1,090 research outputs found
Gibbs free energy of reactions involving SiC, Si3N4, H2, and H2O as a function of temperature and pressure
Silicon carbide and silicon nitride are considered for application as structural materials and coating in advanced propulsion systems including nuclear thermal. Three-dimensional Gibbs free energy were constructed for reactions involving these materials in H2 and H2/H2O. Free energy plots are functions of temperature and pressure. Calculations used the definition of Gibbs free energy where the spontaneity of reactions is calculated as a function of temperature and pressure. Silicon carbide decomposes to Si and CH4 in pure H2 and forms a SiO2 scale in a wet atmosphere. Silicon nitride remains stable under all conditions. There was no apparent difference in reaction thermodynamics between ideal and Van der Waals treatment of gaseous species
Quantising on a category
We review the problem of finding a general framework within which one can
construct quantum theories of non-standard models for space, or space-time. The
starting point is the observation that entities of this type can typically be
regarded as objects in a category whose arrows are structure-preserving maps.
This motivates investigating the general problem of quantising a system whose
`configuration space' (or history-theory analogue) is the set of objects
\Ob\Q in a category \Q.
We develop a scheme based on constructing an analogue of the group that is
used in the canonical quantisation of a system whose configuration space is a
manifold , where and are Lie groups. In particular, we
choose as the analogue of the monoid of `arrow fields' on \Q. Physically,
this means that an arrow between two objects in the category is viewed as an
analogue of momentum. After finding the `category quantisation monoid', we show
how suitable representations can be constructed using a bundle (or, more
precisely, presheaf) of Hilbert spaces over \Ob\Q. For the example of a
category of finite sets, we construct an explicit representation structure of
this type.Comment: To appear in a volume dedicated to the memory of James Cushin
A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows
This paper is the third in a series whose goal is to develop a fundamentally
new way of viewing theories of physics. Our basic contention is that
constructing a theory of physics is equivalent to finding a representation in a
topos of a certain formal language that is attached to the system. In paper II,
we studied the topos representations of the propositional language PL(S) for
the case of quantum theory, and in the present paper we do the same thing for
the, more extensive, local language L(S). One of the main achievements is to
find a topos representation for self-adjoint operators. This involves showing
that, for any physical quantity A, there is an arrow
\breve{\delta}^o(A):\Sig\map\SR, where \SR is the quantity-value object for
this theory. The construction of is an extension of the
daseinisation of projection operators that was discussed in paper II. The
object \SR is a monoid-object only in the topos, , of the theory,
and to enhance the applicability of the formalism, we apply to \SR a topos
analogue of the Grothendieck extension of a monoid to a group. The resulting
object, \kSR, is an abelian group-object in . We also discuss
another candidate, \PR{\mathR}, for the quantity-value object. In this
presheaf, both inner and outer daseinisation are used in a symmetric way.
Finally, there is a brief discussion of the role of unitary operators in the
quantum topos scheme.Comment: 38 pages, no figure
Solutions of Quantum Gravity Coupled to the Scalar Field
We consider the Wheeler-De Witt equation for canonical quantum gravity
coupled to massless scalar field. After regularizing and renormalizing this
equation, we find a one-parameter class of its solutions.Comment: 8 pages, LaTe
A Topos Perspective on State-Vector Reduction
A preliminary investigation is made of possible applications in quantum
theory of the topos formed by the collection of all -sets, where is a
monoid. Earlier results on topos aspects of quantum theory can be rederived in
this way. However, the formalism also suggests a new way of constructing a
`neo-realist' interpretation of quantum theory in which the truth values of
propositions are determined by the actions of the monoid of strings of finite
projection operators. By these means, a novel topos perspective is gained on
the concept of state-vector reduction
Entropy of Classical Histories
We consider a number of proposals for the entropy of sets of classical
coarse-grained histories based on the procedures of Jaynes, and prove a series
of inequalities relating these measures. We then examine these as a function of
the coarse-graining for various classical systems, and show explicitly that the
entropy is minimized by the finest-grained description of a set of histories.
We propose an extension of the second law of thermodynamics to the entropy of
histories. We briefly discuss the implications for decoherent or consistent
history formulations of quantum mechanics.Comment: 35 pages RevTeX 3.0 + 5 figures (postscript). Minor corrections and
typos. To appear in Physical Review
General relativity histories theory I: The spacetime character of the canonical description
The problem of time in canonical quantum gravity is related to the fact that
the canonical description is based on the prior choice of a spacelike
foliation, hence making a reference to a spacetime metric. However, the metric
is expected to be a dynamical, fluctuating quantity in quantum gravity. We show
how this problem can be solved in the histories formulation of general
relativity. We implement the 3+1 decomposition using metric-dependent
foliations which remain spacelike with respect to all possible Lorentzian
metrics. This allows us to find an explicit relation of covariant and canonical
quantities which preserves the spacetime character of the canonical
description. In this new construction, we also have a coexistence of the
spacetime diffeomorphisms group, and the Dirac algebra of constraints.Comment: 23 pages, submitted to Class. Quant. Gra
Topos theory and `neo-realist' quantum theory
Topos theory, a branch of category theory, has been proposed as mathematical
basis for the formulation of physical theories. In this article, we give a
brief introduction to this approach, emphasising the logical aspects. Each
topos serves as a `mathematical universe' with an internal logic, which is used
to assign truth-values to all propositions about a physical system. We show in
detail how this works for (algebraic) quantum theory.Comment: 22 pages, no figures; contribution for Proceedings of workshop
"Recent Developments in Quantum Field Theory", MPI MIS Leipzig, July 200
Quantum Logic and the Histories Approach to Quantum Theory
An extended analysis is made of the Gell-Mann and Hartle axioms for a
generalised `histories' approach to quantum theory. Emphasis is placed on
finding equivalents of the lattice structure that is employed in standard
quantum logic. Particular attention is given to `quasi-temporal' theories in
which the notion of time-evolution is less rigid than in conventional
Hamiltonian physics; theories of this type are expected to arise naturally in
the context of quantum gravity and quantum field theory in a curved space-time.
The quasi-temporal structure is coded in a partial semi-group of `temporal
supports' that underpins the lattice of history propositions. Non-trivial
examples include quantum field theory on a non globally-hyperbolic spacetime,
and a simple cobordism approach to a theory of quantum topology.
It is shown how the set of history propositions in standard quantum theory
can be realised in such a way that each history proposition is represented by a
genuine projection operator. This provides valuable insight into the possible
lattice structure in general history theories, and also provides a number of
potential models for theories of this type.Comment: TP/92-93/39 36 pages + one page of diagrams (I could email Apple
laser printer postscript file for anyone who is especially keen
A Class of Exact Solutions of the Wheeler -- De Witt Equation
After carefully regularizing the Wheeler -- De Witt operator, which is the
Hamiltonian operator of canonical quantum gravity, we find a class of exact
solutions of the Wheeler -- De Witt equation.Comment: 9 pages, Latex, (one reference and one conclusion added, minor
corrections in the formulae
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