FFLO states and quantum oscillations in mesoscopic superconductors and superfluid ultracold Fermi gases

We have studied the distinctive features of the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) instability and phase transitions in two--dimensional (2D) mesoscopic superconductors placed in magnetic field of arbitrary orientation and rotating superfluid Fermi gases with imbalanced state populations. Using a generalized version of the phenomenological Ginzburg-Landau theory we have shown that the FFLO states are strongly modified by the effect of the trapping potential confining the condensate. The phenomenon of the inhomogeneous state formation is determined by the interplay of three length scales: (i) length scale of the FFLO instability; (ii) 2D system size; (iii) length scale associated with the orbital effect caused either by the Fermi condensate rotation or magnetic field component applied perpendicular to the superconducting disc. We have studied this interplay and resulting quantum oscillation effects in both superconducting and superfluid finite -- size systems with FFLO instability and described the hallmarks of the FFLO phenomenon in a restricted geometry. The finite size of the system is shown to affect strongly the conditions of the observability of switching between the states with different vorticities.Comment: 11 pages, 5 figures, Submitted to PR

A Semi-Analytic dynamical friction model that reproduces core stalling

We present a new semi-analytic model for dynamical friction based on Chandrasekhar's formalism. The key novelty is the introduction of physically motivated, radially varying, maximum and minimum impact parameters. With these, our model gives an excellent match to full N-body simulations for isotropic background density distributions, both cuspy and shallow, without any fine-tuning of the model parameters. In particular, we are able to reproduce the dramatic core-stalling effect that occurs in shallow/constant density cores, for the first time. This gives us new physical insight into the core-stalling phenomenon. We show that core stalling occurs in the limit in which the product of the Coulomb logarithm and the local fraction of stars with velocity lower than the infalling body tends to zero. For cuspy backgrounds, this occurs when the infalling mass approaches the enclosed background mass. For cored backgrounds, it occurs at larger distances from the centre, due to a combination of a rapidly increasing minimum impact parameter and a lack of slow moving stars in the core. This demonstrates that the physics of core-stalling is likely the same for both massive infalling objects and low-mass objects moving in shallow density backgrounds. We implement our prescription for dynamical friction in the direct summation code NBODY6 as an analytic correction for stars that remain within the Roche volume of the infalling object. This approach is computationally efficient, since only stars in the inspiralling system need to be evolved with direct summation. Our method can be applied to study a variety of astrophysical systems, including young star clusters orbiting near the Galactic Centre; globular clusters moving within the Galaxy; and dwarf galaxies orbiting within dark matter halos.Comment: 16 pages, 21 figures, Accepted for publication in MNRA

A semi-analytic dynamical friction model for cored galaxies

We present a dynamical friction model based on Chandrasekhar's formula that reproduces the fast inspiral and stalling experienced by satellites orbiting galaxies with a large constant density core. We show that the fast inspiral phase does not owe to resonance. Rather, it owes to the background velocity distribution function for the constant density cores being dissimilar from the usually-assumed Maxwellian distribution. Using the correct background velocity distribution function and the semi-analytic model from Petts et al. (2015), we are able to correctly reproduce the infall rate in both cored and cusped potentials. However, in the case of large cores, our model is no longer able to correctly capture core-stalling. We show that this stalling owes to the tidal radius of the satellite approaching the size of the core. By switching off dynamical friction when rt(r) = r (where rt is the tidal radius at the satellite's position) we arrive at a model which reproduces the N-body results remarkably well. Since the tidal radius can be very large for constant density background distributions, our model recovers the result that stalling can occur for Ms/Menc << 1, where Ms and Menc are the mass of the satellite and the enclosed galaxy mass, respectively. Finally, we include the contribution to dynamical friction that comes from stars moving faster than the satellite. This next-to-leading order effect becomes the dominant driver of inspiral near the core region, prior to stalling.Comment: 13 pages, 12 figures, resubmitted to MNRAS after responding to feedback from the refere

Network Synthesis of Linear Dynamical Quantum Stochastic Systems

The purpose of this paper is to develop a synthesis theory for linear dynamical quantum stochastic systems that are encountered in linear quantum optics and in phenomenological models of linear quantum circuits. In particular, such a theory will enable the systematic realization of coherent/fully quantum linear stochastic controllers for quantum control, amongst other potential applications. We show how general linear dynamical quantum stochastic systems can be constructed by assembling an appropriate interconnection of one degree of freedom open quantum harmonic oscillators and, in the quantum optics setting, discuss how such a network of oscillators can be approximately synthesized or implemented in a systematic way from some linear and non-linear quantum optical elements. An example is also provided to illustrate the theory.Comment: Revised and corrected version, published in SIAM Journal on Control and Optimization, 200

More on A Statistical Analysis of Log-Periodic Precursors to Financial Crashes

We respond to Sornette and Johansen's criticisms of our findings regarding log-periodic precursors to financial crashes. Included in this paper are discussions of the Sornette-Johansen theoretical paradigm, traditional methods of identifying log-periodic precursors, the behavior of the first differences of a log-periodic price series, and the distribution of drawdowns for a securities price.Comment: 12 LaTex pages, no figure

Field induced superconductivity with enhanced and tunable paramagnetic limit

We demonstrate that in a superconducting multilayered system with alternating interlayer coupling a new type of nonuniform superconducting state can be realized under in-plane magnetic field. The Zeeman effect in this state is compensated by the energy splitting between bonding and antibonding levels. Such compensation mechanism at low temperature leads to the field-induced superconductivity. We discuss the conditions for the experimental observation of the predicted phenomena.Comment: 5 pages, 4 figures include

Serotonin Modulates Oscillations of the Membrane Potential in Isolated Spinal Neurons from Lampreys

Studies were performed on spinal neurons from lampreys isolated by an enzymatic/mechanical method using pronase. The effects of 100 µM serotonin (5-HT) on membrane potential oscillations induced by a variety of excitatory amino acids were studied. 5-HT was found to depolarize branched cells (presumptive motoneurons and interneurons) by 2–6 mV without inducing membrane potential oscillations. However, when oscillations were already present because of an excitatory amino acid, 5-HT changed the parameters of these oscillations, increasing the amplitudes of all types of oscillations, increasing the frequency of irregular oscillations, and increasing the duration of the depolarization plateaus accompanied by action potentials. Serotonin modulation of the effects of excitatory amino acids and the electrical activity of cells in the neural locomotor network facilitates motor activity and leads to increases in the contraction of truncal muscles and more intense movements by the animal. The possible mechanisms of receptor coactivation are discussed, along with increases in action potential frequency and changes in the parameters of the locomotor rhythm

The Effects of Serotonin on Functionally Diverse Isolated Lamprey Spinal Cord Neurons

The experiments reported here showed that application of serotonin (5-hydroxytryptamine, 5-HT) (100 µ M) did not induce any significant current through the membranes of any of the spinal neurons studied (n = 62). At the same time, the membranes of most motoneurons and interneurons (15 of 18) underwent slight depolarization (2–6 mV) in the presence of 5-HT, which was not accompanied by any change in the input resistance of the cells. Depolarization to 10–20 mV occurred in some cells (3 of 18) of these functional groups, this being accompanied by 20–60% decreases in input resistance. The same concentration of 5-HT induced transient low-amplitude depolarization of most sensory spinal neurons (dorsal sensory cells), this changing smoothly to long-term hyperpolarization by 2–7 mV. The input resistance of the cell membranes in these cases showed no significant change (n = 8). Data were obtained which provided a better understanding of the mechanism by which 5-HT modulates the activity of spinal neurons. Thus, 5-HT facilitates chemoreceptive currents induced by application of NMDA to motoneurons and interneurons, while the NMDA responses of dorsal sensory cells were decreased by 5-HT. 5-HT affected the post-spike afterresponses of neurons. 5-HT significantly decreased the amplitude of afterhyperpolarization arising at the end of the descending phase of action potentials in motoneurons and interneurons and increased the amplitude of afterdepolarization in these types of cells. In sensory spinal neurons, 5-HT had no great effect on post-spike afterresponses. The results obtained here support the suggestion that 5-HT significantly modulates the activity of spinal neurons of different functional types. 5-HT facilitates excitation induced by subthreshold depolarization in motoneurons and some interneurons, facilitating the generation of rhythmic discharges by decreasing afterhyperpolarization. In sensory cells, 5-HT enhances inhibition due to hyperpolarization, suppressing NMDA currents. The differences in the effects of 5-HT on functionally diverse neurons are presumed to be associated with the combination of different types of 5-HT receptors on the membranes of these types of spinal neurons