Towards the timely detection of toxicants

We address the problem of enhancing the sensitivity of biosensors to the influence of toxicants, with an entropy method of analysis, denoted as CASSANDRA, recently invented for the specific purpose of studying non-stationary time series. We study the specific case where the toxicant is tetrodotoxin. This is a very poisonous substance that yields an abrupt drop of the rate of spike production at t approximatively 170 minutes when the concentration of toxicant is 4 nanomoles. The CASSANDRA algorithm reveals the influence of toxicants thirty minutes prior to the drop in rate at a concentration of toxicant equal to 2 nanomoles. We argue that the success of this method of analysis rests on the adoption of a new perspective of complexity, interpreted as a condition intermediate between the dynamic and the thermodynamic state.Comment: 6 pages and 3 figures. Accepted for publication in the special issue of Chaos Solitons and Fractal dedicated to the conference "Non-stationary Time Series: A Theoretical, Computational and Practical Challenge", Center for Nonlinear Science at University of North Texas, from October 13 to October 19, 2002, Denton, TX (USA

Solitary wave complexes in two-component mixture condensates

Axisymmetric three-dimensional solitary waves in uniform two-component mixture Bose-Einstein condensates are obtained as solutions of the coupled Gross-Pitaevskii equations with equal intracomponent but varying intercomponent interaction strengths. Several families of solitary wave complexes are found: (1) vortex rings of various radii in each of the components, (2) a vortex ring in one component coupled to a rarefaction solitary wave of the other component, (3) two coupled rarefaction waves, (4) either a vortex ring or a rarefaction pulse coupled to a localised disturbance of a very low momentum. The continuous families of such waves are shown in the momentum-energy plane for various values of the interaction strengths and the relative differences between the chemical potentials of two components. Solitary wave formation, their stability and solitary wave complexes in two-dimensions are discussed.Comment: 4 pages, 2 figures, 2 table

On the "Causality Paradox" of Time-Dependent Density Functional Theory

I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to a new expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the new formulation.Comment: 21 page

Behavioral pricing of energy swing options by stochastic bilevel optimization

Holders of energy swing options are free to specify the amounts of energy to be delivered on short notice, paying a fixed price per unit delivered. Due to the complexity of potential demand patterns, risk elimination by replication of these contract at energy exchange markets is not possible. As a consequence, when selling delivery contracts, the energy producer has to explicitly consider the risk emanating from fluctuations in supply cost. The impact of these risk factors can be mitigated by the contract seller, who is an energy producer, to a certain extent: Supply cost fluctuations can be absorbed by the own generation portfolio whereas demand uncertainties can be influenced by the choice of the strike price, implicitly changing the buyer's behavior. Considering this, the determination of the optimal strike price can be formulated a a stochastic bilevel problem where the optimal decision of upper level player (price setting and production) depends on the optimal decision of a lower level player (demand depending on the price). We present a solution algorithm tailored to the resulting specific stochastic bilevel problem. We illstrate the effects of the behavioral pricing approach by studying behavioral price setting for natural gas swing options, highlighting in particulr the influence of the seller's production and contract portfolio as well as of the market liquidity on optimal exercise prices

The four-fermion interaction in D=2,3,4: a nonperturbative treatment

A new nonperturbative approach is used to investigate the Gross-Neveu model of four fermion interaction in the space-time dimensions 2, 3 and 4, the number $N$ of inner degrees of freedom being a fixed integer. The spontaneous symmetry breaking is shown to exist in $D=2,3$ and the running coupling constant is calculated. The four dimensional theory seems to be trivial.Comment: a minor correction: one more acknowledgement is added. Latex 2.09 file, 15 pages, no figures, accepted for publication to Int.J.Mod.Phys.

Beyond Mean-Field Theory for Attractive Bosons under Transverse Harmonic Confinement

We study a dilute gas of attractive bosons confined in a harmonic cylinder, i.e. under cylindric confinement due to a transverse harmonic potential. We introduce a many-body wave function which extends the Bethe ansatz proposed by McGuire (J. Math. Phys. {\bf 5}, 622 (1964)) by including a variational transverse Gaussian shape. We investigate the ground state properties of the system comparing them with the ones of the one-dimensional (1D) attractive Bose gas. We find that the gas becomes ultra 1D as a consequence of the attractive interaction: the transverse width of the Bose gas reduces by increasing the number of particles up to a critical width below which there is the collapse of the cloud. In addition, we derive a simple analytical expression for the simmetry-breaking solitonic density profile of the ground-state, which generalize the one deduced by Calogero and Degasperis (Phys. Rev. A {\bf 11}, 265 (1975)). This bright-soliton analytical solution shows near the collapse small deviations with respect to the 3D mean-field numerical solution. Finally, we show that our variational Gauss-McGuire theory is always more accurate than the McGuire theory. In addition, we prove that for small numbers of particles the Gauss-McGuire theory is more reliable than the mean-field theory described by the 3D Gross-Pitaevskii equation.Comment: To be published in J. Phys. B.: At. Mol. Opt. Phy

Sound propagation in a cylindrical Bose-condensed gas

We study the normal modes of a cylindrical Bose condensate at $T = 0$ using the linearized time-dependent Gross-Pitaevskii equation in the Thomas-Fermi limit. These modes are relevant to the recent observation of pulse propagation in long, cigar-shaped traps. We find that pulses generated in a cylindrical condensate propagate with little spread at a speed $c = \sqrt{g\bar n /m}$, where $\bar n$ is the average density of the condensate over its cross-sectional area.Comment: 4 pages, 2 Postscript figure

Direct evaluation of the isotope effect within the framework of density functional theory for superconductors

Within recent developments of density functional theory, its numerical implementation and of the superconducting density functional theory is nowadays possible to predict the superconducting critical temperature, Tc, with sufficient accuracy to anticipate the experimental verification. In this paper we present an analytical derivation of the isotope coefficient within the superconducting density functional theory. We calculate the partial derivative of Tc with respect to atomic masses. We verified the final expression by means of numerical calculations of isotope coefficient in monatomic superconductors (Pb) as well as polyatomic superconductors (CaC6). The results confirm the validity of the analytical derivation with respect to the finite difference methods, with considerable improvement in terms of computational time and calculation accuracy. Once the critical temperature is calculated (at the reference mass(es)), various isotope exponents can be simply obtained in the same run. In addition, we provide the expression of interesting quantities like partial derivatives of the deformation potential, phonon frequencies and eigenvectors with respect to atomic masses, which can be useful for other derivations and applications

The Josephson effect throughout the BCS-BEC crossover

We study the stationary Josephson effect for neutral fermions across the BCS-BEC crossover, by solving numerically the Bogoliubov-de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.Comment: 4 pages, 3 figures; improved version to appear in Phys. Rev. Let

Microscopic Structure of a Vortex Line in a Superfluid Fermi Gas

The microscopic properties of a single vortex in a dilute superfluid Fermi gas at zero temperature are examined within the framework of self-consistent Bogoliubov-de Gennes theory. Using only physical parameters as input, we study the pair potential, the density, the energy, and the current distribution. Comparison of the numerical results with analytical expressions clearly indicates that the energy of the vortex is governed by the zero-temperature BCS coherence length.Comment: 4 pages, 4 embedded figures. Added references. To be published in Physical Review Letter