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.

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

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

Exact Three Dimensional Casimir Force Amplitude, CC-function and Binder's Cumulant Ratio: Spherical Model Results

The three dimensional mean spherical model on a hypercubic lattice with a film geometry $L\times \infty ^2$ under periodic boundary conditions is considered in the presence of an external magnetic field $H$. The universal Casimir amplitude $\Delta$ and the Binder's cumulant ratio $B$ are calculated exactly and found to be $\Delta =-2\zeta (3)/(5\pi)\approx -0.153051$ and $B=2\pi /(\sqrt{5}\ln ^3[(1+\sqrt{5})/2]).$ A discussion on the relations between the finite temperature $C$-function, usually defined for quantum systems, and the excess free energy (due to the finite-size contributions to the free energy of the system) scaling function is presented. It is demonstrated that the $C$-function of the model equals 4/5 at the bulk critical temperature $T_c$. It is analytically shown that the excess free energy is a monotonically increasing function of the temperature $T$ and of the magnetic field $|H|$ in the vicinity of $T_c.$ This property is supposed to hold for any classical $d$-dimensional $O(n),n>2,$ model with a film geometry under periodic boundary conditions when $d\leq 3$. An analytical evidence is also presented to confirm that the Casimir force in the system is negative both below and in the vicinity of the bulk critical temperature $T_c.$Comment: 12 pages revtex, one eps figure, submitted to Phys. Rev E A set of references added with the text needed to incorporate them. Small changes in the title and in the abstrac

Casimir forces in binary liquid mixtures

If two ore more bodies are immersed in a critical fluid critical fluctuations of the order parameter generate long ranged forces between these bodies. Due to the underlying mechanism these forces are close analogues of the well known Casimir forces in electromagnetism. For the special case of a binary liquid mixture near its critical demixing transition confined to a simple parallel plate geometry it is shown that the corresponding critical Casimir forces can be of the same order of magnitude as the dispersion (van der Waals) forces between the plates. In wetting experiments or by direct measurements with an atomic force microscope the resulting modification of the usual dispersion forces in the critical regime should therefore be easily detectable. Analytical estimates for the Casimir amplitudes Delta in d=4-epsilon are compared with corresponding Monte-Carlo results in d=3 and their quantitative effect on the thickness of critical wetting layers and on force measurements is discussed.Comment: 34 pages LaTeX with revtex and epsf style, to appear in Phys. Rev.

Universality of the thermodynamic Casimir effect

Recently a nonuniversal character of the leading spatial behavior of the thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys. Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this observation and show that there is no such leading nonuniversal term in systems with short-ranged interactions if one treats properly the effects generated by a sharp momentum cutoff in the Fourier transform of the interaction potential. We also conclude that lattice and continuum models then produce results in mutual agreement independent of the cutoff scheme, contrary to the aforementioned report. All results are consistent with the {\em universal} character of the Casimir force in systems with short-ranged interactions. The effects due to dispersion forces are discussed for systems with periodic or realistic boundary conditions. In contrast to systems with short-ranged interactions, for $L/\xi \gg 1$ one observes leading finite-size contributions governed by power laws in $L$ due to the subleading long-ranged character of the interaction, where $L$ is the finite system size and $\xi$ is the correlation length.Comment: 11 pages, revtex, to appear in Phys. Rev. E 68 (2003

Fluctuation - induced forces in critical fluids

The current knowledge about fluctuation - induced long - ranged forces is summarized. Reference is made in particular to fluids near critical points, for which some new insight has been obtained recently. Where appropiate, results of analytic theory are compared with computer simulations and experiments.Comment: Topical review, 24 pages RevTeX, 6 figure

Casimir Forces between Spherical Particles in a Critical Fluid and Conformal Invariance

Mesoscopic particles immersed in a critical fluid experience long-range Casimir forces due to critical fluctuations. Using field theoretical methods, we investigate the Casimir interaction between two spherical particles and between a single particle and a planar boundary of the fluid. We exploit the conformal symmetry at the critical point to map both cases onto a highly symmetric geometry where the fluid is bounded by two concentric spheres with radii R_- and R_+. In this geometry the singular part of the free energy F only depends upon the ratio R_-/R_+, and the stress tensor, which we use to calculate F, has a particularly simple form. Different boundary conditions (surface universality classes) are considered, which either break or preserve the order-parameter symmetry. We also consider profiles of thermodynamic densities in the presence of two spheres. Explicit results are presented for an ordinary critical point to leading order in epsilon=4-d and, in the case of preserved symmetry, for the Gaussian model in arbitrary spatial dimension d. Fundamental short-distance properties, such as profile behavior near a surface or the behavior if a sphere has a `small' radius, are discussed and verified. The relevance for colloidal solutions is pointed out.Comment: 37 pages, 2 postscript figures, REVTEX 3.0, published in Phys. Rev. B 51, 13717 (1995

Spin-dynamics simulations of the triangular antiferromagnetic XY model

Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic behavior of the classical, antiferromagnetic XY model on a triangular lattice with linear sizes $L \leq 300$. The temporal evolutions of spin configurations were obtained by solving numerically the coupled equations of motion for each spin using fourth-order Suzuki-Trotter decompositions of exponential operators. From space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms we obtained the dynamic structure factor $S({\bf q},w)$ for momentum ${\bf q}$ and frequency $\omega$. Below $T_{KT}$(Kosterlitz-Thouless transition), both the in-plane ($S^{xx}$) and the out-of-plane ($S^{zz}$) components of $S({\bf q},\omega)$ exhibit very strong and sharp spin-wave peaks. Well above $T_{KT}$, $S^{xx}$ and $S^{zz}$ apparently display a central peak, and spin-wave signatures are still seen in $S^{zz}$. In addition, we also observed an almost dispersionless domain-wall peak at high $\omega$ below $T_{c}$(Ising transition), where long-range order appears in the staggered chirality. Above $T_{c}$, the domain-wall peak disappears for all $q$. The lineshape of these peaks is captured reasonably well by a Lorentzian form. Using a dynamic finite-size scaling theory, we determined the dynamic critical exponent $z$ = 1.002(3). We found that our results demonstrate the consistency of the dynamic finite-size scaling theory for the characteristic frequeny $\omega_{m}$ and the dynamic structure factor $S({\bf q},\omega)$ itself.Comment: 8 pages, RevTex, 10 figures, submitted to PR

Critical adsorption on curved objects

A systematic fieldtheoretic description of critical adsorption on curved objects such as spherical or rodlike colloidal particles immersed in a fluid near criticality is presented. The temperature dependence of the corresponding order parameter profiles and of the excess adsorption are calculated explicitly. Critical adsorption on elongated rods is substantially more pronounced than on spherical particles. It turns out that, within the context of critical phenomena in confined geometries, critical adsorption on a microscopically thin `needle' represents a distinct universality class of its own. Under favorable conditions the results are relevant for the flocculation of colloidal particles.Comment: 52 pages, 10 figure