A dynamic new look at the lambda transition

We discuss aspects of the theory of critical phenomena and explore the superfluid transition in 4He. We review some of the recent experimental and theoretical work on helium in nonequilibrium conditions and summarize some future space experiments that might shed light on disagreements between theory and experiment

Recounting Dyons in N=4 String Theory

A recently discovered relation between 4D and 5D black holes is used to derive weighted BPS black hole degeneracies for 4D N=4 string theory from the well-known 5D degeneracies. They are found to be given by the Fourier coefficients of the unique weight 10 automorphic form of the modular group Sp(2,Z). This result agrees exactly with a conjecture made some years ago by Dijkgraaf, Verlinde and Verlinde.Comment: 5 page

A Link Quality Model for Generalised Frequency Division Multiplexing

5G systems aim to achieve extremely high data rates, low end-to-end latency and ultra-low power consumption. Recently, there has been considerable interest in the design of 5G physical layer waveforms. One important candidate is Generalised Frequency Division Multiplexing (GFDM). In order to evaluate its performance and features, system-level studies should be undertaken in a range of scenarios. These studies, however, require highly complex computations if they are performed using bit-level simulators. In this paper, the Mutual Information (MI) based link quality model (PHY abstraction), which has been regularly used to implement system-level studies for Orthogonal Frequency Division Multiplexing (OFDM), is applied to GFDM. The performance of the GFDM waveform using this model and the bit-level simulation performance is measured using different channel types. Moreover, a system-level study for a GFDM based LTE-A system in a realistic scenario, using both a bit-level simulator and this abstraction model, has been studied and compared. The results reveal the accuracy of this model using realistic channel data. Based on these results, the PHY abstraction technique can be applied to evaluate the performance of GFDM based systems in an effective manner with low complexity. The maximum difference in the Packet Error Rate (PER) and throughput results in the abstraction case compared to bit-level simulation does not exceed 4% whilst offering a simulation time saving reduction of around 62,000 times.Comment: 5 pages, 8 figures, accepted in VTC- spring 201

A study of singularities on rational curves via syzygies

Consider a rational projective curve C of degree d over an algebraically closed field k. There are n homogeneous forms g_1,...,g_n of degree d in B=k[x,y] which parameterize C in a birational, base point free, manner. We study the singularities of C by studying a Hilbert-Burch matrix phi for the row vector [g_1,...,g_n]. In the "General Lemma" we use the generalized row ideals of phi to identify the singular points on C, their multiplicities, the number of branches at each singular point, and the multiplicity of each branch. Let p be a singular point on the parameterized planar curve C which corresponds to a generalized zero of phi. In the "Triple Lemma" we give a matrix phi' whose maximal minors parameterize the closure, in projective 2-space, of the blow-up at p of C in a neighborhood of p. We apply the General Lemma to phi' in order to learn about the singularities of C in the first neighborhood of p. If C has even degree d=2c and the multiplicity of C at p is equal to c, then we apply the Triple Lemma again to learn about the singularities of C in the second neighborhood of p. Consider rational plane curves C of even degree d=2c. We classify curves according to the configuration of multiplicity c singularities on or infinitely near C. There are 7 possible configurations of such singularities. We classify the Hilbert-Burch matrix which corresponds to each configuration. The study of multiplicity c singularities on, or infinitely near, a fixed rational plane curve C of degree 2c is equivalent to the study of the scheme of generalized zeros of the fixed balanced Hilbert-Burch matrix phi for a parameterization of C.Comment: Typos corrected and minor changes made. To appear in the Memoirs of the AM

Two-channel Kondo physics in odd impurity chains

We study odd-membered chains of spin-(1/2) impurities, with each end connected to its own metallic lead. For antiferromagnetic exchange coupling, universal two-channel Kondo (2CK) physics is shown to arise at low energies. Two overscreening mechanisms are found to occur depending on coupling strength, with distinct signatures in physical properties. For strong inter-impurity coupling, a residual chain spin-(1/2) moment experiences a renormalized effective coupling to the leads; while in the weak-coupling regime, Kondo coupling is mediated via incipient single-channel Kondo singlet formation. We also investigate models where the leads are tunnel-coupled to the impurity chain, permitting variable dot filling under applied gate voltages. Effective low-energy models for each regime of filling are derived, and for even-fillings where the chain ground state is a spin singlet, an orbital 2CK effect is found to be operative. Provided mirror symmetry is preserved, 2CK physics is shown to be wholly robust to variable dot filling; in particular the single-particle spectrum at the Fermi level, and hence the low-temperature zero-bias conductance, is always pinned to half-unitarity. We derive a Friedel-Luttinger sum rule and from it show that, in contrast to a Fermi liquid, the Luttinger integral is non-zero and determined solely by the `excess' dot charge as controlled by gate voltage. The relevance of the work to real quantum dot devices, where inter-lead charge-transfer processes fatal to 2CK physics are present, is also discussed. Physical arguments and numerical renormalization group techniques are used to obtain a detailed understanding of these problems.Comment: 21 pages, 19 figure

Constraining the dark fluid

Cosmological observations are normally fit under the assumption that the dark sector can be decomposed into dark matter and dark energy components. However, as long as the probes remain purely gravitational, there is no unique decomposition and observations can only constrain a single dark fluid; this is known as the dark degeneracy. We use observations to directly constrain this dark fluid in a model-independent way, demonstrating in particular that the data cannot be fit by a dark fluid with a single constant equation of state. Parameterizing the dark fluid equation of state by a variety of polynomials in the scale factor $a$, we use current kinematical data to constrain the parameters. While the simplest interpretation of the dark fluid remains that it is comprised of separate dark matter and cosmological constant contributions, our results cover other model types including unified dark energy/matter scenarios.Comment: 5 pages, 5 figures incorporated. Updated to new observational data including SHOES determination of H0; new citations adde