Theory of controlled quantum dynamics

We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general linear, and it amounts to introduce additional quadratic and linear time-dependent terms to the given potential. In this way one can construct for general systems either coherent packets moving with constant dispersion, or dynamically squeezed packets whose spreading remains bounded for all times. In the standard operatorial framework our scheme corresponds to a suitable generalization of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator.Comment: LaTeX, A4wide, 28 pages, no figures. To appear in J. Phys. A: Math. Gen., April 199

Dymanics of Generalized Coherent States

We show that generalized coherent states follow Schr\"{o}dinger dynamics in time-dependent potentials. The normalized wave-packets follow a classical evolution without spreading; in turn, the Schr\"{o}dinger potential depends on the state through the classical trajectory. This feedback mechanism with continuous dynamical re-adjustement allows the packets to remain coherent indefinetely.Comment: 8 pages, plain latex, no figure

On the strategy frequency problem in batch Minority Games

Ergodic stationary states of Minority Games with S strategies per agent can be characterised in terms of the asymptotic probabilities $\phi_a$ with which an agent uses $a$ of his strategies. We propose here a simple and general method to calculate these quantities in batch canonical and grand-canonical models. Known analytic theories are easily recovered as limiting cases and, as a further application, the strategy frequency problem for the batch grand-canonical Minority Game with S=2 is solved. The generalization of these ideas to multi-asset models is also presented. Though similarly based on response function techniques, our approach is alternative to the one recently employed by Shayeghi and Coolen for canonical batch Minority Games with arbitrary number of strategies.Comment: 17 page

Diffusion Processes and Coherent States

It is shown that stochastic processes of diffusion type possess, in all generality, a structure of uncertainty relations and of coherent and squeezed states. This fact is used to obtain, via Nelson stochastic formulation of quantum mechanics, the harmonic-oscillator coherent and squeezed states. The method allows to derive new minimum uncertainty states in time-dependent oscillator potentials and for the Caldirola-Kanai model of quantum damped oscillator.Comment: 11 pages, plain LaTe

ESR theory for interacting 1D quantum wires

We compute the electron spin resonance (ESR) intensity for one-dimensional quantum wires in semiconductor heterostructures, taking into account electron-electron interactions and spin-orbit coupling. The ESR spectrum is shown to be very sensitive to interactions. While in the absence of interactions, the spectrum is a flat band, characteristic threshold singularities appear in the interacting limit. This suggests the practical use of ESR to reveal spin dynamics in a Luttinger liquid.Comment: 7 pages, 2 figures. To be published in Europhys. Let

On the transition to efficiency in Minority Games

The existence of a phase transition with diverging susceptibility in batch Minority Games (MGs) is the mark of informationally efficient regimes and is linked to the specifics of the agents' learning rules. Here we study how the standard scenario is affected in a mixed population game in which agents with the `optimal' learning rule (i.e. the one leading to efficiency) coexist with ones whose adaptive dynamics is sub-optimal. Our generic finding is that any non-vanishing intensive fraction of optimal agents guarantees the existence of an efficient phase. Specifically, we calculate the dependence of the critical point on the fraction $q$ of `optimal' agents focusing our analysis on three cases: MGs with market impact correction, grand-canonical MGs and MGs with heterogeneous comfort levels.Comment: 12 pages, 3 figures; contribution to the special issue "Viewing the World through Spin Glasses" in honour of David Sherrington on the occasion of his 65th birthda

Constraining f(R) gravity with PLANCK data on galaxy cluster profiles

Models of $f(R)$ gravity that introduce corrections to the Newtonian potential in the weak field limit are tested at the scale of galaxy clusters. These models can explain the dynamics of spiral and elliptical galaxies without resorting to dark matter. We compute the pressure profiles of 579 galaxy clusters assuming that the gas is in hydrostatic equilibrium within the potential well of the modified gravitational field. The predicted profiles are compared with the average profile obtained by stacking the data of our cluster sample in the Planck foreground clean map SMICA. We find that the resulting profiles of these systems fit the data without requiring a dominant dark matter component, with model parameters similar to those required to explain the dynamics of galaxies. Our results do not rule out that clusters are dynamically dominated by Dark Matter but support the idea that Extended Theories of Gravity could provide an explanation to the dynamics of self-gravitating systems and to the present period of accelerated expansion, alternative to the concordance cosmological model.Comment: 10 pages, 5 figures, accepted for publication in MNRA