An introduction to lattice QCD at non--zero temperature and density

This is an informal overview of methods and results on the QCD phase diagram and lattice termodynamics aimed at specialists in nearby fields.Comment: 15 pages; lecture at the GISELDA Meeting held in Frascati, Italy, 14-18 January 200

Channels’ Confirmation and Predictions’ Confirmation: From the Medical Test to the Raven Paradox

After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple proposed the Raven Paradox. Then, Carnap used the increment of logical probability as the confirmation measure. So far, many confirmation measures have been proposed. Measure F proposed by Kemeny and Oppenheim among them possesses symmetries and asymmetries proposed by Elles and Fitelson, monotonicity proposed by Greco et al., and normalizing property suggested by many researchers. Based on the semantic information theory, a measure b* similar to F is derived from the medical test. Like the likelihood ratio, measures b* and F can only indicate the quality of channels or the testing means instead of the quality of probability predictions. Furthermore, it is still not easy to use b*, F, or another measure to clarify the Raven Paradox. For this reason, measure c* similar to the correct rate is derived. Measure c* supports the Nicod Criterion and undermines the Equivalence Condition, and hence, can be used to eliminate the Raven Paradox. An example indicates that measures F and b* are helpful for diagnosing the infection of Novel Coronavirus, whereas most popular confirmation measures are not. Another example reveals that all popular confirmation measures cannot be used to explain that a black raven can confirm “Ravens are black” more strongly than a piece of chalk. Measures F, b*, and c* indicate that the existence of fewer counterexamples is more important than more positive examples’ existence, and hence, are compatible with Popper’s falsification thought

Interference Phenomena in Electronic Transport Through Chaotic Cavities: An Information-Theoretic Approach

We develop a statistical theory describing quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of systems, ranging from atomic nuclei to microwave cavities; the main application here is to electronic transport through ballistic microstructures. The theory describes the regime in which there are two distinct time scales, associated with a prompt and an equilibrated response, and is cast in terms of the matrix of scattering amplitudes S. The prompt response is related to the energy average of S which, through ergodicity, is expressed as the average over an ensemble of systems. We use an information-theoretic approach: the ensemble of S-matrices is determined by (1) general physical features-- symmetry, causality, and ergodicity, (2) the specific energy average of S, and (3) the notion of minimum information in the ensemble. This ensemble, known as Poisson's kernel, is meant to describe those situations in which any other information is irrelevant. Thus, one constructs the one-energy statistical distribution of S using only information expressible in terms of S itself without ever invoking the underlying Hamiltonian. This formulation has a remarkable predictive power: from the distribution of S we derive properties of the quantum conductance of cavities, including its average, its fluctuations, and its full distribution in certain cases, both in the absence and presence prompt response. We obtain good agreement with the results of the numerical solution of the Schrodinger equation for cavities in which either prompt response is absent or there are two widely separated time scales. Good agreement with experimental data is obtained once temperature smearing and dephasing effects are taken into account.Comment: 38 pages, 11 ps files included, uses IOP style files and epsf.st

Introduction to Quantum-Gravity Phenomenology

After a brief review of the first phase of development of Quantum-Gravity Phenomenology, I argue that this research line is now ready to enter a more advanced phase: while at first it was legitimate to resort to heuristic order-of-magnitude estimates, which were sufficient to establish that sensitivity to Planck-scale effects can be achieved, we should now rely on detailed analyses of some reference test theories. I illustrate this point in the specific example of studies of Planck-scale modifications of the energy/momentum dispersion relation, for which I consider two test theories. Both the photon-stability analyses and the Crab-nebula synchrotron-radiation analyses, which had raised high hopes of ``beyond-Plankian'' experimental bounds, turn out to be rather ineffective in constraining the two test theories. Examples of analyses which can provide constraints of rather wide applicability are the so-called ``time-of-flight analyses'', in the context of observations of gamma-ray bursts, and the analyses of the cosmic-ray spectrum near the GZK scale.Comment: 46 pages, LaTex. Based on lectures given at the 40th Karpacz Winter School in Theoretical Physic

Qualitative individuation in permutation-invariant quantum mechanics

In this article I expound an understanding of the quantum mechanics of so-called "indistinguishable" systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This understanding has heterodox consequences for the understanding of the states of constituent systems in an assembly and for the notion of entanglement. It corrects widespread misconceptions about the inter-theoretic relations between quantum mechanics and both classical particle mechanics and quantum field theory. The most striking of the heterodox consequences are: (i) that fermionic states ought not always to be considered entangled; (ii) it is possible for two fermions or two bosons to be discerned using purely monadic quantities; and that (iii) fermions (but not bosons) may always be so discerned.Comment: 58 pages, 5 figure

Statistical Inference and the Plethora of Probability Paradigms: A Principled Pluralism

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability