Search

In this chapter the physical aspects of the global optimization of the geometry of atomic clusters are elucidated. In particular, I examine the structural principles that determine the nature of the lowest-energy structure, the physical reasons why some clusters are especially difficult to optimize and how the basin-hopping transformation of the potential energy surface enables these difficult clusters to be optimized., Comment: 37 pages, 18 figures, chapter for forthcoming Kluwer book on global optimization

In this article, we review basic facts about disordered systems, especially the existence of many metastable states and and the resulting failure of dimensional reduction. Besides techniques based on the Gaussian variational method and replica-symmetry breaking (RSB), the functional renormalization group (FRG) is the only general method capable of attacking strongly disordered systems. We explain the basic ideas of the latter method and why it is difficult to implement. We finally review current progress for elastic manifolds in disorder., Plenary lecture held at RG-2002

The energy-energy correlation function of the two-dimensional Ising model with weakly fluctuating random bonds is evaluated in the large scale limit. Two correlation lengths exist in contrast to one correlation length in the pure 2D Ising model: one is finite whereas the other is divergent at the critical points. The corresponding exponent of the divergent correlation length is $\nu_e=1/2$ in contrast to the pure system where $\nu_e=1$. The calculation is based on a previously developed effective field theory for the energy density fluctuations., Comment: 8 pages, RevTeX 3.0, TKM-preprint

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the equation. A line of nontrivial fixed point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively., 18 pages, 12 figures. Minor corrections to one figure

We give three methods for entangling quantum states in quantum dots. We do this by showing how to tailor the resonant energy (Foerster-Dexter) transfer mechanisms and the biexciton binding energy in a quantum dot molecule. We calculate the magnitude of these two electrostatic interactions as a function of dot size, interdot separation, material composition, confinement potential and applied electric field by using an envelope function approximation in a two-cuboid dot molecule. In the first implementation, we show that it is desirable to suppress the Foerster coupling and to create entanglement by using the biexciton energy alone. We show how to perform universal quantum logic in a second implementation which uses the biexciton energy together with appropriately tuned laser pulses: by selecting appropriate materials parameters high fidelity logic can be achieved. The third implementation proposes generating quantum entanglement by switching the Foerster interaction itself. We show that the energy transfer can be fast enough in certain dot structures that switching can occur on a timescale which is much less than the typical decoherence times., Comment: 20 pages, 20 figures

The 38-atom Lennard-Jones cluster has a paradigmatic double-funnel energy landscape. One funnel ends in the global minimum, a face-centred-cubic (fcc) truncated octahedron. At the bottom of the other funnel is the second lowest energy minimum which is an incomplete Mackay icosahedron. We characterize the energy landscape in two ways. Firstly, from a large sample of minima and transition states we construct a disconnectivity tree showing which minima are connected below certain energy thresholds. Secondly we compute the free energy as a function of a bond-order parameter. The free energy profile has two minima, one which corresponds to the fcc funnel and the other which at low temperature corresponds to the icosahedral funnel and at higher temperatures to the liquid-like state. These two approaches show that the greater width of the icosahedral funnel, and the greater structural similarity between the icosahedral structures and those associated with the liquid-like state, are the cause of the smaller free energy barrier for entering the icosahedral funnel from the liquid-like state and therefore of the cluster's preferential entry into this funnel on relaxation down the energy landscape. Furthermore, the large free energy barrier between the fcc and icosahedral funnels, which is energetic in origin, causes the cluster to be trapped in one of the funnels at low temperature. These results explain in detail the link between the double-funnel energy landscape and the difficulty of global optimization for this cluster., 12 pages, 11 figures, revtex

We show how to construct a complete set of eigenstates of the hamiltonian of the one-dimensional Hubbard model on a lattice of even length $L$. This is done by using the nested Bethe Ansatz {\it and} the $SO(4)$ symmetry of the model. We discuss in detail how the counting of independent eigenstates is carried out., 33 pages, using latex, to appear in Nucl.Phys. B (FS)

In this paper we demonstrate a striking regularity in the way people place limit orders in financial markets, using a data set consisting of roughly seven million orders from the London Stock Exchange. We define the relative limit price as the difference between the limit price and the best price available. Merging the data from 50 stocks, we demonstrate that for both buy and sell orders, the unconditional cumulative distribution of relative limit prices decays roughly as a power law with exponent approximately 1.5. This behavior spans more than two decades, ranging from a few ticks to about 2000 ticks. Time series of relative limit prices show interesting temporal structure, characterized by an autocorrelation function that asymptotically decays as tau^(-0.4). Furthermore, relative limit price levels are positively correlated with and are led by price volatility. This feedback may potentially contribute to clustered volatility.

The excitation spectrum of spin-Peierls antiferromagnets is discussed taking into acount phonon dynamics but treating inter-chain elastic couplings in mean field theory. This gives a ladder of soliton -anti-soliton boundstates, with no soliton continuum, until soliton deconfinement takes place at a transition into a non-dimerized phase., 5 pages, Latex, 1 postscript figure

We consider the one-dimensional half-filled Hubbard model. We show that the excitation spectrum is given by the scattering states of four elementary excitations, which form the fundamental representation of $SU(2)\times SU(2)$. We determine the exact two-particle Scattering matrix, which a solution of the Yang-Baxter equation and reflects the $SO(4)$ symmetry of the model. The results for repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom., 29 pages, jyTeX (macro included - just TeX the file) ITP-SB-93-45, BONN-HE-93-39

We have located the global minimum for all lead clusters with up to 160 atoms using a glue potential to model the interatomic interactions. The lowest-energy structures are not face-centred cubic as suggested previously. Rather, for N, 9 pages, 6 figures

In recent experiments on sodium chloride clusters structural transitions between nanocrystals with different cuboidal shapes were detected. Here we presents results for the thermodynamics and dynamics of one of these clusters, (NaCl)35Cl-. As the time scales for the structural transitions can be much longer than those accessible by conventional dynamics simulations, we use a master equation to describe the probability flow within a large sample of potential energy minima. We characterize the processes contributing to probability flow between the different nanocrystals, and obtain rate constants and activation energies for comparison with the experimental values., Comment: 11 pages, 8 figures, revtex

We calculate analytically the exact dynamical response of a droplet of N interacting electrons in a quantum dot with an arbitrarily time-dependent parabolic confinement potential \omega(t) and a perpendicular magnetic field. We find that, for certain frequency ranges, a sinusoidal perturbation acts like an attractive effective interaction between electrons. In the absence of a time-averaged confinement potential, the N electrons can bind together to form a stable, free-standing droplet., Comment: 10 pages, RevTex, 3 Postscript figures. This version to appear as a Rapid Communication in PRB

We study a string of neutral atoms with nearest neighbor interaction in a 1D beam splitter configuration, where the longitudinal motion is controlled by a moving optical lattice potential. The dynamics of the atoms crossing the beam splitter maps to a 1D spin model with controllable time dependent parameters, which allows the creation of maximally entangled states of atoms by crossing a quantum phase transition. Furthermore, we show that this system realizes protected quantum memory, and we discuss the implementation of one- and two-qubit gates in this setup., Comment: 4 pages, REVTEX, revised version: improvements in introduction and figures

We present a variational estimate for the binding energy of a Frenkel exciton in the insulating cuprate superconductors. Starting from the three band Hubbard model we perform a canonical transformation to O($t^2$), where $t$ is the bare nearest neighbour copper-oxygen hopping integral. An effective Hamiltonian is then derived to describe the hopping of the exciton through the copper oxide plane. The critical parameter in the model is the nearest neighbour copper-oxygen coulomb repulsion, $V$. It is found that a critical value of $V$ is needed to observe bound Frenkel excitons, and that these excitons have the same symmetry as the parent copper orbital, $d_{x^2-y^2}$. We determine the critical value of $V$ using a variational approach, and attempt to fit the parameters of the model to known experimental results., Comment: Latex document. Figures on request.

We use a random walk in the ensemble of impurity configurations to generate a Brownian motion model for energy levels in disordered conductors. Treating arc-length along the random walk as fictitous time, the resulting Langevin equation relates spectral statistics to eigenfunction correlations. Solving this equation at energy scales large compared with the mean level spacing, we obtain the spectral form factor, and its parametric dependence., 4 pages in REVTeX format including 1 postscript figure; to be published in Phys. Rev. Letters, 1996

A two state (2-MO) model for the low-lying long axis-polarised excitations of poly(p-phenylene) oligomers and polymers is developed. First we derive such a model from the underlying Pariser-Parr-Pople (P-P-P) model of pi-conjugated systems. The two states retained per unit cell are the Wannier functions associated with the valence and conduction bands. By a comparison of the predictions of this model to a four state model (which includes the non-bonding states) and a full P-P-P model calculation on benzene and biphenyl, it is shown quantitatively how the 2-MO model fails to predict the correct excitation energies. The 2-MO model is then solved for oligophenylenes of up to 15 repeat units using the density matrix renormalisation group (DMRG) method. It is shown that the predicted lowest lying, dipole allowed excitation is ca. 1 eV higher than the experimental result. The failure of the 2-MO model is a consequence of the fact that the original HOMO and LUMO single particle basis does not provide an adequate representation for the many body processes of the electronic system., LaTeX, 12 pages, 3 eps figures included using epsf. To appear in Chemical Physics, 1999

We consider the probability $P(t)$ that a given site remains unvisited by any of a set of random walkers in $d$ dimensions undergoing the reaction $A+A\to0$ when they meet. We find that asymptotically $P(t)\sim t^{-\theta}$ with a universal exponent $\theta=\ffrac12-O(\epsilon)$ for $d=2-\epsilon$, while, for $d>2$, $\theta$ is non-universal and depends on the reaction rate. The analysis, which uses field-theoretic renormalisation group methods, is also applied to the reaction $kA\to0$ with $k>2$. In this case, a stretched exponential behaviour is found for all $d\geq1$, except in the case $k=3$, $d=1$, where $P(t)\sim {\rm e}^{-\const (\ln t)^{3/2}}$., Comment: 10 pages, (revised version with abstract included) OUTP-94-35S

We consider a completely integrable lattice regularization of the sine-Gordon model with discrete space and continuous time. We derive a determinant representation for a correlation function which in the continuum limit turns into the correlation function of local fields. The determinant is then embedded into a system of integrable integro-differential equations. The leading asymptotic behaviour of the correlation function is described in terms of the solution of a Riemann Hilbert Problem (RHP) related to the system of integro-differential equations. The leading term in the asymptotical decomposition of the solution of the RHP is obtained., Comment: 30 pages Latex2e, 2 Figures, epsf. Significantly extended and revised version

Density matrix renormalisation group calculations of a suitably parametrised model of long polyenes (polyacetylene oligomers), which incorporates both long range Coulomb interactions and adiabatic lattice relaxation, are presented. The triplet and 2Ag states are found to have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The 1Bu state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag state lies below that of the 1Bu state. The soliton/anti-soliton pairs are bound., RevTeX, 5 pages, 4 eps figures included using epsf. To appear in Physical Review Letters. Fig. 1 fixed up

The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V, is determined. Phase separation takes place above a critical value of $V$ when the Cu2+ to Cu+ valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger Liquid theory applies and calculate the contours of the charge-charge correlation exponent K_{\rho}. We show that anomalous flux quantization occurs as K_{\rho} diverges. At n = 1, for V > t, a gap opens in the spectrum and the ground state is a charge-density wave.

A single model is presented which represents both of the two apparently unrelated localisation problems of the title. The phase diagram of this model is examined using scaling ideas and numerical simulations. It is argued that the localisation length in a spin-degenerate Landau level diverges at two distinct energies, with the same critical behaviour as in a spin-split Landau level, and that all states of a charged particle moving in two dimensions, in a random magnetic field with zero average, are localised., Comment: 7 pages (RevTeX 3.0) plus 4 postscript figures

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form factor in two ways. First, describing the dynamics using a Fokker-Planck equation, we make a physically motivated decoupling, obtaining the spectral correlations in terms of the quantum return probability. Second, from an identity which we derive between two- and three-particle correlation functions, we make a mathematically controlled decoupling to obtain the same result. We also calculate weak localization corrections to this result, and show for two dimensional systems (which are of most interest) that corrections vanish to three-loop order., 35 pages in REVTeX format including 10 postscript figures; to be published in a special issue (on Topics in Mesoscopic Physics) of the Journal of Mathematical Physics, October 1996

A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the height function. For a harmonic traveling wave on the surface, we find many different regimes in which the radiation is restricted to certain directions. It is shown that high frequency photons are emitted in a beam with relatively low angular dispersion whose direction can be controlled by the mechanical deformations of the plate., Comment: 4 pages, 2 eps figues included, final version as appeared in PRA

Analytic phenomenological scaling is carried out for the random field Ising model in general dimensions using a bar geometry. Domain wall configurations and their decorated profiles and associated wandering and other exponents $(\zeta,\gamma,\delta,\mu)$ are obtained by free energy minimization. Scaling between different bar widths provides the renormalization group (RG) transformation. Its consequences are (1) criticality at $h=T=0$ in $d \leq 2$ with correlation length $\xi(h,T)$ diverging like $\xi(h,0) \propto h^{-2/(2-d)}$ for $d, Comment: RevTex v3.0, 5 pages, plus 4 figures uuencoded

We locate putative global minima for (C_60)_N clusters modelled by the potential of Pacheco and Prates-Ramalho up to N=105. These minima are based on icosahedral packing up to N=15, but above this size the lowest-energy structures are decahedral or close-packed. Although structures based on the 98-molecule Leary tetrahedron, which have been inferred from experiment, are not lowest in energy for this potential, an examination of the energetics of a growth sequence leading to the Leary tetrahedron lends further support to the experimental assignments. An analysis of the potential energy surface topography and the thermodynamics of two example clusters indicates that the multiple-funnel topography is likely to have a strong influence on the dynamics of structure formation and that solid-solid transitions driven by differences in vibrational entropy are likely to be common., 13 pages, 8 figures

Models with competing interactions, for example the ANNNI model, can have special points at which the ground state is infinitely degenerate, so-called multiphase points. Small perturbations can lift this degeneracy and give rise to infinite sequences of long-period phases. This paper compares the effect of three possible perturbations, quantum fluctuations, thermal fluctuations and the softening of the spins from their quantised positions., 14 pages, Revtex, 3 Figs. available upon request Oxford University

We consider a class of multi-matrix models with an action which is O(D) invariant, where D is the number of NxN Hermitian matrices X_\mu, \mu=1,...,D. The action is a function of all the elementary symmetric functions of the matrix $T_{\mu\nu}=Tr(X_\mu X_\nu)/N$. We address the issue whether the O(D) symmetry is spontaneously broken when the size N of the matrices goes to infinity. The phase diagram in the space of the parameters of the model reveals the existence of a critical boundary where the O(D) symmetry is maximally broken., Comment: LaTeX, 18 pages, 2 figures

We consider quantum correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that for a magnetic field close to the critical field $h_c$ (for the critical magnetic field the ground state is ferromagnetic) certain correlation functions can be expressed in terms of the solution of the Painlev\'e V transcendent. This establishes a relation between solutions of Painlev\'e differential equations and quantum correlation functions in models of {\sl interacting} fermions. Painlev\'e transcendents were known to describe correlation functions in models with free fermionic spectra., Comment: 10 pages, LaTeX2e

The theory of aperiodic order is concerned with the development of ideas stimulated by the discovery of quasicrystals. We give a gentle introduction to some mathematical aspects of aperiodic order, aimed at a more general audience., Comment: 27 pages, many colour pictures

Phase transitions of first and second order can easily be distinguished in small systems in the microcanonical ensemble. Configurations of phase coexistence, which are suppressed in the canonical formulation, carry important information about the main characteristics of first order phase transitions like the transition temperature, the latent heat, and the interphase surface tension. The characterisitc backbending of the micro- canonical caloric equation of state T(E) (not to be confused with the well known Van der Waals loops in ordinary thermodynamics) leading to a negative specific heat is intimatly linked to the interphase surface entropy., Latex, 4 eps-figures, graphicx.sty

Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an approximate scaling and heavy tails of the return distributions, long-ranged volatility-volatility correlations (volatility clustering) and return-volatility correlations (leverage effect). Free parameters of the model are fixed over the long term by fitting 100+ years of daily prices of the Dow Jones 30 Industrial Average. The multivariate probability density functions which we have constructed can be used for pricing derivative securities and risk management., Talk given by M. I. Krivoruchenko at the International Conference of Computational Methods in Sciences and Engineering 2003 (ICCMSE 2003), Kastoria, Greece, 12-16 September 2003; 16 pages, 4 Postscript figures, REVTeX. Extended abstract appeared in: Proceedings of the International Conference of Computational Methods in Sciences and Engineering 2003 (ICCMSE 2003), Ed. T.E. Simos (World Scientific Publishing Co., Singapore, 2003), pp. 323-326

We study a generic model for self-referential behaviour in financial markets, where agents attempt to use some (possibly fictitious) causal correlations between a certain quantitative information and the price itself. This correlation is estimated using the past history itself, and is used by a fraction of agents to devise active trading strategies. The impact of these strategies on the price modify the observed correlations. A potentially unstable feedback loop appears and destabilizes the market from an efficient behaviour. For large enough feedbacks, we find a `phase transition' beyond which non trivial correlations spontaneously set in and where the market switches between two long lived states, that we call conventions. This mechanism leads to overreaction and excess volatility, which may be considerable in the convention phase. A particularly relevant case is when the source of information is the price itself. The two conventions then correspond then to either a trend following regime or to a contrarian (mean reverting) regime. We provide some empirical evidence for the existence of these conventions in real markets, that can last for several decades., Comment: 15 pages, 12 .eps figures

(2+1)-dimensional Georgi-Glashow model is explored in the regime when the Higgs boson is not infinitely heavy, but its mass is rather of the same order of magnitude as the mass of the W boson. In the weak-coupling limit, the Debye mass of the dual photon and the expression for the monopole potential are found. The cumulant expansion applied to the average over the Higgs field is checked to be convergent for the known data on the monopole fugacity. These results are further generalized to the SU(N)-case. In particular, it is found that the requirement of convergence of the cumulant expansion establishes a certain upper bound on the number of colours. This bound, expressed in terms of the parameter of the weak-coupling approximation, allows the number of colours to be large enough. Finally, the string tension and the coupling constant of the so-called rigidity term of the confining string are found at arbitrary number of colours., 9 pages, LaTeX2e, no figures

Two-phase flow systems in porous media have complex dynamics. It is well established that a wide range of system parameters like viscosities and porosity as well as flow parameters such as pressure gradient and fluid saturation have strong impact on the dynamics. The transition from single-phase flow to two-phase flow is a dynamical phase transition. We discuss the order of the transition and investigate the phase diagram in parameter space, using a network simulator for two-phase flow. A semi-empirical theory for the location of the phase boundaries is provided., Comment: 11 pages, 7 figures, 26 .eps-files

We proposed a scheme to realize a controlled-NOT quantum logic gate in a dimer of exchange coupled single-molecule magnets, $[\textrm{Mn}_4]_2$. We chosen the ground state and the three low-lying excited states of a dimer in a finite longitudinal magnetic field as the quantum computing bases and introduced a pulsed transverse magnetic field with a special frequency. The pulsed transverse magnetic field induces the transitions between the quantum computing bases so as to realize a controlled-NOT quantum logic gate. The transition rates between the quantum computing bases and between the quantum computing bases and other excited states are evaluated and analyzed., 7 pages, 2 figures

Buying and selling stocks causes price changes, which are described by the price impact function. To explain the shape of this function, we study the Island ECN orderbook. In addition to transaction data, the orderbook contains information about potential supply and demand for a stock. The virtual price impact calculated from this information is four times stronger than the actual one and explains it only partially. However, we find a strong anticorrelation between price changes and order flow, which strongly reduces the virtual price impact and provides for a quantitative explanation of the empirical price impact function., 4 pages, 4 figures; figure 4a corrected, reference added, typos corrected

The process of multicomponent condensation is considered. The theory taking into account several channels of nucleation is constructed. The analytical approximate description of the whole condensation process is given. The specific phenomena of the secondary nucleation is described analytically. The possibility of the partial reverse condensation is discussed., Comment: LATEX

We develop the cluster expansion and the Mayer expansion for the self-gravitating thermal gas and prove the existence and stability of the thermodynamic limit N, V to infty with N/V^{1/3} fixed. The essential (dimensionless) variable is here eta = [G m^2 N]/[V^{1/3} T] (which is kept fixed in the thermodynamic limit). We succeed in this way to obtain the expansion of the grand canonical partition function in powers of the fugacity. The corresponding cluster coefficients behave in the thermodynamic limit as [eta/N]^{j-1} c_j where c_j are pure numbers. They are expressed as integrals associated to tree cluster diagrams. A bilinear recurrence relation for the coefficients c_j is obtained from the mean field equations in the Abel form. In this way the large j behaviour of the c_j is calculated. This large j behaviour provides the position of the nearest singularity which corresponds to the critical point (collapse) of the self-gravitating gas in the grand canonical ensemble. Finally, we discuss why other attempts to define a thermodynamic limit for the self-gravitating gas fail., Comment: LaTex 12 pages, 1 figure .ps

In this paper we discuss a scaling approach to business fluctuations. Our starting point consists in recognizing that concepts and methods derived from physics have allowed economists to (re)discover a set of stylized facts which have to be satisfactorily accounted for in their models. Standard macroeconomics, based on a reductionist approach centered on the representative agent, is definitely badly equipped for this task. On the contrary, we show that a simple financial fragility agent-based model, based on complex interactions of heterogeneous agents, is able to replicate a large number of scaling type stylized facts with a remarkable high degree of statistical precision., Comment: 35 pages. Accepted by "Journal of Economic Behaviour and Organisation"

Modeling the dielectric behavior of molecular materials made up of large pi-conjugated molecules is an interesting and complex task. Here we address linear polarizabilities, and the related dielectric constant, of molecular crystals and aggregates made up of closed-shell pi-conjugated molecules with either a non-polar or largely polar ground-state, and also examine the behavior of mixed-valence (or charge-transfer) organic salts. We recognize important collective phenomena due to supramolecular interactions in materials with large molecular polarizabilities, and underline large vibrational contributions to the polarizability in materials with largely delocalized electrons., 18 pages, including 9 figures

The analytical bounce solution is derived in terms of the polygamma function in the Caldeira-Leggett's dissipative quantum tunneling model. The classical action for the bounce solution lies between the upper and lower bounds in the full range of $\alpha$, where $\alpha$ is a dissipation coefficient. The bounce peak point increases from 1 to 4/3 with increase of $\alpha$. In spite of various nice features we have shown that the solution we have derived is not exact one by making use of the zero mode argument in the linearized fluctuation equation. However, our solution can be a starting point for approximate computation of the prefactor in this model., Comment: 9pages, 4 figures

The unusually narrow features in the fluorescence from Rubidium-85 driven by cooling and repumper laser fields, reported in an earlier experiment [1] are explained on the basis of a four-level density matrix calculation. Quantum effects alter the efficiency of atom transfer by the probe (repumper) laser to the levels connected by the pump (cooling) laser. This combined with the double resonance condition [1], results in velocity selection from co-propagating and counter propagating probe and pump beams resulting in narrow fluorescence peaks from a thermal gas at room temperature., 7 pages, 5 figures, needs epl.cls

We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the presence of transaction costs. We illustrate the method on plain vanilla options when the price returns follow a Student-t distribution. We show that in the presence of fat-tails, our strategy allows to significantly reduce extreme risks, and generically leads to low Gamma hedging. Similarly, the inclusion of transaction costs reduces the Gamma of the optimal strategy., 23 pages, 7 figures, 8 tables

We study the properties of elongated Bose-Einstein condensates. First, we show that the dimensions of the condensate after expansion differs from the 3D Thomas-Fermi regime. We also study the coherence length of such elongated condensates., Comment: proceeding of Quantum Gases in Low Dimension, Les Houches 2003, 8 pages, 5 figures

We propose a new principle for a compact solid-state laser in the 1-100 THz regime. This is a frequency range where attempts to fabricate small size lasers up till now have met severe technical problems. The proposed laser is based on a new mechanism for creating spin-flip processes in ferromagnetic conductors. The mechanism is due to the interaction of light with conduction electrons; the interaction strength, being proportional to the large exchange energy, exceeds the Zeeman interaction by orders of magnitude. On the basis of this interaction, a giant lasing effect is predicted in a system where a population inversion has been created by tunneling injection of spin-polarized electrons from one ferromagnetic conductor to another -- the magnetization of the two ferromagnets having different orientations. Using experimental data for ferromagnetic manganese perovskites with nearly 100% spin polarization we show the laser frequency to be in the range 1-100 THz. The optical gain is estimated to be of order 10^7 cm^{-1}, which exceeds the gain of conventional semiconductor lasers by 3 or 4 orders of magnitude. A relevant experimental study is proposed and discussed., Comment: 4 pages, 3 figures

We apply Lindstedt's method and multiple scale perturbation theory to analyze spatio-temporal structures in nonlinear Schr\"odinger equations and thereby study the dynamics of quasi-one-dimensional Bose-Einstein condensates with mean-field interactions. We determine the dependence of the intensity of modulated amplitude waves on their wave number. We also explore the band structure of Bose-Einstein condensates in detail using Hamiltonian perturbation theory and supporting numerical simulations., Comment: 24 pages, 20 figs (numbered to 9), 6 tables, to appear in Chaos

This paper deals with the conversion between atoms and molecules in optical lattices. We show that in the absence of collisional interaction, the atomic and molecular components in different lattice wells combine into states with macroscopic condensate fractions, which can be observed as a strong diffraction signal, if the particles are abruptly released from the lattice. The condensate population, and the diffraction signal are governed not only by the mean number of atoms or molecules in each well, but by the precise amplitudes on state vector components with different numbers of particles. We discuss ways to control these amplitudes and to maximize the condensate fraction in the molecular formation process., Comment: Invited talk at 'Quantum Challenges', Falenty, Poland, Sep. 2003. Submitted to J. Mod. Opt

We develop a phenomenological model to study magnetic hysteresis in two samples designed as possible perpendicular recording media. A stochastic cellular automata model captures cooperative behavior in the nucleation of magnetic domains. We show how this simple model turns broad hysteresis loops into loops with sharp drops like those observed in these samples, and explains their unusual features. We also present, and experimentally verify, predictions of this model, and suggest how insights from this model may apply more generally., 4.5 pages, 5 figures

We continue the study of the two-component charged Bose gas initiated by Dyson in 1967. He showed that the ground state energy for $N$ particles is at least as negative as $-CN^{7/5}$ for large $N$ and this power law was verified by a lower bound found by Conlon, Lieb and Yau in 1988. Dyson conjectured that the exact constant $C$ was given by a mean-field minimization problem that used, as input, Foldy's calculation (using Bogolubov's 1947 formalism) for the one-component gas. Earlier we showed that Foldy's calculation is exact insofar as a lower bound of his form was obtained. In this paper we do the same thing for Dyson's conjecture. The two-component case is considerably more difficult because the gas is very non-homogeneous in its ground state., 49 pages, Dedicated to Freeman J. Dyson on the occasion of his 80th birthday. Final version (only minor changes) to appear in Commun. math. Phys