arXiv subjects

A. M. Martin

Publications and source records attributed to A. M. Martin.

71 records · Page 4Linked to original sources

arXiv2007

Dynamical Instability of a Rotating Dipolar Bose-Einstein Condensate

We calculate the hydrodynamic solutions for a dilute Bose-Einstein condensate with long-range dipolar interactions in a rotating, elliptical harmonic trap, and analyse their dynamical stability. The static solutions and their regimes of instability vary non-trivially on the strength of the dipolar interactions. We comprehensively map out this behaviour, and in particular examine the experimental routes towards unstable dynamics, which, in analogy to conventional condensates, may lead to vortex lattice formation. Furthermore, we analyse the centre of mass and breathing modes of a rotating dipolar condensate.

cond-mat.other↗

arXiv2007

Vortices in Bose-Einstein Condensates: Theory

Vortices are pervasive in nature, representing the breakdown of laminar fluid flow and hence playing a key role in turbulence. The fluid rotation associated with a vortex can be parameterized by the circulation $Γ=\oint {\rm d}{\bf r}\cdot{\bf v}({\bf r})$ about the vortex, where ${\bf v}({\bf r})$ is the fluid velocity field. While classical vortices can take any value of circulation, superfluids are irrotational, and any rotation or angular momentum is constrained to occur through vortices with quantized circulation. Quantized vortices also play a key role in the dissipation of transport in superfluids. In BECs quantized vortices have been observed in several forms, including single vortices, vortex lattices, and vortex pairs and rings. The recent observation of quantized vortices in a fermionic gas was taken as a clear signature of the underlying condensation and superfluidity of fermion pairs. In addition to BECs, quantized vortices also occur in superfluid Helium, nonlinear optics, and type-II superconductors.

cond-mat.other↗

arXiv2007

The Arecibo Legacy Fast ALFA Survey: III. HI Source Catalog of the Northern Virgo Cluster Region

We present the first installment of HI sources extracted from the Arecibo Legacy Fast ALFA (ALFALFA) extragalactic survey, initiated in 2005. Sources have been extracted from 3-D spectral data cubes and then examined interactively to yield global HI parameters. A total of 730 HI detections are catalogued within the solid angle 11h44m < R.A.(J2000) < 14h00m and +12deg < Dec.(J2000) < +16deg, and redshift range -1600 \kms < cz < 18000 \kms. In comparison, the HI Parkes All-Sky Survey (HIPASS) detected 40 HI signals in the same region. Optical counterparts are assigned via examination of digital optical imaging databases. ALFALFA HI detections are reported for three distinct classes of signals: (a) detections, typically with S/N > 6.5; (b) high velocity clouds in the Milky Way or its periphery; and (c) signals of lower S/N (to ~ 4.5) which coincide spatially with an optical object of known similar redshift. Although this region of the sky has been heavily surveyed by previous targeted observations based on optical flux-- or size-- limited samples, 69% of the extracted sources are newly reported HI detections. The resultant positional accuracy of HI sources is 20" (median). The median redshift of the sample is ~7000 \kms and its distribution reflects the known local large scale structure including the Virgo cluster. Several extended HI features are found in the vicinity of the Virgo cluster. A small percentage (6%) of HI detections have no identifiable optical counterpart, more than half of which are high velocity clouds in the Milky Way vicinity; the remaining 17 objects do not appear connected to or associated with any known galaxy.

astro-ph↗

arXiv2006

Transmission and Reflection of Bose-Einstein Condensates Incident on a Gaussian Potential Barrier

We investigate how Bose-Einstein condensates, whose initial state is either irrotational or contains a single vortex, scatter off a one-dimensional Gaussian potential barrier. We find that for low atom densities the vortex structure within the condensate is maintained during scattering, whereas at medium and high densities, multiple additional vortices can be created by the scattering process, resulting in complex dynamics and disruption of the atom cloud. This disruption originates from two different mechanisms associated respectively with the initial rotation of the atom cloud and the interference between the incident and reflected matter waves. We investigate how the reflection probability depends on the vorticity of the initial state and on the incident velocity of the Bose-Einstein condensate. To interpret our results, we derive a general analytical expression for the reflection coefficient of a rotating Bose-Einstein condensate that scatters off a spatially-varying one-dimensional potential.

cond-mat.other↗

arXiv2006

Instabilities leading to vortex lattice formation in rotating Bose-Einstein condensates

We present a comprehensive theoretical study of vortex lattice formation in atomic Bose-Einstein condensates confined by a rotating elliptical trap. We consider rotating solutions of the classical hydrodynamic equations, their response to perturbations, as well as time-dependent simulations. We discriminate three distinct, experimentally testable, regimes of instability: {\em ripple}, {\em interbranch}, and {\em catastrophic}. Under symmetry-breaking perturbations these instabilities lead to lattice formation even at zero temperature. While our results are consistent with previous theoretical and experimental results, they shed new light on lattice formation.

cond-mat.other↗

arXiv2006

Collisions between solitary waves of three-dimensional Bose-Einstein condensates

We study bright solitary waves of three dimensional trapped Bose-Einstein condensates and their collisions. For a single solitary wave, in addition to an upper critical number, we also find a {\em lower} cut-off, below which no stable state can be found. Collisions between solitary waves can be elastic, inelastic with either reduced or increased outgoing speed, or completely unstable due to a collapse instability. A $π$-phase difference between the waves promotes elastic collisions, and gives excellent agreement with recent experimental results over long timescales.

cond-mat.other↗

arXiv2005

Anomalous quantum reflection of Bose-Einstein condensates from a silicon surface: the role of dynamical excitations

We investigate the effect of inter-atomic interactions on the quantum-mechanical reflection of Bose-Einstein condensates from regions of rapid potential variation. The reflection process depends critically on the density and incident velocity of the condensate. For low densities and high velocities, the atom cloud has almost the same form before and after reflection. Conversely, at high densities and low velocities, the reflection process generates solitons and vortex rings that fragment the condensate. We show that this fragmentation can explain the anomalously low reflection probabilities recently measured for low-velocity condensates incident on a silicon surface.

cond-mat.other↗

arXiv2003

Model for Breakdown of Laminar Flow of a Quantum Hall Fluid Around a Charged Impurity: Comparison with Experiment

In samples used to maintain the US resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the generation of magneto-excitons when the quantum Hall fluid flows past an ionised impurity above a critical velocity. The calculated generation rate gives a voltage step height in good agreement with measurements. We also compare this model to a hydrodynamic description of breakdown.

cond-mat.mes-hall↗

arXiv2003

A Model for the Voltage Steps in the Breakdown of the Integer Quantum Hall Effect

In samples used to maintain the US resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the generation of magneto-excitons when the quantum Hall fluid flows past an ionised impurity above a critical velocity. The calculated generation rate gives a voltage step height in good agreement with measurements on both electron and hole gases. We also compare this model to a hydrodynamic description of breakdown.

cond-mat.mes-hall↗

arXiv2002

Creation of solitons and vortices by Bragg reflection of Bose-Einstein condensates in an optical lattice

We study the dynamics of Bose-Einstein condensates in an optical lattice and harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semiclassical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection. For high atom densities, the first Bragg reflection generates a train of solitons and vortices, which destabilize the condensate and trigger explosive expansion. At lower densities, soliton and vortex formation requires multiple Bragg reflections, and damps the center-of-mass motion.

cond-mat↗

arXiv2001

The charge and low-frequency response of normal-superconducting heterostructures

The charge distribution is a basic aspect of electrical transport. In this work we investigate the self-consistent charge response of normal-superconducting heterostructures. Of interest is the variation of the charge density due to voltage changes at contacts and due to changes in the potential. We present response functions in terms of functional derivatives of the scattering matrix. We discuss corrections to the Lindhard function due to the proximity of the superconductor. We use these results to find the dynamic conductance matrix to lowest order in frequency. We illustrate similarities and differences between normal systems and heterostructures for specific examples like a ballistic wire, a resonator, and a quantum point contact.

cond-mat.mes-hall↗

arXiv2000

Frustration in d-wave Superconducting Circuits: $π$-Ring Behaviour

A closed superconducting circuit containing an odd number of $π$-junctions, a $π$-ring, has a finite current in the ground state. We explicitly construct such rings for d-wave superconductors and demonstrate the existence of spontaneous currents by direct self-consistent solutions to the Bogoliubov de Gennes equations. We show that the current has a topological origin due to the frustration of the d-wave order parameter, which is only partially explained by the Sigrist-Rice tunneling formula.

cond-mat.supr-con↗

arXiv1999

Coherent Potential Approximation for `d - wave' Superconductivity in Disordered Systems

A Coherent Potential Approximation is developed for s-wave and d-wave superconductivity in disordered systems. We show that the CPA formalism reproduces the standard pair-breaking formula, the self-consistent Born Approximation and the self-consistent T-matrix approximation in the appropriate limits. We implement the theory and compute T_c for s-wave and d-wave pairing using an attractive nearest neighbor Hubbard model featuring both binary alloy disorder and a uniform distribution of scattering site potentials. We determine the density of states and examine its consequences for low temperature heat capacity. We find that our results are in qualitative agreement with measurements on Zn doped YBCO superconductors.

cond-mat.supr-con↗

arXiv1998

Tilt Grain-Boundary Effects in S- and D-Wave Superconductors

We calculate the s- and d-wave superconductor order parameter in the vicinity of a tilt grain boundary. We do this self-consistently within the Bogoliubov de Gennes equations, using a realistic microscopic model of the grain boundary. We present the first self-consistent calculations of supercurrent flows in such boundaries, obtaining the current-phase characteristics of grain boundaries in both s-wave and d-wave superconductors.

cond-mat.supr-con↗

arXiv1998

The importance of self-consistency in determining interface properties of S-I-N and D-I-N structures

We develop a method to solve the Bogoliubov de Gennes equation for superconductors self-consistently, using the recursion method. The method allows the pairing interaction to be either local or non-local corresponding to $s$ and $d$--wave superconductivity, respectively. Using this method we examine the properties of various $S-I-N$ and $D-I-N$ interfaces. In particular we self-consistently calculate the spatially varying density of states and the superconducting order parameter. We see that changing the strength of the insulating barrier, at the interface, does not, in the case of an $s$--wave superconductor, dramatically, change the low energy local density of states, in the superconducting region near the interface. This is in stark contrast to what we see in the case of a $D-I-N$ interface where the local particle density of states is changed dramatically. Hence we deduce that in calculating such properties as the conductance of $S-I-N$ and $D-I-N$ structures it is far more important to carry out a self-consistent calculations in the $d$--wave case.

cond-mat.supr-con↗

arXiv1998

Van Hove Singularity and D-Wave Pairing in Disordered Superconductors

We apply the coherent potential approximation (CPA) to a simple model for disordered superconductors with d-wave pairing. We demonstrate that whilst the effectiveness of an electronic Van Hove singularity to enhance the transition temperature T$_c$ is reduced by disorder it is not eliminated. In fact we give a qualitative account of changes in the T$_c$ vs. doping curve with increasing disorder and compare our results with experiments on the Y_{0.8}Ca_{0.2}Ba_2(Cu_{1-c}Zn_c)_{3}O_{7-δ} alloys.

cond-mat.supr-con↗

arXiv1997

Self-consistent interface properties of d and s-wave superconductors

We develop a method to solve the Bogoliubov de Gennes equation for superconductors self-consistently, using the recursion method. The method allows the pairing interaction to be either local or non-local corresponding to s and d-wave superconductivity, respectively. Using this method we examine the properties of various S-N and S-S interfaces. In particular we calculate the spatially varying density of states and order parameter for the following geometries (i) s-wave superconductor to normal metal, (ii) d-wave superconductor to normal metal, (iii) d-wave superconductor to s-wave superconductor. We show that the density of states at the interface has a complex structure including the effects of normal surface Friedel oscillations, the spatially varying gap and Andeev states within the gap, and the subtle effects associated with the interplay of the gap and the normal van Hove peaks in the density of states. In the case of bulk d-wave superconductors the surface leads to mixing of different order parameter symmetries near the interface and substantial local filling in of the gap.

cond-mat.supr-con↗