Skyrmion mass and a new kind of the cyclotron resonance for 2DEG

The skyrmionic mass was calculated in the main order of the gradient expansion in derivatives of the rotation matrix. The mass is proportinal to the topological invariant which is the absolut value of the degree of the mapping. The coefficient is defined by the exchange interaction. The charged skyrmions in magnetic field give rise to a special branch of cyclotron resonance with the frequency defined by the exchange interaction and have the corresponding term in their minimal energy. The possibility of an extra bound electron and neutral skyrmions is discussed.Comment: 4 pages, Latex (submitted to JETP lett.

Reentrant Melting of Soliton Lattice Phase in Bilayer Quantum Hall System

At large parallel magnetic field $B_\parallel$, the ground state of bilayer quantum Hall system forms uniform soliton lattice phase. The soliton lattice will melt due to the proliferation of unbound dislocations at certain finite temperature leading to the Kosterlitz-Thouless (KT) melting. We calculate the KT phase boundary by numerically solving the newly developed set of Bethe ansatz equations, which fully take into account the thermal fluctuations of soliton walls. We predict that within certain ranges of $B_\parallel$, the soliton lattice will melt at $T_{\rm KT}$. Interestingly enough, as temperature decreases, it melts at certain temperature lower than $T_{\rm KT}$ exhibiting the reentrant behaviour of the soliton liquid phase.Comment: 11 pages, 2 figure

Theory of Microwave Parametric Down Conversion and Squeezing Using Circuit QED

We study theoretically the parametric down conversion and squeezing of microwaves using cavity quantum electrodynamics of a superconducting Cooper pair box (CPB) qubit located inside a transmission line resonator. The non-linear susceptibility \chi_2 describing three-wave mixing can be tuned by dc gate voltage applied to the CPB and vanishes by symmetry at the charge degeneracy point. We show that the coherent coupling of different cavity modes through the qubit can generate a squeezed state. Based on parameters realized in recent successful circuit QED experiments, squeezing of 95% ~ 13dB below the vacuum noise level should be readily achievable.Comment: 4 pages, accepted for publication in Phys. Rev. Let

Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions

The $\nu = 1$ quantum Hall ground state in materials like GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electron spins spontaneously. The gapless Goldstone modes are the angular deviations of the magnetisation vector from its fixed ground state orientation. Furthermore, the system is known to support electrically charged spin skyrmion configurations. It has been claimed in the literature that these skyrmions are fermionic owing to an induced topological Hopf term in the effective action governing the Goldstone modes. However, objections have been raised against the method by which this term has been obtained from the microscopics of the system. In this article, we use the technique of the derivative expansion to derive, in an unambiguous manner, the effective action of the angular degrees of freedom, including the Hopf term. Furthermore, we have coupled perturbative electromagnetic fields to the microscopic fermionic system in order to study their effect on the spin excitations. We have obtained an elegant expression for the electromagnetic coupling of the angular variables describing these spin excitations.Comment: 23 pages, Plain TeX, no figure

Maximal induced matchings in triangle-free graphs

An induced matching in a graph is a set of edges whose endpoints induce a $1$-regular subgraph. It is known that any $n$-vertex graph has at most $10^{n/5} \approx 1.5849^n$ maximal induced matchings, and this bound is best possible. We prove that any $n$-vertex triangle-free graph has at most $3^{n/3} \approx 1.4423^n$ maximal induced matchings, and this bound is attained by any disjoint union of copies of the complete bipartite graph $K_{3,3}$. Our result implies that all maximal induced matchings in an $n$-vertex triangle-free graph can be listed in time $O(1.4423^n)$, yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph.Comment: 17 page

Strong Correlation to Weak Correlation Phase Transition in Bilayer Quantum Hall Systems

At small layer separations, the ground state of a nu=1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence and has a charged-excitation gap E_g. The evolution of this state with increasing layer separation d has been a matter of controversy. In this letter we report on small system exact diagonalization calculations which suggest that a single phase transition, likely of first order, separates coherent incompressible (E_g >0) states with strong interlayer correlations from incoherent compressible states with weak interlayer correlations. We find a dependence of the phase boundary on d and interlayer tunneling amplitude that is in very good agreement with recent experiments.Comment: 4 pages, 4 figures included, version to appear in Phys. Rev. Let

Comparison of T1 mapping techniques for ECV quantification. histological validation and reproducibility of ShMOLLI versus multibreath-hold T1 quantification equilibrium contrast CMR

BACKGROUND: Myocardial extracellular volume (ECV) is elevated in fibrosis or infiltration and can be quantified by measuring the haematocrit with pre and post contrast T1 at sufficient contrast equilibrium. Equilibrium CMR (EQ-CMR), using a bolus-infusion protocol, has been shown to provide robust measurements of ECV using a multibreath-hold T1 pulse sequence. Newer, faster sequences for T1 mapping promise whole heart coverage and improved clinical utility, but have not been validated. METHODS: Multibreathhold T1 quantification with heart rate correction and single breath-hold T1 mapping using Shortened Modified Look-Locker Inversion recovery (ShMOLLI) were used in equilibrium contrast CMR to generate ECV values and compared in 3 ways.Firstly, both techniques were compared in a spectrum of disease with variable ECV expansion (n=100, 50 healthy volunteers, 12 patients with hypertrophic cardiomyopathy, 18 with severe aortic stenosis, 20 with amyloid). Secondly, both techniques were correlated to human histological collagen volume fraction (CVF%, n=18, severe aortic stenosis biopsies). Thirdly, an assessment of test:retest reproducibility of the 2 CMR techniques was performed 1 week apart in individuals with widely different ECVs (n=10 healthy volunteers, n=7 amyloid patients). RESULTS: More patients were able to perform ShMOLLI than the multibreath-hold technique (6% unable to breath-hold). ECV calculated by multibreath-hold T1 and ShMOLLI showed strong correlation (r(2)=0.892), little bias (bias -2.2%, 95%CI -8.9% to 4.6%) and good agreement (ICC 0.922, range 0.802 to 0.961, p<0.0001). ECV correlated with histological CVF% by multibreath-hold ECV (r(2)= 0.589) but better by ShMOLLI ECV (r(2)= 0.685). Inter-study reproducibility demonstrated that ShMOLLI ECV trended towards greater reproducibility than the multibreath-hold ECV, although this did not reach statistical significance (95%CI -4.9% to 5.4% versus 95%CI -6.4% to 7.3% respectively, p=0.21). CONCLUSIONS: ECV quantification by single breath-hold ShMOLLI T1 mapping can measure ECV by EQ-CMR across the spectrum of interstitial expansion. It is procedurally better tolerated, slightly more reproducible and better correlates with histology compared to the older multibreath-hold FLASH techniques