Static and Dynamic Properties of Trapped Fermionic Tonks-Girardeau Gases

We investigate some exact static and dynamic properties of one-dimensional fermionic Tonks-Girardeau gases in tight de Broglie waveguides with attractive p-wave interactions induced by a Feshbach resonance. A closed form solution for the one-body density matrix for harmonic trapping is analyzed in terms of its natural orbitals, with the surprising result that for odd, but not for even, numbers of fermions the maximally occupied natural orbital coincides with the ground harmonic oscillator orbital and has the maximally allowed fermionic occupancy of unity. The exact dynamics of the trapped gas following turnoff of the p-wave interactions are explored.Comment: 4 pages, 2 figures, submitted to PR

The Effects of Prehydration on Cement Performance

This study investigated the effects of cement prehydration on cement’s engineering properties. Anhydrous cement was exposed over a saturated KCl solution to maintain 85% RH, for 7 and 28 days. Mortar and cement pastes were tested for strength, workability and setting time, with sample analysis by XRD and DTA. Results showed a decreased reactivity of the prehydrated cements resulting in reduced strength and increased setting times. We propose that this may be due to an upset of the sulphate balance in the cement upon prehydration

The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry

An S-matrix satisying the Yang-Baxter equation with symmetries relevant to the AdS_5xS^5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS_5xS^5 superstring worldsheet S-matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the S-matrix in the generalized rapidity plane.Comment: 27 pages, no figures; v2: sign typo fixed in (24), everything else unchange

Dynamics of Energy Transport in a Toda Ring

We present results on the relationships between persistent currents and the known conservation laws in the classical Toda ring. We also show that perturbing the integrability leads to a decay of the currents at long times, with a time scale that is determined by the perturbing parameter. We summarize several known results concerning the Toda ring in 1-dimension, and present new results relating to the frequency, average kinetic and potential energy, and mean square displacement in the cnoidal waves, as functions of the wave vector and a parameter that determines the non linearity.Comment: 34 pages, 11 figures. Small changes made in response to referee's comment

PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold

The $PT$ symmetric potential $V_0[\cos(2\pi x/a)+i\lambda\sin(2\pi x/a)]$ has a completely real spectrum for $\lambda\le 1$, and begins to develop complex eigenvalues for $\lambda>1$. At the symmetry-breaking threshold $\lambda=1$ some of the eigenvectors become degenerate, giving rise to a Jordan-block structure for each degenerate eigenvector. In general this is expected to result in a secular growth in the amplitude of the wave. However, it has been shown in a recent paper by Longhi, by numerical simulation and by the use of perturbation theory, that for a broad initial wave packet this growth is suppressed, and instead a saturation leading to a constant maximum amplitude is observed. We revisit this problem by explicitly constructing the Bloch wave-functions and the associated Jordan functions and using the method of stationary states to find the dependence on the longitudinal distance $z$ for a variety of different initial wave packets. This allows us to show in detail how the saturation of the linear growth arises from the close connection between the contributions of the Jordan functions and those of the neighbouring Bloch waves.Comment: 15 pages, 7 figures Minor corrections, additional reference

Vafa-Witten theorem and Lee-Yang singularities

We prove the analyticity of the finite volume QCD partition function for complex values of the theta-vacuum parameter. The absence of singularities different from Lee-Yang zeros only permits ^ cusp singularities in the vacuum energy density and never v cusps. This fact together with the Vafa-Witten diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros at theta=0 and has an important consequence: the absence of a first order phase transition at theta=0. The result provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vector-like gauge theories and follows from renormalizability, unitarity, positivity and existence of BPS bounds. Generalizations of this theorem to other physical systems are also discussed, with particular interest focused on the non-linear CPn sigma model.Comment: 9 page

Evolution of spherical cavitation bubbles: parametric and closed-form solutions

We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. In the simplest case when the effects of surface tension are neglected, the known parametric solutions for the radius and time evolution of the bubble in terms of a hypergeometric function are briefly reviewed. By including the surface tension, we show the connection between the Rayleigh-Plesset equation and Abel's equation, and obtain the parametric rational Weierstrass periodic solutions following the Abel route. In the same Abel approach, we also provide a discussion of the nonintegrable case of nonzero viscosity for which we perform a numerical integrationComment: 9 pages, 5 figures, 14 references, version accepted for publication at Phys. Fluid

Zero modes on cosmic strings in an external magnetic field

A classical analysis suggests that an external magnetic field can cause trajectories of charge carriers on a superconducting domain wall or cosmic string to bend, thus expelling charge carriers with energy above the mass threshold into the bulk. We study this process by solving the Dirac equation for a fermion of mass $m_f$ and charge $e$, in the background of a domain wall and a magnetic field of strength $B$. We find that the modes of the charge carriers get shifted into the bulk, in agreement with classical expectations. However the dispersion relation for the zero modes changes dramatically -- instead of the usual linear dispersion relation, $\omega_k =k$, the new dispersion relation is well fit by $\omega \approx m_f tanh(k/k_*)$ where $k_*=m_f$ for a thin wall in the weak field limit, and $k_*=eBw$ for a thick wall of width $w$. This result shows that the energy of the charge carriers on the domain wall remains below the threshold for expulsion even in the presence of an external magnetic field. If charge carriers are expelled due to an additional perturbation, they are most likely to be ejected at the threshold energy $\sim m_f$.Comment: 9 pages, 4 figure

Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again

We show that a simple approximation based on concepts underlying the Kibble-Zurek theory of second order phase transition dynamics can be used to treat avoided level crossing problems. The approach discussed in this paper provides an intuitive insight into quantum dynamics of two level systems, and may serve as a link between the theory of dynamics of classical and quantum phase transitions. To illustrate these ideas we analyze dynamics of a paramagnet-ferromagnet quantum phase transition in the Ising model. We also present exact unpublished solutions of the Landau-Zener like problems.Comment: 12 pages & 6 figures, minor corrections, version accepted in Phys. Rev.