Charged Vortex Dynamics in Ginzburg-Landau Theory of the Fractional Quantum Hall Effect

We write a Ginzburg-Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2+1 dimensions. Using the method of Lund we derive a collective coordinate action for vortex defects in the order parameter and demonstrate that the vortices are charged. We examine the classical dynamics of the vortices and then quantize their motion, demonstrating that their peculiar classical motion is a result of the fact that the quantum motion takes place in the lowest Landau level. The classical and quantum motion in two dimensional regions with boundaries is also investigated. The quantum theory is not invariant under magnetic translations. Magnetic translations add total time derivative terms to the collective action, but no extra constants of the motion result.Comment: 28 pages + 1 Figure, new phyzzx macro (included), MAD/TH-92-0

Slippery Wave Functions V2.01

Superfluids and superconductors are ordinary matter that show a very surprising behavior at low temperatures. As their temperature is reduced, materials of both kinds can abruptly fall into a state in which they will support a persistent, essentially immortal, flow of particles. Unlike anything in classical physics, these flows engender neither friction nor resistance. A major accomplishment of Twentieth Century physics was the development of an understanding of this very surprising behavior via the construction of partially microscopic and partially macroscopic quantum theories of superfluid helium and superconducting metals. Such theories come in two parts: a theory of the motion of particle-like excitations, called quasiparticles, and of the persistent flows itself via a huge coherent excitation, called a condensate. Two people, above all others, were responsible for the construction of the quasiparticle side of the theories of these very special low-temperature behaviors: Lev Landau and John Bardeen. Curiously enough they both partially ignored and partially downplayed the importance of the condensate. In both cases, this neglect of the actual superfluid or superconducting flow interfered with their ability to understand the implications of the theory they had created. They then had difficulty assessing the important advances that occurred immediately after their own great work. Some speculations are offered about the source of this unevenness in the judgments of these two leading scientists.Comment: 30 pages, 3 figure

Magnetic Phenomena in Holographic Superconductivity with Lifshitz Scaling

We investigate the effects of Lifshitz dynamical critical exponent z on a family of minimal D=4+1 holographic superconducting models, with a particular focus on magnetic phenomena. We see that it is possible to have a consistent Ginzburg-Landau approach to holographic superconductivity in a Lifshitz background. By following this phenomenological approach we are able to compute a wide array of physical quantities. We also calculate the Ginzburg-Landau parameter for different condensates, and conclude that in systems with higher dynamical critical exponent, vortex formation is more strongly unfavored energetically and exhibit a stronger Type I behavior. Finally, following the perturbative approach proposed by Maeda, Natsuume and Okamura, we calculate the critical magnetic field of our models for different values of z.Comment: 32 page

Properties of dirty two-bands superconductors with repulsive interband interaction: normal modes, length scales, vortices and magnetic response

Disorder in two-band superconductors with repulsive interband interaction induces a frustrated competition between the phase-locking preferences of the various potential and kinetic terms. This frustrated interaction can result in the formation of an $s+is$ superconducting state, that breaks the time-reversal symmetry. In this paper we study the normal modes and their associated coherence lengths in such materials. We especially focus on the consequences of the soft modes stemming from the frustration and time-reversal-symmetry breakdown. We find that two-bands superconductors with such impurity-induced frustrated interactions display a rich spectrum of physical properties that are absent in their clean counterparts. It features a mixing of Leggett's and Anderson-Higgs modes, and a soft mode with diverging coherence length at the impurity-induced second order phase transition from $s_{\pm}/s_{++}$ states to the $s+is$ state. Such a soft mode generically results in long-range attractive intervortex forces that can trigger the formation of vortex clusters. We find that, if such clusters are formed, their size and internal flux density have a characteristic temperature dependence that could be probed in muon-spin-rotation experiments. We also comment on the appearance of spontaneous magnetic fields due to spatially varying impurities.Comment: Added discussion of spontaneous magnetic fields due to spatially varying impurities; Replaced with a version in print in Phys. Rev. B; 17 pages, 8 figure

Coarsening and Pinning in the Self-consistent Solution of Polymer Blends Phase-Separation Kinetics

We study analytically a continuum model for phase-separation in binary polymer blends based on the Flory-Huggins-De Gennes free energy, by means of the self-consistent large-$n$ limit approach. The model is solved for values of the parameters corresponding to the weak and strong segregation limits. For deep quenches we identify a complex structure of intermediate regimes and crossovers characterized by the existence of a time domain such that phase separation is pinned, followed by a preasymptotic regime which in the scalar case corresponds to surface diffusion. The duration of the pinning is analytically computed and diverges in the strong segregation limit. Eventually a late stage dynamics sets in, described by scaling laws and exponents analogous to those of the corresponding small molecule systems.Comment: 16 pages, 5 figures. Submitted to Phys. Rev.

Mass of highly magnetized white dwarfs exceeding the Chandrasekhar limit: An analytical view

In recent years a number of white dwarfs has been observed with very high surface magnetic fields. We can expect that the magnetic field in the core of these stars would be much higher (~ 10^{14} G). In this paper, we analytically study the effect of high magnetic field on relativistic cold electron, and hence its effect on the stability and the mass-radius relation of a magnetic white dwarf. In strong magnetic fields, the equation of state of the Fermi gas is modified and Landau quantization comes into play. For relatively very high magnetic fields (with respect to the energy density of matter) the number of Landau levels is restricted to one or two. We analyse the equation of states for magnetized electron degenerate gas analytically and attempt to understand the conditions in which transitions from the zero-th Landau level to first Landau level occur. We also find the effect of the strong magnetic field on the star collapsing to a white dwarf, and the mass-radius relation of the resulting star. We obtain an interesting theoretical result that it is possible to have white dwarfs with mass more than the mass set by Chandrasekhar limit.Comment: 18 pages including 3 figures; to appear in Modern Physics Letters

Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation

We formulate and study dynamics from a complex Ginzburg-Landau system with saturable nonlinearity, including asymmetric cross-phase modulation (XPM) parameters. Such equations can model phenomena described by complex Ginzburg-Landau systems under the added assumption of saturable media. When the saturation parameter is set to zero, we recover a general complex cubic Ginzburg-Landau system with XPM. We first derive conditions for the existence of bounded dynamics, approximating the absorbing set for solutions. We use this to then determine conditions for amplitude death of a single wavefunction. We also construct exact plane wave solutions, and determine conditions for their modulational instability. In a degenerate limit where dispersion and nonlinearity balance, we reduce our system to a saturable nonlinear Schr\"odinger system with XPM parameters, and we demonstrate the existence and behavior of spatially heterogeneous stationary solutions in this limit. Using numerical simulations we verify the aforementioned analytical results, while also demonstrating other interesting emergent features of the dynamics, such as spatiotemporal chaos in the presence of modulational instability. In other regimes, coherent patterns including uniform states or banded structures arise, corresponding to certain stable stationary states. For sufficiently large yet equal XPM parameters, we observe a segregation of wavefunctions into different regions of the spatial domain, while when XPM parameters are large and take different values, one wavefunction may decay to zero in finite time over the spatial domain (in agreement with the amplitude death predicted analytically). While saturation will often regularize the dynamics, such transient dynamics can still be observed - and in some cases even prolonged - as the saturability of the media is increased, as the saturation may act to slow the timescale.Comment: 36 page