408 research outputs found
Yoichiro Nambu: Remembering an unusual physicist, a mentor and a friend
I was lucky to meet Yoichiro Nambu at the beginning of my scientific activity. The experience of working with him influenced my subsequent research and in the following I will try to convey what he transmitted to me. It was also a friendship that continued for decades in spite of the rare occasions to meet after our collaboration
Renormalization Group and Probability Theory
The renormalization group has played an important role in the physics of the
second half of the twentieth century both as a conceptual and a calculational
tool. In particular it provided the key ideas for the construction of a
qualitative and quantitative theory of the critical point in phase transitions
and started a new era in statistical mechanics. Probability theory lies at the
foundation of this branch of physics and the renormalization group has an
interesting probabilistic interpretation as it was recognized in the middle
seventies. This paper intends to provide a concise introduction to this aspect
of the theory of phase transitions which clarifies the deep statistical
significance of critical universality
A New Look at the Schouten-Nijenhuis, Fr\"olicher-Nijenhuis and Nijenhuis-Richardson Brackets for Symplectic Spaces
In this paper we re-express the Schouten-Nijenhuis, the Fr\"olicher-Nijenhuis
and the Nijenhuis-Richardson brackets on a symplectic space using the extended
Poisson brackets structure present in the path-integral formulation of
classical mechanics.Comment: 27+1 pages, Latex, no figure
Stochastic Resonance in Two Dimensional Landau Ginzburg Equation
We study the mechanism of stochastic resonance in a two dimensional Landau
Ginzburg equation perturbed by a white noise. We shortly review how to
renormalize the equation in order to avoid ultraviolet divergences. Next we
show that the renormalization amplifies the effect of the small periodic
perturbation in the system. We finally argue that stochastic resonance can be
used to highlight the effect of renormalization in spatially extended system
with a bistable equilibria
Onsager reciprocity relations without microscopic reversibility
In this paper we show that Onsager--Machlup time reversal properties of
thermodynamic fluctuations and Onsager reciprocity relations for transport
coefficients can hold also if the microscopic dynamics is not reversible. This
result is based on the explicit construction of a class of conservative models
which can be analysed rigorously.Comment: revtex, no figure
Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates
This work describes the statistics for the occupation numbers of quantum
levels in a large isolated quantum system, where all possible superpositions of
eigenstates are allowed, provided all these superpositions have the same fixed
energy. Such a condition is not equivalent to the conventional micro-canonical
condition, because the latter limits the participating eigenstates to a very
narrow energy window. The statistics is obtained analytically for both the
entire system and its small subsystem. In a significant departure from the
Boltzmann-Gibbs statistics, the average occupation numbers of quantum states
exhibit in the present case weak algebraic dependence on energy. In the
macroscopic limit, this dependence is routinely accompanied by the condensation
into the lowest energy quantum state. This work contains initial numerical
tests of the above statistics for finite systems, and also reports the
following numerical finding: When the basis states of large but finite random
matrix Hamiltonians are expanded in terms of eigenstates, the participation of
eigenstates in such an expansion obeys the newly obtained statistics. The above
statistics might be observable in small quantum systems, but for the
macroscopic systems, it rather reenforces doubts about self-sufficiency of
non-relativistic quantum mechanics for justifying the Boltzmann-Gibbs
equilibrium.Comment: 20 pages, 3 figure
Large deviation approach to non equilibrium processes in stochastic lattice gases
We present a review of recent work on the statistical mechanics of non
equilibrium processes based on the analysis of large deviations properties of
microscopic systems. Stochastic lattice gases are non trivial models of such
phenomena and can be studied rigorously providing a source of challenging
mathematical problems. In this way, some principles of wide validity have been
obtained leading to interesting physical consequences.Comment: Extended version of the lectures given by G. Jona-Lasinio at the 9th
Brazilian school of Probability, August 200
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