8,513 research outputs found
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
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
Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics
By resorting to the Fock--Bargmann representation, we incorporate the quantum
Weyl--Heisenberg (-WH) algebra into the theory of entire analytic functions.
The main tool is the realization of the --WH algebra in terms of finite
difference operators. The physical relevance of our study relies on the fact
that coherent states (CS) are indeed formulated in the space of entire analytic
functions where they can be rigorously expressed in terms of theta functions on
the von Neumann lattice. The r\^ole played by the finite difference operators
and the relevance of the lattice structure in the completeness of the CS system
suggest that the --deformation of the WH algebra is an essential tool in the
physics of discretized (periodic) systems. In this latter context we define a
quantum mechanics formalism for lattice systems.Comment: 22 pages, TEX file, DFF188/9/93 Firenz
Topology-Induced Inverse Phase Transitions
Inverse phase transitions are striking phenomena in which an apparently more
ordered state disorders under cooling. This behavior can naturally emerge in
tricritical systems on heterogeneous networks and it is strongly enhanced by
the presence of disassortative degree correlations. We show it both
analytically and numerically, providing also a microscopic interpretation of
inverse transitions in terms of freezing of sparse subgraphs and coupling
renormalization.Comment: 4 pages, 4 figure
How does informational heterogeneity affect the quality of forecasts?
We investigate a toy model of inductive interacting agents aiming to forecast
a continuous, exogenous random variable E. Private information on E is spread
heterogeneously across agents. Herding turns out to be the preferred
forecasting mechanism when heterogeneity is maximal. However in such conditions
aggregating information efficiently is hard even in the presence of learning,
as the herding ratio rises significantly above the efficient-market expectation
of 1 and remarkably close to the empirically observed values. We also study how
different parameters (interaction range, learning rate, cost of information and
score memory) may affect this scenario and improve efficiency in the hard
phase.Comment: 11 pages, 5 figures, updated version (to appear in Physica A
Constraining f(R) gravity with PLANCK data on galaxy cluster profiles
Models of 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
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