Classical Rotons in Cold Atomic Traps

We predict the emergence of a roton minimum in the dispersion relation of elementary excitations in cold atomic gases in the presence of diffusive light. In large magneto-topical traps, multiple-scattering of light is responsible for the collective behavior of the system, which is associated to an effective Coulomb-like interaction between the atoms. In optically thick clouds, the re-scattered light undergoes diffusive propagation, which is responsible for a stochastic short-range force acting on the atoms. We show that the dynamical competition between these two forces results on a new polariton mode, which exhibits a roton minimum. Making use of Feynman's formula for the static structure factor, we show that the roton minimum is related to the appearance of long-range order in the system.Comment: 5 pages, 3 figure

Structural Properties of the Disordered Spherical and other Mean Field Spin Models

We extend the approach of Aizenman, Sims and Starr for the SK-type models to their spherical versions. Such an extension has already been performed for diluted spin glasses. The factorization property of the optimal structures found by Guerra for the SK model, which holds for diluted models as well, is verified also in the case of spherical systems, with the due modifications. Hence we show that there are some common structural features in various mean field spin models. These similarities seem to be quite paradigmatic, and we summarize the various techniques typically used to prove the structural analogies and to tackle the computation of the free energy per spin in the thermodynamic limit.Comment: 24 page

Path integrals and symmetry breaking for optimal control theory

This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar to the transformation used to relate the classical Hamilton-Jacobi equation to the Schr\"odinger equation. As a result of the linearity, the usual backward computation can be replaced by a forward diffusion process, that can be computed by stochastic integration or by the evaluation of a path integral. It is shown, how in the deterministic limit the PMP formalism is recovered. The significance of the path integral approach is that it forms the basis for a number of efficient computational methods, such as MC sampling, the Laplace approximation and the variational approximation. We show the effectiveness of the first two methods in number of examples. Examples are given that show the qualitative difference between stochastic and deterministic control and the occurrence of symmetry breaking as a function of the noise.Comment: 21 pages, 6 figures, submitted to JSTA

Orbital M1 versus E2 strength in deformed nuclei: A new energy weighted sum rule

Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum rule for low energy orbital 1$^+$ excitations in even-even deformed nuclei S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon (B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2^2) \mu^2_N with B(E2) the E2 strength for the transition from the ground state to the first excited state in the ground state rotational band, $$ the charge r.m.s. radius squared and $\epsilon$ the binding energy per nucleon in the nuclear ground state. It is shown that this energy weighted sum rule is in good agreement with available experimental data. The sum rule is derived using a simple ansatz for the intrinsic ground state wave function that predicts also high energy 1$^+$ strength at 2$\hbar \omega$ carrying 50\% of the total $m_1$ moment of the orbital M1 operator.Comment: REVTEX (3.0), 9 pages, RU924

Description of single and double analog states in the f7/2 shell: The Ti isotopes

The excitation energies of single analog states in even-odd Ti isotopes and double analog states in even-even Ti isotopes are microscopically described in a single j-shell formalism. A projection procedure for generalized BCS states has been used. As an alternative description a particle-core formalism is presented. The latter picture provides a two-parameter expression for excitation energies, which describes fairly well the data in four odd and three even isotopes of Ti.Comment: 14 pages,7 figures, 2 tables. To appear in Phys. Rev.

Effects of Position of Rainfed Rice Field in a Toposequence on Water Availability and Rice Yield in Central Java, Indonesia

The productivity of rainfed rice needs to be increased in order to support the Indonesian Food Security programs, especially rice. Rainfall is one of the main sources of the water availability on the rainfed rice field. This research was conducted from October 2000 to February 2001 at four sites in Central Java Province. The objectives of this research were to study thevariability of water availability that influenced by toposequen's position and to analyze the rice yields due to treatments on toposequence. This experiment was carried out in the farmers' field using “Group Balanced Block in Split-Split Plot Design” and Inceptisols soil order. Mainplots were the four positions in toposequence (top, upper middle, lower middle, and bottom), and the four villages were used as replication. The sub-plot wastreatments group and sub-sub-plot consists of group-1: farmer's practice and without weeding; group-2: farmer's practice without fertilizer and added recommended fertilizer. The research showed that rainfall affected the fluctuation of ground water table and standing water periods. The straw and unhulled rice/grain yields at the bottom position was the highest, and was significantly different from the top position of the toposequence, namely 7.1 and 5.6 t ha-1 for straw yield while 5.2 and 4.0 t ha-1 for grainyield. Without weeding, the straw and grain yields decreased by 1.0 t ha-1 (6.1 to 5.1 t ha-1) and 0.8 t ha-1 (4.6 to 3.8 t ha-1). While, without fertilization, the straw and grain yields were produced only 4.4 and 3.8 t ha-1. Straw and grain yields increased up to 7.0 and 5.1 t ha-1, respectively, when recommended fertilizers were applied

Effects of T=0 two body matrix elements on M1 and Gamow-Teller transitions: isospin decomposition

We perform calculations for M1 transitions and allowed Gamow Teller (GT) transitions in the even-even Titanium isotopes - $^{44}$Ti, $^{46}$Ti, and $^{48}$Ti. We first do calculations with the FPD6 interaction. Then to study the effect of T=0 matrix elements on the M1 and GT rates we introduce a second interaction in which all the T=0 matrix elements are set equal to zero and a third in which all the T=0 matrix elements are set to a constant. For the latter two interactions the T=1 matrix elements are the same as for FPD6. We are thus able to study the effects of the fluctuating T=0 matrix elements on M1 and GT rates