arXiv subjects

Paul M. Goldbart

Publications and source records attributed to Paul M. Goldbart.

105 records · Page 6Linked to original sources

arXiv1998

Antiferromagnetic hedgehogs with superconducting cores

Excitations of the antiferromagnetic state that resemble antiferromagnetic hedgehogs at large distances but are predominantly superconducting inside a core region are discussed within the context of Zhang's SO(5)-symmetry-based approach to the physics of high-temperature superconducting materials. Nonsingular, in contrast with their hedgehog cousins in pure antiferromagnetism, these texture excitations are what hedgehogs become when the antiferromagnetic order parameter is permitted to "escape" into superconducting directions. The structure of such excitations is determined in a simple setting, and a number of their experimental implications are examined.

cond-mat.supr-con↗

arXiv1998

Observing the Berry phase in diffusive conductors: Necessary conditions for adiabaticity

In a recent preprint (cond-mat/9803170), van~Langen, Knops, Paasschens and Beenakker attempt to re-analyze the proposal of Loss, Schoeller and Goldbart (LSG) [Phys. Rev. B~48, 15218 (1993)] concerning Berry phase effects in the magnetoconductance of diffusive systems. Van Langen et al. claim that the adiabatic approximation for the Cooperon previously derived by LSG is not valid in the adiabatic regime identified by LSG. It is shown that the claim of van~Langen et al. is not correct, and that, on the contrary, the magnetoconductance does exhibit the Berry phase effect within the LSG regime of adiabaticity. The conclusion reached by van~Langen et al. is based on a misinterpretation of field-induced dephasing effects, which can mask the Berry phase (and any other phase coherent phenomena) for certain parameter values.

cond-mat.mes-hall↗

arXiv1998

Elasticity near the vulcanization transition

Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A semi-microscopic statistical-mechanical theory is presented of the latter signature that accounts for both thermal fluctuations and quenched disorder. It is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.

cond-mat.dis-nn↗

arXiv1998

Domain walls and the conductivity of mesoscopic ferromagnets

Quantum interference phenomena in the conductivity of mesoscopic ferromagnets are considered, particularly with regard to the effects of geometric phases acquired by electrons propagating through regions of spatially varying magnetization (due, e.g., to magnetic domain walls). Weak localization and electron-electron interaction quantum corrections to the conductivity and universal conductance fluctuations are discussed. Experiments are proposed for multiply-connected geometries that should reveal conductance oscillations with variations of the profile of the magnetization.

cond-mat.mes-hall↗

arXiv1997

Intrinsic resistivity and the SO(5) theory of high-temperature superconductors

The topological structure of the order parameter in Zhang's SO(5) theory of superconductivity allows for an unusual type of dissipation mechanism via which current-carrying states can decay. The resistivity due to this mechanism, which involves orientation rather than amplitude order-parameter fluctuations, is calculated for the case of a thin superconducting wire. The approach is a suitably modified version of that pioneered by Langer and Ambegaokar for conventional superconductors.

cond-mat.supr-con↗

arXiv1997

Multiply-connected Bose-Einstein condensed alkali gases: Current-carrying states and their decay

The ability to support metastable current-carrying states in multiply-connected settings is one of the prime signatures of superfluidity. Such states are investigated theoretically for the case of trapped Bose condensed alkali gases, particularly with regard to the rate at which they decay via thermal fluctuations. The lifetimes of metastable currents can be either longer or shorter than experimental time-scales. A scheme for the experimental detection of metastable states is sketched.

cond-mat.stat-mech↗

arXiv1997

Quasi-Andreev reflection in inhomogeneous Luttinger liquids

Reflection of charge excitations at the step in the interaction strength in a Luttinger liquid can be of the Andreev type, even if the interactions are purely repulsive. The region with stronger repulsion plays the role of a normal metal in a normal-metal /superconductor junction, whereas the region with weaker repulsion plays the role of a superconductor. It is shown that this quasi-Andreev reflection leads to a number of proximity-like effects, including the local enhancement (suppression) of superconducting fluctuations on the quasi-normal (quasi-superconducting) side of the step, significant modification of the local density of states, as well as others. The observable consequences of these proximity effects are analyzed for the case of single- and two-particle tunneling from a normal-metal or superconducting tip into an inhomogeneous Luttinger-liquid wire.

cond-mat.mes-hall↗

arXiv1997

Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field

The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free energy and entropy, which are argued to be self-averaging in the thermodynamic limit. These thermodynamic functions are shown to coincide exactly with those of a Generalized Random Energy Model, in agreement with previous results obtained using Gaussian field theories in an ultrametric space.

cond-mat.mes-hall↗

arXiv1997

Universality and its Origins at the Amorphous Solidification Transition

Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling functions that describe the order parameter and (equivalently) the statistical distribution of localization lengths for these localized particles. The purpose of this Paper is to discuss the origins and consequences of this universality, and in doing so, three themes are explored. First, a replica-Landau-type approach is formulated for the universality class of systems that are composed of extended objects connected by permanent random constraints and undergo amorphous solidification at a critical density of constraints. This formulation generalizes the cases of randomly cross-linked and end-linked macromolecular systems, discussed previously. The universal replica free energy is constructed, in terms of the replica order parameter appropriate to amorphous solidification, the value of the order parameter is obtained in the liquid and amorphous solid states, and the chief universal characteristics are determined. Second, the theory is reformulated in terms of the distribution of local static density fluctuations rather than the replica order parameter. It is shown that a suitable free energy can be constructed, depending on the distribution of static density fluctuations, and that this formulation yields precisely the same conclusions as the replica approach. Third, the universal predictions of the theory are compared with the results of extensive numerical simulations of randomly cross-linked macromolecular systems, due to Barsky and Plischke, and excellent agreement is found.

cond-mat.dis-nn↗

arXiv1997

Dynamical signatures of the vulcanization transition

Dynamical properties of vulcanized polymer networks are addressed via a Rouse-type model that incorporates the effect of permanent random crosslinks. The incoherent intermediate scattering function is computed in the sol and gel phases, and at the vulcanization transition between them. At any nonzero crosslink density within the sol phase Kohlrausch relaxation is found. The critical point is signalled by divergence of the longest time-scale, and at this point the scattering function decays algebraically, whereas within the gel phase it acquires a time-persistent part identified with the gel fraction.

cond-mat.soft↗

arXiv1996

Induction of non-d-wave order-parameter components by currents in d-wave superconductors

It is shown, within the framework of the Ginzburg-Landau theory for a superconductor with d_{x^2-y^2} symmetry, that the passing of a supercurrent through the sample results, in general, in the induction of order-parameter components of distinct symmetry. The induction of s-wave and d_{xy(x^2-y^2)-wave components are considered in detail. It is shown that in both cases the order parameter remains gapless; however, the structure of the lines of nodes and the lobes of the order parameter are modified in distinct ways, and the magnitudes of these modifications differ in their dependence on the (a-b plane) current direction. The magnitude of the induced s-wave component is estimated using the results of the calculations of Ren et al. [Phys. Rev. Lett. 74, 3680 (1995)], which are based on a microscopic approach.

cond-mat.supr-con↗

arXiv1996

Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State

As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equi- librium phase transition, the liquid state, in which all macromolecules are delocalised, is transformed into a solid state, in which a nonzero fraction of macromolecules have spontaneously become localised. This solid state is a most unusual one: localisation occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanisation transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter. In this review we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanisation transition.

cond-mat↗

arXiv1995

Quantization of Superflow Circulation and Magnetic Flux with a Tunable Offset

Quantization of superflow-circulation and of magnetic-flux are considered for systems, such as superfluid $^3$He-A and unconventional superconductors, having nonscalar order parameters. The circulation is shown to be the anholonomy in the parallel transport of the order parameter. For multiply-connected samples free of distributed vorticity, circulation and flux are predicted to be quantized, but generically to nonintegral values that are tunably offset from integers. This amounts to a version of Aharonov-Bohm physics. Experimental settings for testing these issues are discussed.

cond-mat↗

arXiv1995

Josephson Current and Proximity Effect in Luttinger Liquids

A theory describing a one-dimensional Luttinger liquid in contact with superconductor is developed. Boundary conditions for the fermion fields describing Andreev reflection at the contacts are derived and used to construct a bosonic representation of the fermions. The Josephson current through a superconductor/Luttinger liquid/superconductor junction is considered for both perfectly and poorly transmitting interfaces. In the former case, the Josephson current at low temperatures is found to be essentially unaffected by electron-electron interactions. In the latter case, significant renormalization of the Josephson current occurs. The profile of the (induced) condensate wavefunction in a semi-infinite Luttinger liquid in contact with a superconductor is shown to decay as a power-law, the exponent depending on the sign and strength of the interactions. In the case of repulsive (attractive) interactions the decay is faster (slower) than in their absence. An equivalent method of calculating the Josephson current through a Luttinger liquid, which employs the bosonization of the system as a whole (i.e., superconductor, as well as Luttinger liquid) is developed and shown to give the results equivalent to those obtained via boundary conditions describing Andreev reflection.

cond-mat↗

arXiv1995

Chaos in Andreev Billiards

A new type of classical billiard - the Andreev billiard - is investigated using the tangent map technique. Andreev billiards consist of a normal region surrounded by a superconducting region. In contrast with previously studied billiards, Andreev billiards are integrable in zero magnetic field, {\it regardless of their shape}. A magnetic field renders chaotic motion in a generically shaped billiard, which is demonstrated for the Bunimovich stadium by examination of both Poincaré sections and Lyapunov exponents. The issue of the feasibility of certain experimental realizations is addressed.

cond-mat↗