Microscopic Derivation of the Ginzburg-Landau Equations for a d-wave Superconductor

The Ginzburg-Landau (GL) equations for a d-wave superconductor are derived within the context of two microscopic lattice models used to describe the cuprates: the extended Hubbard model and the Antiferromagnetic-van Hove model. Both models have pairing on nearest-neighbour links, consistent with theories for d-wave superconductivity mediated by spin fluctuations. Analytical results obtained for the extended Hubbard model at low electron densities and weak-coupling are compared to results reported previously for a d-wave superconductor in the continuum. The variation of the coefficients in the GL equations with carrier density, temperature, and coupling constants are calculated numerically for both models. The relative importance of anisotropic higher-order terms in the GL free energy is investigated, and the implications for experimental observations of the vortex lattice are considered.Comment: ReVTeX, 18 pages, 7 postscript figures. To appear in Phys. Rev. B (Jan. 1, 1997

Multiple Invaded Consolidating Materials

We study a multiple invasion model to simulate corrosion or intrusion processes. Estimated values for the fractal dimension of the invaded region reveal that the critical exponents vary as function of the generation number $G$, i.e., with the number of times the invasion process takes place. The averaged mass $M$ of the invaded region decreases with a power-law as a function of $G$, $M\sim G^{\beta}$, where the exponent $\beta\approx 0.6$. We also find that the fractal dimension of the invaded cluster changes from $d_{1}=1.887\pm0.002$ to $d_{s}=1.217\pm0.005$. This result confirms that the multiple invasion process follows a continuous transition from one universality class (NTIP) to another (optimal path). In addition, we report extensive numerical simulations that indicate that the mass distribution of avalanches $P(S,L)$ has a power-law behavior and we find that the exponent $\tau$ governing the power-law $P(S,L)\sim S^{-\tau}$ changes continuously as a function of the parameter $G$. We propose a scaling law for the mass distribution of avalanches for different number of generations $G$.Comment: 8 pages and 16 figure

Self-consistent fragmented excited states of trapped condensates

Self-consistent excited states of condensates are solutions of the Gross-Pitaevskii (GP) equation and have been amply discussed in the literature and related to experiments. By introducing a more general mean-field which includes the GP one as a special case, we find a new class of self-consistent excited states. In these states macroscopic numbers of bosons reside in different one-particle functions, i.e., the states are fragmented. Still, a single chemical potential is associated with the condensate. A numerical example is presented, illustrating that the energies of the new, fragmented, states are much lower than those of the GP excited states, and that they are stable to variations of the particle number and shape of the trap potential.Comment: (11 pages 2 figures, submitted to PRL

Skeleton and fractal scaling in complex networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in-silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.Comment: 4 pages, 2 figures, final version published in PR

Testing equivalence of pure quantum states and graph states under SLOCC

A set of necessary and sufficient conditions are derived for the equivalence of an arbitrary pure state and a graph state on n qubits under stochastic local operations and classical communication (SLOCC), using the stabilizer formalism. Because all stabilizer states are equivalent to a graph state by local unitary transformations, these conditions constitute a classical algorithm for the determination of SLOCC-equivalence of pure states and stabilizer states. This algorithm provides a distinct advantage over the direct solution of the SLOCC-equivalence condition for an unknown invertible local operator S, as it usually allows for easy detection of states that are not SLOCC-equivalent to graph states.Comment: 9 pages, to appear in International Journal of Quantum Information; Minor typos corrected, updated references

Analytical results for a trapped, weakly-interacting Bose-Einstein condensate under rotation

We examine the problem of a repulsive, weakly-interacting and harmonically trapped Bose-Einstein condensate under rotation. We derive a simple analytic expression for the energy incorporating the interactions when the angular momentum per particle is between zero and one and find that the interaction energy decreases linearly as a function of the angular momentum in agreement with previous numerical and limiting analytical studies.Comment: 3 pages, RevTe

Shape deformations and angular momentum transfer in trapped Bose-Einstein condensates

Angular momentum can be transferred to a trapped Bose-Einstein condensate by distorting its shape with an external rotating field, provided the rotational frequency is larger than a critical frequency fixed by the energy and angular momentum of the excited states of the system. By using the Gross-Pitaevskii equation and sum rules, we explore the dependence of such a critical frequency on the multipolarity of the excitations and the asymmetry of the confining potential. We also discuss its possible relevance for vortex nucleation in rotating traps.Comment: 4 pages revtex, 2 figures include