Stavros Theodorakis

Bound states in a nonlinear Kronig - Penney model

We study the bound states of a Kronig Penney potential for a nonlinear one-dimensional Schrodinger equation. This potential consists of a large, but not necessarily infinite, number of equidistant -function wells. We show that the ground state can be highly degenerate. Under certain conditions furthermore, even the bound state that would normally be the highest can have almost the same energy as the ground state. This holds for other simple periodic potentials as well.

Heavy family masses: Analytic results

Abstract We solve analytically the one-loop renormalization group equations for the fermion mass matrices and the quartic coupling, assuming a perturbative SU(3)×SU(2)×U(1) desert, one elementary Higgs boson and any number of families. The low energy asymptotic forms of our exact results show how the infrared fixed point structure arises and leads to predictions of heavy family masses. The sum of the squares of the quark masses is (290 GeV) 2 and the Higgs mass is 240 GeV, for one heavy family; similar predictions hold if there are more families.

Vortices and NMR in rotating3He-B

The core structure of singly quantized vortices in3He-B is studied in the Ginzburg-Landau regime. For zero magnetic field, variational estimates indicate a core anisotropy; the gap is suppressed along the component of n in the plane perpendicular to the vortex axis within a core of radius ∼6ξ. For large fields (∼300 Oe) parallel to the vortex axis, a similar transverse anisotropy occurs, but its azimuthal direction is degenerate to leading order. The effective coupling constant λ in a rotating system arises from the kinetic energy of the flow, with anisotropy contributions smaller by two orders of magnitude. Predictions about the transverse NMR are compared with the observed resonances; detection of the corresponding longitudinal modes could help confirm the theoretical description.

Hierarchy of Tc's in the thallium high-Tc superconductors

Abstract We present a phenomenological formalism determining the critical temperatures of the various superconducting phases in the newly discovered thallium high- T c superconductors. T c cannot exceed 146 K (164 K) for the compounds with bilayer (monolayer) Tl-O sheets.

Emergence of approximate translation invariance in finite intervals as a speed selection mechanism for propagating fronts

We introduce a velocity selection criterion for fronts propagating into unstable and metastable states. We restrict these fronts to large finite intervals in the comoving frame of reference and require that their centers be insensitive to the locations of the ends of the finite intervals, thus exhibiting effectively an approximate translation invariance. Only one monotonic front has this behavior, and its velocity is the one that is physically selected. We present analytic results in the case of piecewise parabolic potentials and numerical results in other cases.

Inequivalent layers in the phenomenology of high Tc superconductors

Abstract We present a phenomenological model describing the high Tc superconductors. The model accounts for the observed positive curvature in the temperature dependence of the H⊥c2, in terms of a proximity effect between the superconducting and insulating layers forming the unit cell of various copper oxides.

A phenomenological model for high Tc superconductors

Abstract We propose a phenomenological model describing the high T c superconductors. Adjacent Cu-O layers have negative Josephson couplings, forcing the order paramater to change sign from one layer to the next. The number of closely spaed layers determines T c .

The wavefunction of the collapsing Bose–Einstein condensate

Bose–Einstein condensates with tunable interatomic interactions have been studied intensely in recent experiments. The investigation of the collapse of a condensate following a sudden change in the nature of the interaction from repulsive to attractive has led to the observation of a remnant condensate that did not undergo further collapse. We suggest that this high-density remnant is in fact the absolute minimum of the energy, if the attractive atomic interactions are nonlocal, and is therefore inherently stable. We show that a variational trial function consisting of a superposition of two distinct gaussians is an accurate representation of the wavefunction of the ground state of the conventional local Gross–Pitaevskii field equation for an attractive condensate and gives correctly the points of emergence of instability. We then use such a superposition of two gaussians as a variational trial function in order to calculate the minima of the energy when it includes a nonlocal interaction term. We use experimental data in order to study the long range of the nonlocal interaction, showing that they agree very well with a dimensionally derived expression for this range.

Lopsided vortex cells in rotating Bose–Einstein condensates

The amplitude of the wavefunction of a repulsive Bose–Einstein condensate in a two-dimensional axisymmetric harmonic trap decreases as we go from the center of the condensate towards its edge. Consequently the wavefunction amplitude at the edge of a vortex cell in a vortex lattice in a rotating repulsive condensate should be greater for the inner cells. Continuity of the wavefunction amplitude between neighboring cells requires then that varies along the edge of each vortex cell, so that it is greater at the points that are closer to the center of the condensate. In other words, the wavefunction amplitude is lopsided in each vortex cell. We show this explicitly via an analytic variational calculation where a simple lopsided wavefunction amplitude is used for each vortex cell. This wavefunction amplitude varies continuously as we go from one cell to the next. The results agree quite well with experimental observations.

The paradox of the floating candle that continues to burn

What happens after lighting a paraffin candle that is barely floating in water and kept upright with the aid of an appropriately weighted nail attached to its bottom? Presumably, it should sink because the buoyant force will decrease more than the weight. Surprisingly, the candle will continue to burn, rising slowly above the surface of the water. The reason for this is that the flame forms a well around the wick filled with molten paraffin, while the water keeps the outer walls of the candle cool and unscathed. Thus, the buoyancy hardly changes while the weight is reduced through burning, resulting in a floating candle that will rise above water. We present a quantitative model that describes the formation of the well and verify it experimentally, examining first the case of a candle in the air and then the case of a candle immersed in water.