148,065 research outputs found
Quantum Network Models and Classical Localization Problems
A review is given of quantum network models in class C which, on a suitable
2d lattice, describe the spin quantum Hall plateau transition. On a general
class of graphs, however, many observables of such models can be mapped to
those of a classical walk in a random environment, thus relating questions of
quantum and classical localization. In many cases it is possible to make
rigorous statements about the latter through the relation to associated
percolation problems, in both two and three dimensions.Comment: 23 pages. To appear in '50 years of Anderson Localization', E
Abrahams, ed. (World Scientific)
Bethe Ansatz and Classical Hirota Equation
We discuss an interrelation between quantum integrable models and classical
soliton equations with discretized time. It appeared that spectral
characteristics of quantum integrable systems may be obtained from entirely
classical set up. Namely, the eigenvalues of the quantum transfer matrix and
the scattering -matrix itself are identified with a certain -functions
of the discrete Liouville equation. The Bethe ansatz equations are obtained as
dynamics of zeros. For comparison we also present the Bethe ansatz equations
for elliptic solutions of the classical discrete Sine-Gordon equation. The
paper is based on the recent study of classical integrable structures in
quantum integrable systems, hep-th/9604080.Comment: 15 pages, Latex, special World Scientific macros include
Quantum cosmology and late-time singularities
The development of dark energy models has stimulated interest to cosmological
singularities, which differ from the traditional Big Bang and Big Crunch
singularities. We review a broad class of phenomena connected with soft
cosmological singularities in classical and quantum cosmology. We discuss the
classification of singularities from the geometrical point of view and from the
point of view of the behaviour of finite size objects, crossing such
singularities. We discuss in some detail quantum and classical cosmology of
models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus
dust), of models based on the Born-Infeld-type fields and of the model of a
scalar field with a potential inversely proportional to the field itself. We
dwell also on the phenomenon of the phantom divide line crossing in the scalar
field models with cusped potentials. Then we discuss the Friedmann equations
modified by quantum corrections to the effective action of the models under
considerations and the influence of such modification on the nature and the
existence of soft singularities. We review also quantum cosmology of models,
where the initial quantum state of the universe is presented by the density
matrix (mixed state). Finally, we discuss the exotic singularities arising in
the brane-world cosmological models.Comment: final version, published in Classical and Quantum Gravity as a
topical revie
Quantum Information Dynamics and Open World Science
One of the fundamental insights of quantum mechanics is that complete knowledge of the state of a quantum system is not possible. Such incomplete knowledge of a physical system is the norm rather than the exception. This is becoming increasingly apparent as we apply scientific methods to increasingly complex situations. Empirically intensive disciplines in the biological, human, and geosciences all operate in situations where valid conclusions must be drawn, but deductive completeness is impossible. This paper argues that such situations are emerging examples of {it Open World} Science. In this paradigm, scientific models are known to be acting with incomplete information. Open World models acknowledge their incompleteness, and respond positively when new information becomes available. Many methods for creating Open World models have been explored analytically in quantitative disciplines such as statistics, and the increasingly mature area of machine learning. This paper examines the role of quantum theory and quantum logic in the underpinnings of Open World models, examining the importance of structural features of such as non-commutativity, degrees of similarity, induction, and the impact of observation. Quantum mechanics is not a problem around the edges of classical theory, but is rather a secure bridgehead in the world of science to come
Measuring measurement
Measurement connects the world of quantum phenomena to the world of classical
events. It plays both a passive role, observing quantum systems, and an active
one, preparing quantum states and controlling them. Surprisingly - in the light
of the central status of measurement in quantum mechanics - there is no general
recipe for designing a detector that measures a given observable. Compounding
this, the characterization of existing detectors is typically based on partial
calibrations or elaborate models. Thus, experimental specification (i.e.
tomography) of a detector is of fundamental and practical importance. Here, we
present the realization of quantum detector tomography: we identify the optimal
positive-operator-valued measure describing the detector, with no ancillary
assumptions. This result completes the triad, state, process, and detector
tomography, required to fully specify an experiment. We characterize an
avalanche photodiode and a photon number resolving detector capable of
detecting up to eight photons. This creates a new set of tools for accurately
detecting and preparing non-classical light.Comment: 6 pages, 4 figures,see video abstract at
http://www.quantiki.org/video_abstracts/0807244
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