Canonical Trajectories and Critical Coupling of the Bose-Hubbard Hamiltonian in a Harmonic Trap

Quantum Monte Carlo (QMC) simulations and the Local Density Approximation (LDA) are used to map the constant particle number (canonical) trajectories of the Bose Hubbard Hamiltonian confined in a harmonic trap onto the $(\mu/U,t/U)$ phase diagram of the uniform system. Generically, these curves do not intercept the tips of the Mott insulator (MI) lobes of the uniform system. This observation necessitates a clarification of the appropriate comparison between critical couplings obtained in experiments on trapped systems with those obtained in QMC simulations. The density profiles and visibility are also obtained along these trajectories. Density profiles from QMC in the confined case are compared with LDA results.Comment: New version of figure 1

Orderfield property of mixtures of stochastic games

We consider certain mixtures, Γ, of classes of stochastic games and provide sufficient conditions for these mixtures to possess the orderfield property. For 2-player zero-sum and non-zero sum stochastic games, we prove that if we mix a set of states S1 where the transitions are controlled by one player with a set of states S2 constituting a sub-game having the orderfield property (where S1∩S2=∅), the resulting mixture Γ with states S=S1∪S2 has the orderfield property if there are no transitions from S2 to S1. This is true for discounted as well as undiscounted games. This condition on the transitions is sufficient when S1 is perfect information or SC (Switching Control) or ARAT (Additive Reward Additive Transition). In the zero-sum case, S1 can be a mixture of SC and ARAT as well. On the other hand,when S1 is SER-SIT (Separable Reward - State Independent Transition), we provide a counter example to show that this condition is not sufficient for the mixture Γ to possess the orderfield property. In addition to the condition that there are no transitions from S2 to S1, if the sum of all transition probabilities from S1 to S2 is independent of the actions of the players, then Γ has the orderfield property even when S1 is SER-SIT. When S1 and S2 are both SERSIT, their mixture Γ has the orderfield property even if we allow transitions from S2 to S1. We also extend these results to some multi-player games namely, mixtures with one player control Polystochastic games. In all the above cases, we can inductively mix many such games and continue to retain the orderfield property

Orderfield property and algorithms for stochastic games via dependency graphs

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Theory of Insulator Metal Transition and Colossal Magnetoresistance in Doped Manganites

The persistent proximity of insulating and metallic phases, a puzzling characterestic of manganites, is argued to arise from the self organization of the twofold degenerate e_g orbitals of Mn into localized Jahn-Teller(JT) polaronic levels and broad band states due to the large electron - JT phonon coupling present in them. We describe a new two band model with strong correlations and a dynamical mean-field theory calculation of equilibrium and transport properties. These explain the insulator metal transition and colossal magnetoresistance quantitatively, as well as other consequences of two state coexistence

Coarsening and Slow-Dynamics in Granular Compaction

We address the problem of the microscopic reorganization of a granular medium under a compaction process in the framework of Tetris-like models. We point out the existence of regions of spatial organization which we call domains, and study their time evolution. It turns out that after an initial transient, most of the activity of the system is concentrated on the boundaries between domains. One can then describe the compaction phenomenon as a coarsening process for the domains, and a progressive reduction of domain boundaries. We discuss the link between the coarsening process and the slow dynamics in the framework of a model of active walkers on active substrates.Comment: Revtex 4 pages, 4 figures, in press in PRL. More info http://axtnt3.phys.uniroma1.it/Tetri

Colossal magnetoresistance manganites: a new approach

Manganites of the LA1-x Ca xMnO3 family show a variety of new and poorly understood electronic, magnetic and structural effects. Here we outline a new approach recently proposed by us, where we argue that due to strong Jahn-Teller (JT) coupling with phonons the twofold degenerate eg states at the Mn sites dynamically reorganize themselves into localised, JT polaronsl with exponentially small inter-site hopping, and band-like, nonpolaronic statesb, leading to anew 2-band model for manganites which includes strong Coulomb and Hund's couplings. We also discuss some results from a dynamical mean-field theory treatment of the model which explains quantitatively a wide variety of experimental results, including insulator-metal transitions and CMR, in terms of the influence of physical conditions on the relative energies and occupation of thel andb states. We argue that this microscopic coexistence of the two types of electronic states, and their relative occupation and spatial correlation is the key to manganite physics

Zero Temperature Insulator-Metal Transition in Doped Manganites

We study the transition at T=0 from a ferromagnetic insulating to a ferromagnetic metallic phase in manganites as a function of hole doping using an effective low-energy model Hamiltonian proposed by us recently. The model incorporates the quantum nature of the dynamic Jahn-Teller(JT) phonons strongly coupled to orbitally degenerate electrons as well as strong Coulomb correlation effects and leads naturally to the coexistence of localized (JT polaronic) and band-like electronic states. We study the insulator-metal transition as a function of doping as well as of the correlation strength U and JT gain in energy E_{JT}, and find, for realistic values of parameters, a ground state phase diagram in agreement with experiments. We also discuss how several other features of manganites as well as differences in behaviour among manganites can be understood in terms of our model.Comment: To be published in Europhysics Letter

Asymmetric emission of high energy electrons in the two-dimensional hydrodynamic expansion of large xenon clusters irradiated by intense laser fields

Energy spectra and angular distributions have been measured of electrons that are emitted upon disassembly of $Xe_{150000}$ following irradiation by intense (10$^{15}-10^{16}$ W cm$^{-2}$) laser pulses whose durations are varied over the 100-2200 fs range. The cluster explosion dynamics occur in the hydrodynamic regime. Electron emission is found to be unexpectedly asymmetric and exhibits a resonance when the laser pulse duration is $\sim$1 ps. These results are rationalized by extending the hydrodynamic model to also take into account the force that the light field exerts on the polarization charge that is induced on surface of the cluster. We show that the magnitude of this electrostrictive force is comparable to those of Coulombic and the hydrodynamic forces, and it exhibits resonance behavior. Contrary to earlier understanding, we find that low-energy electrons are connected to the resonance in energy absorption by the cluster. The high-energy electrons seem to be produced by a mechanism that is not so strongly influenced by the resonance.Comment: 1 Revtex file, 8 figs. in eps forma