Two types of Hc2(T) dependences in Bi_2Sr_2Ca_(1-x)Y_xCu_2O_(8+delta) with different Yttrium content

We reanalyze the magnetization data collected on Bi_2Sr_2Ca_(1-x)Y_xCu_2O_(8+y) samples (Kim at al, Phys. Rev. B 72, 64525 (2005)) and argue that the method, which was used for the analysis of equilibrium magnetization data, is not adequate to the experimental situation. As a result, the temperature dependencies of the upper critical field Hc2(T) and the magnetic field penetration depth lambda (T), obtained in this work, are misinterpreted. Using a different approach to analysis, we demonstrate that the normalizedHc2(T) curves are rather different from those presented in the original publication and do not follow predictions of the Werthamer-Helfand-Hohenberg theory. Another important observation is that the Hc2(T) dependencies for two samples with different levels of doping are qualitatively different.Comment: 10 pages, 3 figure

Resonance widths for the molecular predissociation

We consider a semiclassical $2\times 2$ matrix Schr\"odinger operator of the form $P=-h^2\Delta {\bf I}_2 + {\rm diag}(V_1(x), V_2(x)) +hR(x,hD_x)$, where $V_1, V_2$ are real-analytic, $V_2$ admits a non degenerate minimum at 0, $V_1$ is non trapping at energy $V_2(0)=0$, and $R(x,hD_x)=(r_{j,k}(x,hD_x))_{1\leq j,k\leq 2}$ is a symmetric off-diagonal $2\times 2$ matrix of first-order pseudodifferential operators with analytic symbols. We also assume that $V_1(0) >0$. Then, denoting by $e_1$ the first eigenvalue of -\Delta + \la V_2"(0)x,x\ra /2, and under some ellipticity condition on $r_{1,2}$ and additional generic geometric assumptions, we show that the unique resonance $\rho_1$ of $P$ such that $\rho_1 = V_2(0) + (e_1+r_{2,2}(0,0))h + {\mathcal O}(h^2)$ (as $h\rightarrow 0_+$) satisfies, $$\Im \rho_1 = -h^{n_0+(1-n_\Gamma)/2}f(h,\ln\frac1{h})e^{-2S/h},$$ where $f(h,\ln\frac1{h}) \sim \sum_{0\leq m\leq\ell} f_{\ell,m}h^\ell(\ln\frac1{h})^m$ is a symbol with $f_{0,0}>0$, $S>0$ is the so-called Agmon distance associated with the degenerate metric $\max(0, \min(V_1,V_2))dx^2$, between 0 and $\{V_1\leq 0\}$, and $n_0\geq 1$, $n_{\Gamma}\geq 0$ are integers that depend on the geometry.Comment: 37 pages, no figur

Comment on "Off-diagonal Long-range Order in Bose Liquids: Irrotational Flow and Quantization of Circulation"

In the context of an application to superfluidity, it is elaborated how to do quantum mechanics of a system with a rotational velocity. Especially, in both the laboratory frame and the non-inertial co-rotating frame, the canonical momentum, which corresponds to the quantum mechanical momentum operator, contains a part due to the rotational velocity.Comment: 2 page, comment on cond-mat/010435

On the interpretation of the equilibrium magnetization in the mixed state of high-Tc superconductors

We apply a recently developed scaling procedure to the analysis of equilibrium magnetization M(H) data that were obtained for T-2212 and Bi-2212single crystals and were reported in the literature. The temperature dependencies of the upper critical field and the magnetic field penetration depth resulting from our analysis are distinctly different from those obtained in the original publications. We argue that theoretical models, which are usually employed for analyses of the equilibrium magnetization in the mixed state of type-II superconductors are not adequate for a quantitative description of high-Tc superconductors. In addition, we demonstrate that the scaled equilibrium magnetization M(H) curve for a Tl-2212 sample reveals a pronounced kink, suggesting a phase transition in the mixed state.Comment: 9 pages, 5figure

A heuristic approach to the weakly interacting Bose gas

Some thermodynamic properties of weakly interacting Bose systems are derived from dimensional and heuristic arguments and thermodynamic relations, without resorting to statistical mechanics

Temperature dependence of the upper critical field of high-Tc superconductors from isothermal magnetization data. Influence of a temperature dependent Ginzburg-Landau parameter

We show that the scaling procedure, recently proposed for the evaluation of the temperature variation of the normalized upper critical field of type-II superconductors, may easily be modified in order to take into account a possible temperature dependence of the Ginzburg-Landau parameter kappa. As an example, we consider kappa (T) as it follows from the microscopic theory of superconductivity.Comment: 7 pages, 4 figur

Bose-Einstein condensation of trapped atoms with dipole interactions

The path integral Monte Carlo method is used to simulate dilute trapped Bose gases and to investigate the equilibrium properties at finite temperatures. The quantum particles have a long-range dipole-dipole interaction and a short-range s-wave interaction. Using an anisotropic pseudopotential for the long-range dipolar interaction and a hard-sphere potential for the short-range s-wave interaction, we calculate the energetics and structural properties as a function of temperature and the number of particles. Also, in order to determine the effects of dipole-dipole forces and the influence of the trapping field on the dipolar condensate, we use two cylindrically symmetric harmonic confinements (a cigar-shaped trap and a disk-shaped trap). We find that the net effect of dipole-dipole interactions is governed by the trapping geometry. For a cigar-shaped trap, the net contribution of dipolar interactions is attractive and the shrinking of the density profiles is observed. For a disk-shaped trap, the net effect of long-range dipolar forces is repulsive and the density profiles expand

New Majoritarian Constitutionalism

Ever since Alexander Bickel coined the phrase “countermajoritarian difficulty,” commentators have frequently described the Supreme Court as either a “majoritarian” or “counter-majoritarian” institution. In this heuristic dichotomy, the Justices either base constitutional law on their own independent and subjective interpretations or they rely on extrinsic indicators to determine constitutional meaning. In practice, however, this dichotomy is neither clearly evident, nor clearly applied, and a third approach—“New Majoritarian” Constitutionalism—has emerged. Under new majoritarian constitutionalism, the Court considers (1) the actual decisions of courts and juries; (2) legislative trends; (3) executive branch practices; and (4) geographic disparities within various jurisdictions. This model of majoritarianism accepts the traditional idea that constitutional decisions must be grounded in conventional lawmaking sources and that interpretations of vague constitutional language should accord with broadly held, majoritarian positions. This approach, however, creatively uses traditional indicators to a far greater extent than others. This Article provides a new typology of majoritarian constitutional theories that reorients our understanding of the role of objective indicators of meaning, with major implications for scholarship and doctrine. In addition to its descriptive power, new majoritarianism has important normative implications—promoting institutional process values such as stability and transparency, while reinforcing the centrality of coordinate branch dialogue in evolving constitutional meaning

New Majoritarian Constitutionalism

Ever since Alexander Bickel coined the phrase “countermajoritarian difficulty,” commentators have frequently described the Supreme Court as either a “majoritarian” or “counter-majoritarian” institution. In this heuristic dichotomy, the Justices either base constitutional law on their own independent and subjective interpretations or they rely on extrinsic indicators to determine constitutional meaning. In practice, however, this dichotomy is neither clearly evident, nor clearly applied, and a third approach—“New Majoritarian” Constitutionalism—has emerged. Under new majoritarian constitutionalism, the Court considers (1) the actual decisions of courts and juries; (2) legislative trends; (3) executive branch practices; and (4) geographic disparities within various jurisdictions. This model of majoritarianism accepts the traditional idea that constitutional decisions must be grounded in conventional lawmaking sources and that interpretations of vague constitutional language should accord with broadly held, majoritarian positions. This approach, however, creatively uses traditional indicators to a far greater extent than others. This Article provides a new typology of majoritarian constitutional theories that reorients our understanding of the role of objective indicators of meaning, with major implications for scholarship and doctrine. In addition to its descriptive power, new majoritarianism has important normative implications—promoting institutional process values such as stability and transparency, while reinforcing the centrality of coordinate branch dialogue in evolving constitutional meaning