Anti-phase locking in a two-dimensional Josephson junction array

We consider theoretically phase locking in a simple two-dimensional Josephson junction array consisting of two loops coupled via a joint line transverse to the bias current. Ring inductances are supposed to be small, and special emphasis is taken on the influence of external flux. Is is shown, that in the stable oscillation regime both cells oscillate with a phase shift equal to $\pi$ (i.e. anti-phase). This result may explain the low radiation output obtained so far in two-dimensional Josephson junction arrays experimentally.Comment: 11 pages, REVTeX, 1 Postscript figure, Subm. to Appl. Phys. Let

Critical Casimir Effect in 3He-4He films

Universal aspects of the thermodynamic Casimir effect in wetting films of 3He-4He mixtures near their bulk tricritical point are studied within suitable models serving as representatives of the corresponding universality class. The effective forces between the boundaries of such films arising from the confinement are calculated along isotherms at several fixed concentrations of 3He. Nonsymmetric boundary conditions impose nontrivial concentration profiles leading to repulsive Casimir forces which exhibit a rich behavior of the crossover between the tricritical point and the line of critical points. The theoretical results agree with published experimental data and emphasize the importance of logarithmic corrections.Comment: 12 pages, 4 figures, submitted to the Phys. Rev. Let

Fluctuation force exerted by a planar self-avoiding polymer

Using results from Schramm Loewner evolution (SLE), we give the expression of the fluctuation-induced force exerted by a polymer on a small impenetrable disk, in various 2-dimensional domain geometries. We generalize to two polymers and examine whether the fluctuation force can trap the object into a stable equilibrium. We compute the force exerted on objects at the domain boundary, and the force mediated by the polymer between such objects. The results can straightforwardly be extended to any SLE interface, including Ising, percolation, and loop-erased random walks. Some are relevant for extremal value statistics.Comment: 7 pages, 22 figure

The coil-globule transition of confined polymers

We study long polymer chains in a poor solvent, confined to the space between two parallel hard walls. The walls are energetically neutral and pose only a geometric constraint which changes the properties of the coil-globule (or "$\theta$-") transition. We find that the $\theta$ temperature increases monotonically with the width $D$ between the walls, in contrast to recent claims in the literature. Put in a wider context, the problem can be seen as a dimensional cross over in a tricritical point of a $\phi^4$ model. We roughly verify the main scaling properties expected for such a phenomenon, but we find also somewhat unexpected very long transients before the asymptotic scaling regions are reached. In particular, instead of the expected scaling $R\sim N^{4/7}$ exactly at the ($D$-dependent) theta point we found that $R$ increases less fast than $N^{1/2}$, even for extremely long chains.Comment: 5 pages, 6 figure

Theory of phase-locking in generalized hybrid Josephson junction arrays

A recently proposed scheme for the analytical treatment of the dynamics of two-dimensional hybrid Josephson junction arrays is extended to a class of generalized hybrid arrays with ''horizontal'' shunts involving a capacitive as well as an inductive component. This class of arrays is of special interest, because the internal cell coupling has been shown numerically to favor in-phase synchronization for certain parameter values. As a result, we derive limits on the circuit design parameters for realizing this state. In addition, we obtain formulas for the flux-dependent frequency including flux-induced switching processes between the in-phase and anti-phase oscillation regime. The treatment covers unloaded arrays as well as arrays shunted via an external load.Comment: 24 pages, REVTeX, 5 Postscript figures, Subm. to Phys. Rev.

Influence of Capillary Condensation on the Near-Critical Solvation Force

We argue that in a fluid, or magnet, confined by adsorbing walls which favour liquid, or (+) phase, the solvation (Casimir) force in the vicinity of the critical point is strongly influenced by capillary condensation which occurs below the bulk critical temperature T_c. At T slightly below and above T_c, a small bulk field h<0, which favours gas, or (-) phase, leads to residual condensation and a solvation force which is much more attractive (at the same large wall separation) than that found exactly at the critical point. Our predictions are supported by results obtained from density-matrix renormalization-group calculations in a two-dimensional Ising strip subject to identical surface fields.Comment: 4 Pages, RevTeX, and 3 figures include

THEORY OF PHASE-LOCKING IN SMALL JOSEPHSON JUNCTION CELLS

Within the RSJ model, we performed a theoretical analysis of phase-locking in elementary strongly coupled Josephson junction cells. For this purpose, we developed a systematic method allowing the investigation of phase-locking in cells with small but non-vanishing loop inductance.The voltages across the junctions are found to be locked with very small phase difference for almost all values of external flux. However, the general behavior of phase-locking is found to be just contrary to that according to weak coupling. In case of strong coupling there is nearly no influence of external magnetic flux on the phases, but the locking-frequency becomes flux-dependent. The influence of parameter splitting is considered as well as the effect of small capacitive shunting of the junctions. Strongly coupled cells show synchronization even for large parameter splitting. Finally, a study of the behavior under external microwave radiation shows that the frequency locking-range becomes strongly flux-dependent, whereas the locking frequency itself turns out to be flux-independent.Comment: 26 pages, REVTEX, 9 PS figures appended in uuencoded form at the end, submitted to Phys. Rev. B

Local functional models of critical correlations in thin-films

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free-energy and scaling of one-point functions in critical thin films. This approach is extended to predict the two-point correlation function G in critical thin-films with symmetric surface fields in arbitrary dimension d. In d=2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths as well as the detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we present new numerical predictions for the universal finite-size correlation length and scaling functions determining the structure of G across the thin-film. Highly accurate analytical closed form expressions for these universal properties are derived in arbitrary dimension.Comment: 4 pages, 1 postscript figure. Submitted to Phys Rev Let

Perturbative calculation of the scaled factorial moments in second-order quark-hadron phase transition within the Ginzburg-Landau description

The scaled factorial moments $F_q$ are studied for a second-order quark-hadron phase transition within the Ginzburg-Landau description. The role played by the ground state of the system under low temperature is emphasized. After a local shift of the order parameter the fluctuations are around the ground state, and a perturbative calculation for $F_q$ can be carried out. Power scaling between $F_q$'s is shown, and a universal scaling exponent $\nu\simeq 1.75$ is given for the case with weak correlations and weak self-interactions.Comment: 12 pages in RevTeX, 12 eps figure

Critical Casimir effect and wetting by helium mixtures

We have measured the contact angle of the interface of phase-separated $^{3}$He-$^{4}$He mixtures against a sapphire window. We have found that this angle is finite and does not tend to zero when the temperature approaches $T_t$, the temperature of the tri-critical point. On the contrary, it increases with temperature. This behavior is a remarkable exception to what is generally observed near critical points, i.e. "critical point wetting''. We propose that it is a consequence of the "critical Casimir effect'' which leads to an effective attraction of the $^{3}$He-$^{4}$He interface by the sapphire near $T_{t}$.Comment: submitted july 13 (2002), published march 20 (2003