379 research outputs found
Folding apparatus Patent
Characteristics of device for folding thin flexible sheets into compact configuratio
Classical Helium Atom with Radiation Reaction
We study a classical model of Helium atom in which, in addition to the
Coulomb forces, the radiation reaction forces are taken into account. This
modification brings in the model a new qualitative feature of a global
character. Indeed, as pointed out by Dirac, in any model of classical
electrodynamics of point particles involving radiation reaction one has to
eliminate, from the a priori conceivable solutions of the problem, those
corresponding to the emission of an infinite amount of energy. We show that the
Dirac prescription solves a problem of inconsistency plaguing all available
models which neglect radiation reaction, namely, the fact that in all such
models most initial data lead to a spontaneous breakdown of the atom. A further
modification is that the system thus acquires a peculiar form of dissipation.
In particular, this makes attractive an invariant manifold of special physical
interest, the zero--dipole manifold, that corresponds to motions in which no
energy is radiated away (in the dipole approximation). We finally study
numerically the invariant measure naturally induced by the time--evolution on
such a manifold, and this corresponds to studying the formation process of the
atom. Indications are given that such a measure may be singular with respect to
that of Lebesgue.Comment: 16 pages, 3 figure
Characterizing mixing and measurement in quantum mechanics
What fundamental constraints characterize the relationship between a mixture
of quantum states, the states being mixed,
and the probabilities ? What fundamental constraints characterize the
relationship between prior and posterior states in a quantum measurement? In
this paper we show that there are many surprisingly strong constraints on these
mixing and measurement processes that can be expressed simply in terms of the
eigenvalues of the quantum states involved. These constraints capture in a
succinct fashion what it means to say that a quantum measurement acquires
information about the system being measured, and considerably simplify the
proofs of many results about entanglement transformation.Comment: 12 page
Metastability and Nucleation for the Blume-Capel Model. Different mechanisms of transition
We study metastability and nucleation for the Blume-Capel model: a
ferromagnetic nearest neighbour two-dimensional lattice system with spin
variables taking values in -1,0,+1. We consider large but finite volume, small
fixed magnetic field h and chemical potential "lambda" in the limit of zero
temperature; we analyze the first excursion from the metastable -1
configuration to the stable +1 configuration. We compute the asymptotic
behaviour of the transition time and describe the typical tube of trajectories
during the transition. We show that, unexpectedly, the mechanism of transition
changes abruptly when the line h=2*lambda is crossed.Comment: 96 pages, 44 tex-figures, 7 postscript figure
Phase transitions and configuration space topology
Equilibrium phase transitions may be defined as nonanalytic points of
thermodynamic functions, e.g., of the canonical free energy. Given a certain
physical system, it is of interest to understand which properties of the system
account for the presence of a phase transition, and an understanding of these
properties may lead to a deeper understanding of the physical phenomenon. One
possible approach of this issue, reviewed and discussed in the present paper,
is the study of topology changes in configuration space which, remarkably, are
found to be related to equilibrium phase transitions in classical statistical
mechanical systems. For the study of configuration space topology, one
considers the subsets M_v, consisting of all points from configuration space
with a potential energy per particle equal to or less than a given v. For
finite systems, topology changes of M_v are intimately related to nonanalytic
points of the microcanonical entropy (which, as a surprise to many, do exist).
In the thermodynamic limit, a more complex relation between nonanalytic points
of thermodynamic functions (i.e., phase transitions) and topology changes is
observed. For some class of short-range systems, a topology change of the M_v
at v=v_t was proved to be necessary for a phase transition to take place at a
potential energy v_t. In contrast, phase transitions in systems with long-range
interactions or in systems with non-confining potentials need not be
accompanied by such a topology change. Instead, for such systems the
nonanalytic point in a thermodynamic function is found to have some
maximization procedure at its origin. These results may foster insight into the
mechanisms which lead to the occurrence of a phase transition, and thus may
help to explore the origin of this physical phenomenon.Comment: 22 pages, 6 figure
Probability distributions consistent with a mixed state
A density matrix may be represented in many different ways as a
mixture of pure states, \rho = \sum_i p_i |\psi_i\ra \la \psi_i|. This paper
characterizes the class of probability distributions that may appear in
such a decomposition, for a fixed density matrix . Several illustrative
applications of this result to quantum mechanics and quantum information theory
are given.Comment: 6 pages, submitted to Physical Review
Remarks on Shannon's Statistical Inference and the Second Law in Quantum Statistical Mechanics
We comment on a formulation of quantum statistical mechanics, which
incorporates the statistical inference of Shannon.
Our basic idea is to distinguish the dynamical entropy of von Neumann, , in terms of the density matrix ,
and the statistical amount of uncertainty of Shannon, , with in the representation where the total
energy and particle numbers are diagonal. These quantities satisfy the
inequality . We propose to interprete Shannon's statistical inference
as specifying the {\em initial conditions} of the system in terms of . A
definition of macroscopic observables which are characterized by intrinsic time
scales is given, and a quantum mechanical condition on the system, which
ensures equilibrium, is discussed on the basis of time averaging.
An interesting analogy of the change of entroy with the running coupling in
renormalization group is noted. A salient feature of our approach is that the
distinction between statistical aspects and dynamical aspects of quantum
statistical mechanics is very transparent.Comment: 16 pages. Minor refinement in the statements in the previous version.
This version has been published in Journal of Phys. Soc. Jpn. 71 (2002) 6
Fluctuations in Stationary non Equilibrium States
In this paper we formulate a dynamical fluctuation theory for stationary non
equilibrium states (SNS) which covers situations in a nonlinear hydrodynamic
regime and is verified explicitly in stochastic models of interacting
particles. In our theory a crucial role is played by the time reversed
dynamics. Our results include the modification of the Onsager-Machlup theory in
the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a
non equilibrium, non linear fluctuation dissipation relation valid for a wide
class of systems
Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall
We consider the electromagnetic field in a cavity with a periodically
oscillating perfectly reflecting boundary and show that the mathematical theory
of circle maps leads to several physical predictions. Notably, well-known
results in the theory of circle maps (which we review briefly) imply that there
are intervals of parameters where the waves in the cavity get concentrated in
wave packets whose energy grows exponentially. Even if these intervals are
dense for typical motions of the reflecting boundary, in the complement there
is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i,
42.60.Da, 42.65.Y
- …