Renormalization Group Analysis of a Gursey Model Inspired Field Theory II

Recently a model, which is equivalent to the scalar form of Gursey model, is shown to be a nontrivial field theoretical model when it is gauged with a SU(N) field. In this paper we study another model that is equivalent to the vector form of the Gursey model. We get a trivial theory when it is coupled with a scalar field. This result changes drastically when it is coupled with an additional SU(N) field. We find a nontrivial field theoretical model under certain conditions.Comment: 10 pages, 10 figures, revtex4, typos corrected, published versio

Transmittivity of a Bose-Einstein condensate on a lattice: interference from period doubling and the effect of disorder

We evaluate the particle current flowing in steady state through a Bose-Einstein condensate subject to a constant force in a quasi-onedimensional lattice and to attractive interactions from fermionic atoms that are localized in various configurations inside the lattice wells. The system is treated within a Bose-Hubbard tight binding model by an out-of-equilibrium Green's function approach. A new band gap opens up when the lattice period is doubled by locating the fermions in alternate wells and yields an interference pattern in the transmittivity on varying the intensity of the driving force. The positions of the transmittivity minima are determined by matching the period of Bloch oscillations and the time for tunnelling across the band gap. Massive disorder in the distribution of the fermions will wash out the interference pattern, but the same period doubling of the lattice can be experimentally realized in a four-beam set-up. We report illustrative numerical results for a mixture of 87Rb and 40K atoms in an optical lattice created by laser beams with a wavelength of 763 nm.Comment: 13 pages, 5 figure

Collective excitations of a trapped boson-fermion mixture across demixing

We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons we find that, as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location.Comment: revtex4, 9 pages, 8 postscript file

Collective excitations in trapped boson-fermion mixtures: from demixing to collapse

We calculate the spectrum of low-lying collective excitations in a gaseous cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over a range of the boson-fermion coupling strength extending from strongly repulsive to strongly attractive. Increasing boson-fermion repulsions drive the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drive it towards implosion (``collapse''). The dynamics of the system is treated in the experimentally relevant collisionless regime by means of a Random-Phase approximation and the behavior of a mesoscopic cloud under isotropic harmonic confinement is contrasted with that of a macroscopic mixture at given average particle densities. In the latter case the locations of both the demixing and the collapse phase transitions are sharply defined by the same stability condition, which is determined by the softening of an eigenmode of either fermionic or bosonic origin. In contrast, the transitions to either demixing or collapse in a mesoscopic cloud at fixed confinement and particle numbers are spread out over a range of boson-fermion coupling strength, and some initial decrease of the frequencies of a set of collective modes is followed by hardening as evidenced by blue shifts of most eigenmodes. The spectral hardening can serve as a signal of the impending transition and is most evident when the number of bosons in the cloud is relatively large. We propose physical interpretations for these dynamical behaviors with the help of suitably defined partial compressibilities for the gaseous cloud under confinement.Comment: 16 pages, 7 figures, revtex

Demixing in mesoscopic boson-fermion clouds inside cylindrical harmonic traps: quantum phase diagram and role of temperature

We use a semiclassical three-fluid thermodynamic model to evaluate the phenomena of spatial demixing in mesoscopic clouds of fermionic and bosonic atoms at high dilution under harmonic confinement, assuming repulsive boson-boson and boson-fermion interactions and including account of a bosonic thermal cloud at finite temperature T. The finite system size allows three different regimes for the equilibrium density profiles at T=0: a fully mixed state, a partially mixed state in which the overlap between the boson and fermion clouds is decreasing, and a fully demixed state where the two clouds have zero overlap. We propose simple analytical rules for the two cross-overs between the three regimes as functions of the physical system parameters and support these rules by extensive numerical calculations. A universal ``phase diagram'' expressed in terms of simple scaling parameters is shown to be valid for the transition to the regime of full demixing, inside which we identify several exotic configurations for the two phase-separated clouds in addition to simple ones consisting of a core of bosons enveloped by fermions and "vice versa". With increasing temperature the main role of the growing thermal cloud of bosons is to transform some exotic configurations into more symmetric ones, until demixing is ultimately lost. For very high values of boson-fermion repulsive coupling we also report demixing between the fermions and the thermally excited bosons.Comment: 11 pages, 8 figure

Back Reaction of Strings in Self-Consistent String Cosmology

We compute the string energy-momentum tensor and {\bf derive} the string equation of state from exact string dynamics in cosmological spacetimes. $1+1,~2+1$ and $D$-dimensional universes are treated for any expansion factor $R$. Strings obey the perfect fluid relation $p = (\gamma -1) \rho$ with three different behaviours: (i) {\it Unstable} for $R \to \infty$ with growing energy density $\rho \sim R^{2-D}$, {\bf negative} pressure, and $\gamma =(D-2)/(D-1)$; (ii){\it Dual} for $R \to 0$, with $\rho \sim R^{-D}$, {\bf positive} pressure and $\gamma = D/(D-1)$ (as radiation); (iii) {\it Stable} for $R \to \infty$ with $\rho \sim R^{1-D}$, {\bf vanishing} pressure and $\gamma = 1$ (as cold matter). We find the back reaction effect of these strings on the spacetime and we take into account the quantum string decay through string splitting. This is achieved by considering {\bf self-consistently} the strings as matter sources for the Einstein equations, as well as for the complete effective string equations. String splitting exponentially suppress the density of unstable strings for large $R$. The self-consistent solution to the Einstein equations for string dominated universes exhibits the realistic matter dominated behaviour $R \sim (X^0)^{2/(D-1)}\;$ for large times and the radiation dominated behaviour $R \sim (X^0)^{2/D}\;$ for early times. De Sitter universe does not emerge as solution of the effective string equations. The effective string action (whatever be the dilaton, its potential and the central charge term) is not the appropriate framework in which to address the question of string driven inflation.Comment: 29 pages, revtex, LPTHE-94-2

Stable and Unstable Circular Strings in Inflationary Universes

It was shown by Garriga and Vilenkin that the circular shape of nucleated cosmic strings, of zero loop-energy in de Sitter space, is stable in the sense that the ratio of the mean fluctuation amplitude to the loop radius is constant. This result can be generalized to all expanding strings (of non-zero loop-energy) in de Sitter space. In other curved spacetimes the situation, however, may be different. In this paper we develop a general formalism treating fluctuations around circular strings embedded in arbitrary spatially flat FRW spacetimes. As examples we consider Minkowski space, de Sitter space and power law expanding universes. In the special case of power law inflation we find that in certain cases the fluctuations grow much slower that the radius of the underlying unperturbed circular string. The inflation of the universe thus tends to wash out the fluctuations and to stabilize these strings.Comment: 15 pages Latex, NORDITA 94/14-

Comparison of different cardiovascular magnetic resonance sequences for native myocardial T1 mapping at 3T

Background: T1 mapping based on cardiovascular magnetic resonance (CMR) is a novel approach using the magnetic relaxation T1 time as a quantitative marker for myocardial tissue composition. Various T1 mapping sequences are being used, with different strengths and weaknesses. Data comparing different sequences head to head however are sparse.Methods: We compared three T1 mapping sequences, ShMOLLI, MOLLI and SASHA in phantoms and in a mid-ventricular slice of 40 healthy individuals (mean age 59 +/- 7 years, 45 % male) with low (68 %) or moderate cardiovascular risk. We calculated global and segmental T1 in vivo through exponential curve fitting and subsequent parametric mapping. We also analyzed image quality and inter-observer reproducibility.Results: There was no association of T1 with cardiovascular risk groups. T1 however differed significantly depending on the sequence, with SASHA providing consistently higher mean values than ShMOLLI and MOLLI (1487 +/- 36 ms vs. 1174 +/- 37 ms and 1199 +/- 28 ms, respectively; p < 0.001). This difference between sequences was much smaller in phantom measurements. In patients, segmental values were lower in the anterior wall for all sequences. Image quality, in general good for the steady-state-free-precession readouts in all sequences, was lower for SASHA parametric maps. On multivariate regression analysis, a longer T1 measured by MOLLI was correlated with lower ejection fraction and female gender. Inter-observer variability as assessed by intra-class correlation coefficients was excellent for all sequences (ShMOLLI: 0.995; MOLLI: 0.991; SASHA: 0.961; all p < 0.001).Conclusion: In a cross-sectional population with low to moderate cardiovascular risk, we observed a variation in T1 mapping results between inversion-recovery vs. saturation-recovery sequences in vivo, which were less evident in phantom images, despite a small interobserver variability. Thus, physiological factors, most likely related to B1 inhomogeneities, and tissue-specific properties, like magnetization transfer, that impact T1 values in vivo, render phantom validation insufficient, and have to be further investigated for a better understanding of the clinical utility of different T1 mapping approaches

The incidence of scarring on the dorsum of the hand

When undertaking image comparison of the hand between accused and perpetrator, it is not unusual for scars to be identified on the back of the hand. To investigate the occurrence of scarring in a discreet sample, a database of 238 individuals was examined, and the dorsum of the right and left hands was gridded for each individual. The position, size and type of scar were recorded within each grid. It was found that, in general, males exhibited a higher incidence of scarring than females. However, males were more likely to show scarring on their left hand whereas females were more likely to exhibit scarring on their right hand. Contrary to the literature, scarring was not most prevalent along the borders of the hand but occurred more frequently in association with the index and middle finger corridor regions. Surgical scars were rare as were large scars whereas linear scars smaller than 6 mm were the most frequently identified. Close to half of the sample did not exhibit scarring on one hand. The importance of understanding the pattern of scarring on the back of the hand is discussed in the light of forensic image comparison analysis

Circular String-Instabilities in Curved Spacetime

We investigate the connection between curved spacetime and the emergence of string-instabilities, following the approach developed by Loust\'{o} and S\'{a}nchez for de Sitter and black hole spacetimes. We analyse the linearised equations determining the comoving physical (transverse) perturbations on circular strings embedded in Schwarzschild, Reissner-Nordstr\"{o}m and de Sitter backgrounds. In all 3 cases we find that the "radial" perturbations grow infinitely for $r\rightarrow 0$ (ring-collapse), while the "angular" perturbations are bounded in this limit. For $r\rightarrow\infty$ we find that the perturbations in both physical directions (perpendicular to the string world-sheet in 4 dimensions) blow up in the case of de Sitter space. This confirms results recently obtained by Loust\'{o} and S\'{a}nchez who considered perturbations around the string center of mass.Comment: 24 pages Latex + 2 figures (not included). Observatoire de Paris, Meudon No. 9305