605 research outputs found
A Quantum-Conceptual Explanation of Violations of Expected Utility in Economics
The expected utility hypothesis is one of the building blocks of classical
economic theory and founded on Savage's Sure-Thing Principle. It has been put
forward, e.g. by situations such as the Allais and Ellsberg paradoxes, that
real-life situations can violate Savage's Sure-Thing Principle and hence also
expected utility. We analyze how this violation is connected to the presence of
the 'disjunction effect' of decision theory and use our earlier study of this
effect in concept theory to put forward an explanation of the violation of
Savage's Sure-Thing Principle, namely the presence of 'quantum conceptual
thought' next to 'classical logical thought' within a double layer structure of
human thought during the decision process. Quantum conceptual thought can be
modeled mathematically by the quantum mechanical formalism, which we illustrate
by modeling the Hawaii problem situation, a well-known example of the
disjunction effect, and we show how the dynamics in the Hawaii problem
situation is generated by the whole conceptual landscape surrounding the
decision situation.Comment: 9 pages, no figure
The Quark Propagator from the Dyson-Schwinger Equations: I. the Chiral Solution
Within the framework of the Dyson-Schwinger equations in the axial gauge, we
study the effect that non-perturbative glue has on the quark propagator. We
show that Ward-Takahashi identities, combined with the requirement of matching
perturbative QCD at high momentum transfer, guarantee the multiplicative
renormalisability of the answer. Technically, the matching with perturbation
theory is accomplished by the introduction of a transverse part to the
quark-gluon vertex. We show that this transverse vertex is crucial for chiral
symmetry breaking, and that massless solutions exist below a critical value of
the strong coupling constant. Using the gluon propagator that we previously
calculated, we obtain small corrections to the quark propagator, which keeps a
pole at the origin in the chiral phase.Comment: 21 pages, 6 figures; McGill/94-24, SHEP 93/94-26 We generalise our
results by showing that they are not sensitive to the specific choice that we
make for the transverse vertex. We illustrate that fact in two new figure
Towards T1-limited magnetic resonance imaging using Rabi beats
Two proof-of-principle experiments towards T1-limited magnetic resonance
imaging with NV centers in diamond are demonstrated. First, a large number of
Rabi oscillations is measured and it is demonstrated that the hyperfine
interaction due to the NV's 14N can be extracted from the beating oscillations.
Second, the Rabi beats under V-type microwave excitation of the three hyperfine
manifolds is studied experimentally and described theoretically.Comment: 6 pages, 8 figure
Quantifying Entanglement Production of Quantum Operations
The problem of entanglement produced by an arbitrary operator is formulated
and a related measure of entanglement production is introduced. This measure of
entanglement production satisfies all properties natural for such a
characteristic. A particular case is the entanglement produced by a density
operator or a density matrix. The suggested measure is valid for operations
over pure states as well as over mixed states, for equilibrium as well as
nonequilibrium processes. Systems of arbitrary nature can be treated, described
either by field operators, spin operators, or any other kind of operators,
which is realized by constructing generalized density matrices. The interplay
between entanglement production and phase transitions in statistical systems is
analysed by the examples of Bose-Einstein condensation, superconducting
transition, and magnetic transitions. The relation between the measure of
entanglement production and order indices is analysed.Comment: 20 pages, Revte
Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell
electrodynamics in vacuum is investigated within the matrix formalism. The
matrix form of electrodynamics includes three real 4 \times 4 matrices. Within
the squaring procedure we construct four formal solutions of the Maxwell
equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem
of separating physical electromagnetic waves in the linear space
\lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3}
is investigated, several particular cases, plane waves and cylindrical waves,
are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk,
Belaru
Classical Logical versus Quantum Conceptual Thought: Examples in Economics, Decision theory and Concept Theory
Inspired by a quantum mechanical formalism to model concepts and their
disjunctions and conjunctions, we put forward in this paper a specific
hypothesis. Namely that within human thought two superposed layers can be
distinguished: (i) a layer given form by an underlying classical deterministic
process, incorporating essentially logical thought and its indeterministic
version modeled by classical probability theory; (ii) a layer given form under
influence of the totality of the surrounding conceptual landscape, where the
different concepts figure as individual entities rather than (logical)
combinations of others, with measurable quantities such as 'typicality',
'membership', 'representativeness', 'similarity', 'applicability', 'preference'
or 'utility' carrying the influences. We call the process in this second layer
'quantum conceptual thought', which is indeterministic in essence, and contains
holistic aspects, but is equally well, although very differently, organized
than logical thought. A substantial part of the 'quantum conceptual thought
process' can be modeled by quantum mechanical probabilistic and mathematical
structures. We consider examples of three specific domains of research where
the effects of the presence of quantum conceptual thought and its deviations
from classical logical thought have been noticed and studied, i.e. economics,
decision theory, and concept theories and which provide experimental evidence
for our hypothesis.Comment: 14 page
Output spectrum of a detector measuring quantum oscillations
We consider a two-level quantum system (qubit) which is continuously measured
by a detector and calculate the spectral density of the detector output. In the
weakly coupled case the spectrum exhibits a moderate peak at the frequency of
quantum oscillations and a Lorentzian-shape increase of the detector noise at
low frequency. With increasing coupling the spectrum transforms into a single
Lorentzian corresponding to random jumps between two states. We prove that the
Bayesian formalism for the selective evolution of the density matrix gives the
same spectrum as the conventional master equation approach, despite the
significant difference in interpretation. The effects of the detector
nonideality and the finite-temperature environment are also discussed.Comment: 8 pages, 6 figure
Mining metrics for buried treasure
The same but different: That might describe two metrics. On the surface
CLASSI may show two metrics are locally equivalent, but buried beneath one may
be a wealth of further structure. This was beautifully described in a paper by
M.A.H. MacCallum in 1998. Here I will illustrate the effect with two flat
metrics -- one describing ordinary Minkowski spacetime and the other describing
a three-parameter family of Gal'tsov-Letelier-Tod spacetimes. I will dig out
the beautiful hidden classical singularity structure of the latter (a structure
first noticed by Tod in 1994) and then show how quantum considerations can
illuminate the riches. I will then discuss how quantum structure can help us
understand classical singularities and metric parameters in a variety of exact
solutions mined from the Exact Solutions book.Comment: 16 pages, no figures, minor grammatical changes, submitted to
Proceedings of the Malcolm@60 Conference (London, July 2004
Chiral symmetry breaking, color superconductivity and color neutral quark matter: a variational approach
We investigate the vacuum realignment for chiral symmetry breaking and color
superconductivity at finite density in Nambu-Jona-Lasinio model in a
variational method. The treatment allows us to investigate simultaneous
formation of condensates in quark antiquark as well as in diquark channels. The
methodology involves an explicit construction of a variational ground state and
minimisation of the thermodynamic potential. Color and electric charge
neutrality conditions are imposed through introduction of appropriate chemical
potentials. Color and flavor dependent condensate functions are determined
through minimisation of the thermodynamic potential. The equation of state is
calculated. Simultaneous existence of a mass gap and superconducting gap is
seen in a small window of quark chemical potential within the model when charge
neutrality conditions are not imposed. Enforcing color and electric charge
neutrality conditions gives rise to existence of gapless superconducting modes
depending upon the magnitude of the gap and the difference of the chemical
potentials of the condensing quarks.Comment: 13 pages, 6 figures,to appear in Phys. Rev.
Warm stellar matter with deconfinement: application to compact stars
We investigate the properties of mixed stars formed by hadronic and quark
matter in -equilibrium described by appropriate equations of state (EOS)
in the framework of relativistic mean-field theory. We use the non- linear
Walecka model for the hadron matter and the MIT Bag and the Nambu-Jona-Lasinio
models for the quark matter. The phase transition to a deconfined quark phase
is investigated. In particular, we study the dependence of the onset of a mixed
phase and a pure quark phase on the hyperon couplings, quark model and
properties of the hadronic model. We calculate the strangeness fraction with
baryonic density for the different EOS. With the NJL model the strangeness
content in the mixed phase decreases. The calculations were performed for T=0
and for finite temperatures in order to describe neutron and proto-neutron
stars. The star properties are discussed. Both the Bag model and the NJL model
predict a mixed phase in the interior of the star. Maximum allowed masses for
proto-neutron stars are larger for the NJL model ( M)
than for the Bag model ( M).Comment: RevTeX,14 figures, accepted to publication in Physical Review
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