The Voltage-Current Characteristic of high T_c DC SQUID: theory, simulation, experiment

The analytical theory for the voltage-current characteristics of the large inductance (L>100 pH) high-T_c DC SQUIDs that has been developed previously is consistently compared with the computer simulations and the experiment. The theoretical voltage modulation for symmetric junctions is shown to be in a good agreement with the results of known computer simulations. It is shown that the asymmetry of the junctions results in the increase of the voltage modulation if the critical current is in excess of some threshold value (about 8 microAmps). Below this value the asymmetry leads to the reduction of the voltage modulation as compared to the symmetric case. The comparison with the experiment shows that the asymmetry can explain a large portion of experimental values of the voltage modulation which lie above the theoretical curve for symmetric DC SQUID. It also explains experimental points which lie below the curve at small critical currents. However, a significant portion of these values which lie below the curve cannot be explained by the junction asymmetry.Comment: 22 pages, 14 figure

Voltage-current and voltage-flux characteristics of asymmetric high TC DC SQUIDs

We report measurements of transfer functions and flux shifts of 20 on-chip high T$_C$ DC SQUIDs half of which were made purposely geometrically asymmetric. All of these SQUIDs were fabricated using standard high T$_C$ thin film technology and they were single layer ones, having 140 nm thickness of YBa$_2$Cu$_3$O$_{7-x}$ film deposited by laser ablation onto MgO bicrystal substrates with 24$^0$ misorientation angle. For every SQUID the parameters of its intrinsic asymmetry, i. e., the density of critical current and resistivity of every junction, were measured directly and independently. We showed that the main reason for the on-chip spreading of SQUIDs' voltage-current and voltage-flux characteristics was the intrinsic asymmetry. We found that for SQUIDs with a relative large inductance ($L>120$ pH) both the voltage modulation and the transfer function were not very sensitive to the junctions asymmetry, whereas SQUIDs with smaller inductance ($L\simeq 65-75$ pH) were more sensitive. The results obtained in the paper are important for the implementation in the sensitive instruments based on high T$_C$ SQUID arrays and gratings.Comment: 11 pages, 4 tables, 17 figures This version is substantially modified. The Introduction and Section 2 are completely rewritten, while experimental part is mainly the same as in previous versio

The check of QCD based on the tau-decay data analysis in the complex q^2-plane

The thorough analysis of the ALEPH data on hadronic tau-decay is performed in the framework of QCD. The perturbative calculations are performed in 3 and 4-loop approximations. The terms of the operator product expansion (OPE) are accounted up to dimension D=8. The value of the QCD coupling constant alpha_s(m_tau^2)=0.355 pm 0.025 was found from hadronic branching ratio R_tau. The V+A and V spectral function are analyzed using analytical properties of polarization operators in the whole complex q^2-plane. Borel sum rules in the complex q^2 plane along the rays, starting from the origin, are used. It was demonstrated that QCD with OPE terms is in agreement with the data for the coupling constant close to the lower error edge alpha_s(m_tau^2)=0.330. The restriction on the value of the gluonic condensate was found =0.006 pm 0.012 GeV^2. The analytical perturbative QCD was compared with the data. It is demonstrated to be in strong contradiction with experiment. The restrictions on the renormalon contribution were found. The instanton contributions to the polarization operator are analyzed in various sum rules. In Borel transformation they appear to be small, but not in spectral moments sum rules.Comment: 24 pages; 1 latex + 13 figure files. V2: misprints are corrected, uncertainty in alpha_s is explained in more transparent way, acknowledgement is adde

Two-loop N=4 Super Yang Mills effective action and interaction between D3-branes

We compute the leading low-energy term in the planar part of the 2-loop contribution to the effective action of $\N=4$ SYM theory in 4 dimensions, assuming that the gauge group $SU(N+1)$ is broken to $SU(N) x U(1)$ by a constant scalar background $X$. While the leading 1-loop correction is the familiar $c_1 F^4/|X|^4$ term, the 2-loop expression starts with $c_2 F^6/|X|^8$. The 1-loop constant $c_1$ is known to be equal to the coefficient of the $F^4$ term in the Born-Infeld action for a probe D3-brane separated by distance $|X|$ from a large number $N$ of coincident D3-branes. We show that the same is true also for the 2-loop constant $c_2$: it matches the coefficient of the $F^6$ term in the D3-brane probe action. In the context of the AdS/CFT correspondence, this agreement suggests a non-renormalization of the coefficient of the $F^6$ term beyond two loops. Thus the result of hep-th/9706072 about the agreement between the $v^6$ term in the D0-brane supergravity interaction potential and the corresponding 2-loop term in the 1+0 dimensional reduction of $\N=4$ SYM theory has indeed a direct generalization to 1+3 dimensions, as conjectured earlier in hep-th/9709087. We also discuss the issue of gauge theory -- supergravity correspondence for higher order ($F^8$, etc.) terms.Comment: 33 pages, late

Factorization of integrals, defining the beta-function, into integrals of total derivatives in N=1 SQED, regularized by higher derivatives

Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the beta-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics in all orders.Comment: 14 page