Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons

We calculate the renormalized effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming 2-body interactions modeled with the combination of a zero-range and energy-dependent pseudopotential. We work to third-order in the scattering length a defined at zero collision energy, which is necessary to obtain both the leading-order effective 4-body interaction and consistently include finite-range corrections for realistic 2-body interactions. The leading-order, effective 3- and 4-body interaction energies are U3 = -(0.85576...)(a/l)^2 + 2.7921(1)(a/l)^3 + O[(a/l)^4] and U4 = +(2.43317...)(a/l)^3 + O[(a\l)^4], where w and l are the harmonic oscillator frequency and length, respectively, and energies are in units of hbar*w. The one-standard deviation error 0.0001 for the third-order coefficient in U3 is due to numerical uncertainty in estimating a slowly converging sum; the other two coefficients are either analytically or numerically exact. The effective 3- and 4-body interactions can play an important role in the dynamics of tightly confined and strongly correlated systems. We also performed numerical simulations for a finite-range boson-boson potential, and it was comparison to the zero-range predictions which revealed that finite-range effects must be taken into account for a realistic third-order treatment. In particular, we show that the energy-dependent pseudopotential accurately captures, through third order, the finite-range physics, and in combination with the multi-body effective interactions gives excellent agreement with the numerical simulations, validating our theoretical analysis and predictions.Comment: Updated introduction, correction of a few typos and sign error

Metastability of Asymptotically Well-Behaved Potential Games

One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. "noise") is introduced in players' behavior. In this context, the solution concept of interest becomes the logit equilibrium, as opposed to Nash equilibria. Logit equilibria are distributions over strategy profiles that possess several nice properties, including existence and uniqueness. However, there are games in which their computation may take time exponential in the number of players. We therefore look at an approximate version of logit equilibria, called metastable distributions, introduced by Auletta et al. [SODA 2012]. These are distributions that remain stable (i.e., players do not go too far from it) for a super-polynomial number of steps (rather than forever, as for logit equilibria). The hope is that these distributions exist and can be reached quickly by logit dynamics. We identify a class of potential games, called asymptotically well-behaved, for which the behavior of the logit dynamics is not chaotic as the number of players increases so to guarantee meaningful asymptotic results. We prove that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics. These distributions can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential. Our proofs build on results which may be of independent interest, including some spectral characterizations of the transition matrix defined by logit dynamics for generic games and the relationship of several convergence measures for Markov chains

Three particles in an external trap: Nature of the complete J=0 spectrum

Three bosonic, spin-polarized atoms in a spherical oscillator potential constitutes the simplest nontrivial Bose-Einstein condensate (BEC). The present paper develops the tools needed to understand the nature of the complete J=0 energy spectrum for this prototype system, assuming a sum of two-body potentials. The resulting spectrum is calculated as a function of the two-body scattering length a_sc, which documents the evolution of certain many-body levels that evolve from BEC-type to molecular-type as the scattering length is decreased. Implications for the behavior of the condensate excited-state spectrum and for condensate formation and decay are elucidated. The energy levels evolve smoothly, even through the regime where the number of two-body bound states N_b increases by 1, and a_{sc} switches from -infinity to infinity. We point out the possibility of suppressing three-body recombination by tuning the two-body scattering length to values that are larger than the size of the condensate ground state. Comparisons with mean-field treatments are presented

The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings

We carry out a numerical and analytic analysis of the Yang-Lee zeros of the 1D Blume-Capel model with periodic boundary conditions and its generalization on Feynman diagrams for which we include sums over all connected and non-connected rings for a given number of spins. In both cases, for a specific range of the parameters, the zeros originally on the unit circle are shown to departure from it as we increase the temperature beyond some limit. The curve of zeros can bifurcate and become two disjoint arcs as in the 2D case. We also show that in the thermodynamic limit the zeros of both Blume-Capel models on the static (connected ring) and on the dynamical (Feynman diagrams) lattice tend to overlap. In the special case of the 1D Ising model on Feynman diagrams we can prove for arbitrary number of spins that the Yang-Lee zeros must be on the unit circle. The proof is based on a property of the zeros of Legendre Polynomials.Comment: 19 pages, 5 figure

Analytical solutions for two heteronuclear atoms in a ring trap

We consider two heteronuclear atoms interacting with a short-range $\delta$ potential and confined in a ring trap. By taking the Bethe-ansatz-type wavefunction and considering the periodic boundary condition properly, we derive analytical solutions for the heteronuclear system. The eigen-energies represented in terms of quasi-momentums can then be determined by solving a set of coupled equations. We present a number of results, which display different features from the case of identical atoms. Our result can be reduced to the well-known Lieb-Liniger solution when two interacting atoms have the same masses.Comment: 6 pages, 6 figure

Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States

The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We introduce the notion of relaxation height in a general energy landscape and we prove sufficient conditions which are valid even in presence of multiple metastable states. We show how these results can be used to approach the problem of multiple metastable states via the use of the modern theories of metastability. We finally apply these general results to the Blume--Capel model for a particular choice of the parameters ensuring the existence of two multiple, and not degenerate in energy, metastable states

On compatibility and improvement of different quantum state assignments

When Alice and Bob have different quantum knowledges or state assignments (density operators) for one and the same specific individual system, then the problems of compatibility and pooling arise. The so-called first Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in terms of possessed or sharp (i. e., probability one) properties. The second BFM condition is shown to be generally invalid in an infinite-dimensional state space. An argument leading to a procedure of improvement of one state assifnment on account of the other and vice versa is presented.Comment: 8 page

Resonant X-Ray Magnetic Scattering from CoO

We analyze the recent experiment [W. Neubeck {\em et al.}, Phys. Rev. B \vol(60,1999,R9912)] for the resonant x-ray magnetic scattering (RXMS) around the K edge of Co in the antiferromagnet CoO. We propose a mechanism of the RXMS to make the $4p$ states couple to the magnetic order: the intraatomic exchange interaction between the $4p$ and the $3d$ states and the $p$-$d$ mixing to the $3d$ states of neighboring Co atoms. These couplings induce the orbital moment in the $4p$ states and make the scattering tensor antisymmetric. Using a cluster model, we demonstrate that this modification gives rise to a large RXMS intensity in the dipole process, in good agreement with the experiment. We also find that the pre-edge peak is generated by the transition to the $3d$ states in the quadrupole process, with negligible contribution of the dipole process. We also discuss the azimuthal angle dependence of the intensity.Comment: 15 pages, 8 figure

Tricritical behaviour of Ising spin glasses with charge fluctuations

We show that tricritical points displaying unusal behaviour exist in phase diagrams of fermionic Ising spin glasses as the chemical potential or the filling assumes characteristic values. Exact results for infinite range interaction and a one loop renormalization group analysis of thermal tricritical fluctuations for finite range models are presented. Surprising similarities with zero temperature transitions and a new $T=0$ tricritical point of metallic quantum spin glasses are derived.Comment: 4 pages, 1 Postscript figure, minor change

Flexible Power Modeling of LTE Base Stations

With the explosion of wireless communications in number of users and data rates, the reduction of network power consumption becomes more and more critical. This is especially true for base stations which represent a dominant share of the total power in cellular networks. In order to study power reduction techniques, a convenient power model is required, providing estimates of the power consumption in different scenarios. This paper proposes such a model, accurate but simple to use. It evaluates the base station power consumption for different types of cells supporting the 3GPP LTE standard. It is flexible enough to enable comparisons between state-of-the-art and advanced configurations, and an easy adaptation to various scenarios. The model is based on a combination of base station components and sub-components as well as power scaling rules as functions of the main system parameters