647 research outputs found
Tomography on f-oscillators
Symplectic tomographies of classical and quantum states are shortly reviewed.
The concept of nonlinear f-oscillators and their properties are recalled. The
tomographic probability representations of oscillator coherent states and the
problem of entanglement are then discussed. The entanglement of even and odd
f-coherent states is evaluated by the linear entropy
Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics
It is shown, that for quantum systems the vectorfield associated with the
equations of motion may admit alternative Hamiltonian descriptions, both in the
Schr\"odinger and Heisenberg pictures. We illustrate these ambiguities in terms
of simple examples.Comment: Latex,14 pages,accepted by Int. Jour.Mod.Phy
Mechanisms of Self-Organization and Finite Size Effects in a Minimal Agent Based Model
We present a detailed analysis of the self-organization phenomenon in which
the stylized facts originate from finite size effects with respect to the
number of agents considered and disappear in the limit of an infinite
population. By introducing the possibility that agents can enter or leave the
market depending on the behavior of the price, it is possible to show that the
system self-organizes in a regime with a finite number of agents which
corresponds to the stylized facts. The mechanism to enter or leave the market
is based on the idea that a too stable market is unappealing for traders while
the presence of price movements attracts agents to enter and speculate on the
market. We show that this mechanism is also compatible with the idea that
agents are scared by a noisy and risky market at shorter time scales. We also
show that the mechanism for self-organization is robust with respect to
variations of the exit/entry rules and that the attempt to trigger the system
to self-organize in a region without stylized facts leads to an unrealistic
dynamics. We study the self-organization in a specific agent based model but we
believe that the basic ideas should be of general validity.Comment: 14 pages, 7 figure
Minimal Agent Based Model for Financial Markets II: Statistical Properties of the Linear and Multiplicative Dynamics
We present a detailed study of the statistical properties of an Agent Based
Model and of its generalization to the multiplicative dynamics. The aim of the
model is to consider the minimal elements for the understanding of the origin
of the Stylized Facts and their Self-Organization. The key elements are
fundamentalist agents, chartist agents, herding dynamics and price behavior.
The first two elements correspond to the competition between stability and
instability tendencies in the market. The herding behavior governs the
possibility of the agents to change strategy and it is a crucial element of
this class of models. The linear approximation permits a simple interpretation
of the model dynamics and, for many properties, it is possible to derive
analytical results. The generalized non linear dynamics results to be extremely
more sensible to the parameter space and much more difficult to analyze and
control. The main results for the nature and Self-Organization of the Stylized
Facts are, however, very similar in the two cases. The main peculiarity of the
non linear dynamics is an enhancement of the fluctuations and a more marked
evidence of the Stylized Facts. We will also discuss some modifications of the
model to introduce more realistic elements with respect to the real markets
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