐČĐŸŃ ĐœĐ°ĐŽĐ”Đ¶ĐœĐŸŃŃŃ Đž, ĐČĐŒĐ”ŃŃĐ” Ń ŃĐ”ĐŒ, ĐżĐŸĐ·ĐČĐŸĐ»ĐžĐ»Đ° ОзŃŃĐžŃŃ Đž ĐČŃŃĐČĐžŃŃ ŃлабŃĐ” ĐŒĐ”ŃŃĐ° ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃĐŸĐČ. ĐŃĐŸĐČĐ”ĐŽĐ”ĐœĐ° ŃĐ°Đ±ĐŸŃĐ° ĐżĐŸ ĐżĐŸĐČŃŃĐ”ĐœĐžŃ ŃŃабОлŃĐœĐŸŃŃĐž ĐœĐ°ĐżŃŃĐ¶Đ”ĐœĐžŃ ĐœĐ° ĐșлОŃŃŃĐŸĐœĐ”, ŃĐŒĐ”ĐœŃŃĐ”ĐœĐžŃ ĐČŃĐ”ĐŒĐ”ĐœĐœĐŸĐłĐŸ ŃазбŃĐŸŃĐ° ĐŸŃ ĐžĐŒĐżŃĐ»ŃŃĐ° Đș ĐžĐŒĐżŃĐ»ŃŃŃ. ĐŃĐžĐČĐŸĐŽŃŃŃŃ ŃДзŃĐ»ŃŃĐ°ŃŃ ĐŽĐ»ĐžŃДлŃĐœĐŸĐč ŃĐșŃплŃĐ°ŃĐ°ŃОО ŃĐžŃĐ°ŃŃĐŸĐœĐŸĐČ ĐąĐĐ1-2500/50 Đž ĐąĐĐ1-5000/50 ĐČ ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃĐ°Ń
ĐŽĐ»Ń ĐżĐžŃĐ°ĐœĐžŃ ĐșлОŃŃŃĐŸĐœĐŸĐČ 5045. ĐĐ·Đ»ĐŸĐ¶Đ”ĐœŃ ŃДзŃĐ»ŃŃĐ°ŃŃ ŃĐ”ŃŃŃŃĐœŃŃ
ĐžŃĐżŃŃĐ°ĐœĐžĐč ŃĐžŃĐ°ŃŃĐŸĐœĐ° ĐąĐĐ1-2500/50 ĐżŃĐž Đ±ĐŸĐ»Đ”Đ” ŃĐ”ĐŒ
ĐŽĐČĐŸĐčĐœĐŸĐč пДŃДгŃŃĐ·ĐșĐ” ĐżĐŸ Đ°ĐŒĐżĐ»ĐžŃŃĐŽĐ” ŃĐŸĐșĐ° ĐČ ĐœĐŸĐŒĐžĐœĐ°Đ»ŃĐœĐŸĐŒ ŃĐ”Đ¶ĐžĐŒĐ” ŃĐ°Đ±ĐŸŃŃ ĐŒĐŸĐŽŃĐ»ŃŃĐŸŃĐ°
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 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 âNN = 5.02 TeV
The second-order Fourier coefficients (Ï
) characterizing the azimuthal distributions of ΄(1S) and ΄(2S) mesons produced in PbPb collisions at = 5.02 TeV are studied. The ΄mesons 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. The scalar product method is used to extract the Ï
coefficients of the azimuthal distributions. Results are reported for the rapidity range |y| < 2.4, in the transverse momentum interval 0 < p < 50 GeV/c, and in three centrality ranges of 10â30%, 30â50% and 50â90%. In contrast to the J/Ï mesons, the measured Ï
values for the ΄ mesons are found to be consistent with zero