Hierarchy of QM SUSYs on a Bounded Domain

We systematically formulate a hierarchy of isospectral Hamiltonians in one-dimensional supersymmetric quantum mechanics on an interval and on a circle, in which two successive Hamiltonians form N=2 supersymmetry. We find that boundary conditions compatible with supersymmetry are severely restricted. In the case of an interval, a hierarchy of, at most, three isospectral Hamiltonians is possible with unique boundary conditions, while in the case of a circle an infinite tower of isospectral Hamiltonians can be constructed with two-parameter family of boundary conditions.Comment: 15 pages, 3 figure

Willmore minimizers with prescribed isoperimetric ratio

Motivated by a simple model for elastic cell membranes, we minimize the Willmore functional among two-dimensional spheres embedded in R^3 with prescribed isoperimetric ratio

Evolution of Topological Defects During Inflation

Topological defects can be formed during inflation by phase transitions as well as by quantum nucleation. We study the effect of the expansion of the Universe on the internal structure of the defects. We look for stationary solutions to the field equations, i.e. solutions that depend only on the proper distance from the defect core. In the case of very thin defects, whose core dimensions are much smaller than the de Sitter horizon, we find that the solutions are well approximated by the flat space solutions. However, as the flat space thickness parameter $\delta_0$ increases we notice a deviation from this, an effect that becomes dramatic as $\delta_0$ approaches $(H)^{-1}/{\sqrt 2}$. Beyond this critical value we find no stationary solutions to the field equations. We conclude that only defects that have flat space thicknesses less than the critical value survive, while thicker defects are smeared out by the expansion.Comment: 14 page

Entropy: From Black Holes to Ordinary Systems

Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better understanding in the thermodynamics of ordinary systems for which a pre-relativistic description is sufficient. First, we investigated the possibility to introduce an alternative definition of the entropy basically related to a local definition of the order in a spacetime model rather than a counting of microstates. We show that such an alternative approach exists and leads to the traditional results provided an equilibrium condition is assumed. This condition introduces a relation between a time interval and the reverse of the temperature. We show that such a relation extensively used in the black hole theory, mainly as a mathematical trick, has a very general and physical meaning here; in particular its derivation is not related to the existence of a canonical density matrix. Our dynamical approach of thermodynamic equilibrium allows us to establish a relation between action and entropy and we show that an identical relation exists in the case of black holes. The derivation of such a relation seems impossible in the Gibbs ensemble approach of statistical thermodynamics. From these results we suggest that the definition of entropy in terms of order in spacetime should be more general that the Boltzmann one based on a counting of microstates. Finally we point out that these results are obtained by reversing the traditional route going from the Schr\"{o}dinger equation to statistical thermodynamics

Curvature-induced phase transitions in the inflationary universe - Supersymmetric Nambu-Jona-Lasinio Model in de Sitter spacetime -

The phase structure associated with the chiral symmetry is thoroughly investigated in de Sitter spacetime in the supersymmetric Nambu-Jona-Lasinio model with supersymmetry breaking terms. The argument is given in the three and four space-time dimensions in the leading order of the 1/N expansion and it is shown that the phase characteristics of the chiral symmetry is determined by the curvature of de Sitter spacetime. It is found that the symmetry breaking takes place as the first order as well as second order phase transition depending on the choice of the coupling constant and the parameter associated with the supersymmetry breaking term. The critical curves expressing the phase boundary are obtained. We also discuss the model in the context of the chaotic inflation scenario where topological defects (cosmic strings) develop during the inflation.Comment: 29 pages, 6 figures, REVTe

Effect of pre-existing baryon inhomogeneities on the dynamics of quark-hadron transition

Baryon number inhomogeneities may be generated during the epoch when the baryon asymmetry of the universe is produced, e.g. at the electroweak phase transition. The regions with excess baryon number will have a lower temperature than the background temperature of the universe. Also the value of the quark hadron transition temperature $T_c$ will be different in these regions as compared to the background region. Since a first-order quark hadron transition is very susceptible to small changes in temperature, we investigate the effect of the presence of such baryonic lumps on the dynamics of quark-hadron transition. We find that the phase transition is delayed in these lumps for significant overdensities. Consequently, we argue that baryon concentration in these regions grows by the end of the transition. We briefly discuss some models which may give rise to such high overdensities at the onset of the quark-hadron transition.Comment: 16 pages, no figures, minor changes, version to appear in Phys. Rev.

Zirconia Translucency and Cement Systems as Factors Influencing the Zirconia-Titanium and Zirconia-Zirconia Shear Bond Strength

Purpose: To evaluate the bonding ability of self-adhesive and dual-cure resin cement systems applied to zirconia materials of different translucency in combination with each other and with titanium. Materials and Methods: Computer-aided design/computer-assisted manufacture (CAD/CAM) disks of three different zirconia materials (Zenostar MO 0 [medium opacity], MT 0 [medium translucency], and T 1 [translucent], Wieland Dental) were milled and hard sintered in order to obtain cylindrical samples of either 12 mm high × 12 mm diameter (used as a substrate) or 12 mm high × 8 mm diameter (to be bonded to the substrate). CAD/CAM disks of titanium (Starbond Ti4 Disc, S&S Scheftner) were milled in order to obtain a cylinder shape (12 mm high × 8 mm diameter to be bonded to the zirconia substrate). The bonding surfaces were sandblasted with alumina particles (70 μm/2 ATM). Two resin cement systems were tested in this study: a self-adhesive resin cement (SpeedCEM Plus, Ivoclar Vivadent) and a dual-cure resin cement (Variolink Esthetic DC, Ivoclar Vivadent) in combination with a primer (Monobond Plus, Ivoclar Vivadent). The smaller cylinders were bonded to the substrate following the manufacturer’s instructions. After 24 hours at 37°C storage, each specimen was subjected to shear bond strength testing in a universal testing machine. The substrate was fixed to the machine, and shear force was applied to the small cylinder close to the bonding interface. Shear bond strength data were statistically analyzed by a three-way analysis of variance (ANOVA) followed by the Tukey test for post hoc comparison (P < .05). Results: No significant differences were found between substrates in the shear bond strength test (P = .078). Variolink Esthetic DC showed a statistically significantly higher bond strength compared with the SpeedCEM Plus (P = .001) with the exception of Zenostar MT substrate (P = .014). Conclusion: The resin cement systems showed high shear bond strength values when zirconia was resin bonded to either titanium or the corresponding zirconia substrate. Different zirconia translucencies did not affect the bond strength. The use of MDP primer and a dual-cure cement showed statistically significantly higher strength compared with the self-adhesive resin cement system with the only exception being the bonding of the translucent zirconia Zenostar MT

L\'evy-Schr\"odinger wave packets

We analyze the time--dependent solutions of the pseudo--differential L\'evy--Schr\"odinger wave equation in the free case, and we compare them with the associated L\'evy processes. We list the principal laws used to describe the time evolutions of both the L\'evy process densities, and the L\'evy--Schr\"odinger wave packets. To have self--adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible L\'evy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the L\'evy--Schr\"odinger wave packets, and in particular of the bi-modality arising in their evolutions: a feature at variance with the typical diffusive uni--modality of both the L\'evy process densities, and the usual Schr\"odinger wave functions.Comment: 41 pages, 13 figures; paper substantially shortened, while keeping intact examples and results; changed format from "report" to "article"; eliminated Appendices B, C, F (old names); shifted Chapters 4 and 5 (old numbers) from text to Appendices C, D (new names); introduced connection between Relativistic q.m. laws and Generalized Hyperbolic law

Are nontopological strings produced at the electroweak phase transition?

We formulate a local condition for a nontopological defect to be present. We apply it for electroweak strings and estimate the probability of their existence at the Ginzburg temperature. As a result we find strings long enough to serve for baryon-number generation are unlikely to be produced.Comment: 12 pages (REVTeX), no figure, Physical Review Letters in pres