93 research outputs found
Conformal Gauge Transformations in Thermodynamics
In this work we consider conformal gauge transformations of the geometric
structure of thermodynamic fluctuation theory. In particular, we show that the
Thermodynamic Phase Space is naturally endowed with a non-integrable
connection, defined by all those processes that annihilate the Gibbs 1-form,
i.e. reversible processes. Therefore the geometry of reversible processes is
invariant under re-scalings, that is, it has a conformal gauge freedom.
Interestingly, as a consequence of the non-integrability of the connection, its
curvature is not invariant under conformal gauge transformations and,
therefore, neither is the associated pseudo-Riemannian geometry. We argue that
this is not surprising, since these two objects are associated with
irreversible processes. Moreover, we provide the explicit form in which all the
elements of the geometric structure of the Thermodynamic Phase Space change
under a conformal gauge transformation. As an example, we revisit the change of
the thermodynamic representation and consider the resulting change between the
two metrics on the Thermodynamic Phase Space which induce Weinhold's energy
metric and Ruppeiner's entropy metric. As a by-product we obtain a proof of the
well-known conformal relation between Weinhold's and Ruppeiner's metrics along
the equilibrium directions. Finally, we find interesting properties of the
almost para-contact structure and of its eigenvectors which may be of physical
interest
Two-dimensional Einstein manifolds in geometrothermodynamics
We present a class of thermodynamic systems with constant thermodynamic
curvature which, within the context of geometric approaches of thermodynamics,
can be interpreted as constant thermodynamic interaction among their
components. In particular, for systems constrained by the vanishing of the
Hessian curvature we write down the systems of partial differential equations.
In such a case it is possible to find a subset of solutions lying on a
circumference in an abstract space constructed from the first derivatives of
the isothermal coordinates. We conjecture that solutions on the characteristic
circumference are of physical relevance, separating them from those of pure
mathematical interest. We present the case of a one-parameter family of
fundamental relations that -- when lying in the circumference -- describe a
polytropic fluid
Height and weight development following cyclical intravenous pamidronate in children and adolescents with chronic recurrent multifocal osteomyelitis (CRMO)
The string model of the Cooper pair in the anisotropic superconductor
The analogy between the Cooper pair in high temperature superconductor and
the quark-antiquark pair in quantum chromodynamics (QCD) is proposed. In QCD
the nonlinear chromodynamical field between a quark and an antiquark is
confined to a tube. So we assume that there is the strong interaction between
phonons which can confine them to some tube too. This tube is described using
the nonlinear Schr\"odinger equation. We show that it has an infinite spectrum
of axially symmetric (string) solutions with negative finite linear energy
density. The one-dimensional nonlinear Schr\"odinger equation has a finite
spectrum (hence, it has a steady-state) which describes the Cooper pair
squezeed between anisotropy planes in the superconductor. It is shown that in
this model the transition temperature is approximately 45 K.Comment: final version, Latex, 9p, to be published in Phys. Rev.
Comment on "Geometrothermodynamics of a Charged Black Hole of String Theory"
We comment on the conclusions found by Larra\~naga and Mojica regarding the
consistency of the Geoemtrothermodynamics programme to describe the critical
behaviour of a Gibbons-Maeda-Garfinkle-Horowitz-Strominger charged black hole.
We argue that making the appropriate choice of metric for the thermodynamic
phase space and, most importantly, considering the homogeneity of the
thermodynamic potential we obtain consistent results for such a black hole.Comment: Comment on arXiv:1012.207
Gravitational fields as generalized string models
We show that Einstein's main equations for stationary axisymmetric fields in
vacuum are equivalent to the motion equations for bosonic strings moving on a
special nonflat background. This new representation is based on the analysis of
generalized harmonic maps in which the metric of the target space explicitly
depends on the parametrization of the base space. It is shown that this
representation is valid for any gravitational field which possesses two
commuting Killing vector fields. We introduce the concept of dimensional
extension which allows us to consider this type of gravitational fields as
strings embedded in D-dimensional nonflat backgrounds, even in the limiting
case where the Killing vector fields are hypersurface orthogonal.Comment: latex, 25 page
Role of Van Hove Singularities and Momentum Space Structure in High-Temperature Superconductivity
There is a great deal of interest in attributing the high critical
temperatures of the cuprates to either the proximity of the Fermi level to a
van Hove singularity or to structure of the superconducting pairing potential
in momentum space far from the Fermi surface. We examine these ideas by
calculating the critical temperature Tc for model Einstein-phonon- and
spin-fluctuation-mediated superconductors within both the standard,
Fermi-surface-restricted Eliashberg theory and the exact mean field theory,
which accounts for the full momentum structure of the pairing potential and the
energy dependence of the density of states. By using two models of
spin-fluctuation-mediated pairing in the cuprates, we demonstrate that our
results are independent of the details of the dynamical susceptibility, which
is taken to be the pairing potential. We also compare these two models against
available neutron scattering data, since these data provide the most direct
constraints on the susceptibility. We conclude that the van Hove singularity
does not drastically alter Tc from its value when the density of states is
constant and that the effect of momentum structure is significant but secondary
in importance to that of the energy dependence in the density of states.Comment: 23 pages, 6 figures upon request, revtex version 2, vHs-
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