57 research outputs found
Quantum chaos: an introduction via chains of interacting spins-1/2
We introduce aspects of quantum chaos by analyzing the eigenvalues and the
eigenstates of quantum many-body systems. The properties of quantum systems
whose classical counterparts are chaotic differ from those whose classical
counterparts are not chaotic. The spectrum of the first exhibits repulsion of
the energy levels. This is one of the main signatures of quantum chaos. We show
how level repulsion develops in one-dimensional systems of interacting spins
1/2 which are devoid of random elements and involve only two-body interactions.
In addition to the statistics of the eigenvalues, we analyze how the structure
of the eigenstates may indicate chaos. The programs used to obtain the data are
available online.Comment: 7 pages, 3 figure
Facts, Values and Quanta
Quantum mechanics is a fundamentally probabilistic theory (at least so far as
the empirical predictions are concerned). It follows that, if one wants to
properly understand quantum mechanics, it is essential to clearly understand
the meaning of probability statements. The interpretation of probability has
excited nearly as much philosophical controversy as the interpretation of
quantum mechanics. 20th century physicists have mostly adopted a frequentist
conception. In this paper it is argued that we ought, instead, to adopt a
logical or Bayesian conception. The paper includes a comparison of the orthodox
and Bayesian theories of statistical inference. It concludes with a few remarks
concerning the implications for the concept of physical reality.Comment: 30 pages, AMS Late
Beyond Gaussian Averages: Redirecting Management Research Toward Extreme Events and Power Laws
The Rhetoric of Failure: A Hyper-Dialog About Method in Economics and How to Get Things Going
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