Spontaneous spinning of a magnet levitating over a superconductor

A permanent magnet levitating over a superconductor is found to spontaneously spin, overcoming resistance to air friction. We explain the physics behind this remarkable effect.Comment: See http://physics.ucsd.edu/~jorge/spinning.html for movie clips of the effec

The Hubbard model with smooth boundary conditions

We apply recently developed smooth boundary conditions to the quantum Monte Carlo simulation of the two-dimensional Hubbard model. At half-filling, where there is no sign problem, we show that the thermodynamic limit is reached more rapidly with smooth rather than with periodic or open boundary conditions. Away from half-filling, where ordinarily the simulation cannot be carried out at low temperatures due to the existence of the sign problem, we show that smooth boundary conditions allow us to reach significantly lower temperatures. We examine pairing correlation functions away from half-filling in order to determine the possible existence of a superconducting state. On a $10\times 10$ lattice for $U=4$, at a filling of $\langle n \rangle = 0.87$ and an inverse temperature of $\beta=10$, we did find enhancement of the $d$-wave correlations with respect to the non-interacting case, a possible sign of $d$-wave superconductivity.Comment: 16 pages RevTeX, 9 postscript figures included (Figure 1 will be faxed on request

Optical sum rule violation, superfluid weight and condensation energy in the cuprates

The model of hole superconductivity predicts that the superfluid weight in the zero-frequency $\delta$-function in the optical conductivity has an anomalous contribution from high frequencies, due to lowering of the system's kinetic energy upon entering the superconducting state. The lowering of kinetic energy, mainly in-plane in origin, accounts for both the condensation energy of the superconductor as well as an increased potential energy due to larger Coulomb repulsion in the paired state. It leads to an apparent violation of the conductivity sum rule, which in the clean limit we predict to be substantially larger for in-plane than for c-axis conductivity. However, because cuprates are in the dirty limit for c-axis transport, the sum rule violation is found to be greatly enhanced in the c-direction. The model predicts the sum rule violation to be largest in the underdoped regime and to decrease with doping, more rapidly in the c-direction that in the plane. So far, experiments have detected sum rule violation in c-axis transport in several cuprates, as well as a decrease and disappearance of this violation for increasing doping, but no violation in-plane. We explore the predictions of the model for a wide range of parameters, both in the absence and in the presence of disorder, and the relation with current experimental knowledge.Comment: submitted to Phys.Rev.

Understanding High-Temperature Superconductors with Quantum Cluster Theories

Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a mean-field approximation. These methods become exact when the cluster size diverges, and most recover the corresponding (dynamical) mean-field approximation when the cluster size becomes one. Here we will review systematic dynamical cluster simulations of the two-dimensional Hubbard model, that display phenomena remarkably similar to those found in the cuprates, including antiferromagnetism, superconductivity and pseudogap behavior. We will then discuss results for the structure of the pairing mechanism in this model, obtained from a combination of dynamical cluster results and diagrammatic techniques.Comment: 8 pages, 12 figures; submitted to proceedings of M2S-HTSC VIII, Dresden 200

Adaptive Sampling Approach to the Negative Sign Problem in the Auxiliary Field Quantum Monte Carlo Method

We propose a new sampling method to calculate the ground state of interacting quantum systems. This method, which we call the adaptive sampling quantum monte carlo (ASQMC) method utilises information from the high temperature density matrix derived from the monte carlo steps. With the ASQMC method, the negative sign ratio is greatly reduced and it becomes zero in the limit $\Delta \tau$ goes to zero even without imposing any constraint such like the constraint path (CP) condition. Comparisons with numerical results obtained by using other methods are made and we find the ASQMC method gives accurate results over wide regions of physical parameters values.Comment: 8 pages, 7 figure

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove

Self-Consistent Quasi-Particle RPA for the Description of Superfluid Fermi Systems

Self-Consistent Quasi-Particle RPA (SCQRPA) is for the first time applied to a more level pairing case. Various filling situations and values for the coupling constant are considered. Very encouraging results in comparison with the exact solution of the model are obtained. The nature of the low lying mode in SCQRPA is identified. The strong reduction of the number fluctuation in SCQRPA vs BCS is pointed out. The transition from superfluidity to the normal fluid case is carefully investigated.Comment: 23 pages, 18 figures and 1 table, submitted to Phys. Rev.

Time-dependent Gutzwiller theory of magnetic excitations in the Hubbard model

We use a spin-rotational invariant Gutzwiller energy functional to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). The method can be viewed as an extension of the previously developed GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. {\bf 86}, 2605 (2001)] with respect to the inclusion of the magnetic excitations. Unlike the charge case, no assumptions about the time evolution of the double occupancy are needed in this case. Interestingly, in a spin-rotational invariant system, we find the correct degeneracy between triplet excitations, showing the consistency of both computations. Since no restrictions are imposed on the symmetry of the underlying saddle-point solution, our approach is suitable for the evaluation of the magnetic susceptibility and dynamical structure factor in strongly correlated inhomogeneous systems. We present a detailed study of the quality of our approach by comparing with exact diagonalization results and show its much higher accuracy compared to the conventional Hartree-Fock+RPA theory. In infinite dimensions, where the GA becomes exact for the Gutzwiller variational energy, we evaluate ferromagnetic and antiferromagnetic instabilities from the transverse magnetic susceptibility. The resulting phase diagram is in complete agreement with previous variational computations.Comment: 12 pages, 8 figure