3,499 research outputs found
A possible cosmological application of some thermodynamic properties of the black body radiation in dimensional Euclidean spaces
In this work we present the generalization of some thermodynamic properties
of the black body radiation (BBR) towards an dimensional Euclidean space.
For this case the Planck function and the Stefan-Boltzmann law have already
been given by Landsberg and de Vos and some adjustments by Menon and Agrawal.
However, since then no much more has been done on this subject and we believe
there are some relevant aspects yet to explore. In addition to the results
previously found we calculate the thermodynamic potentials, the efficiency of
the Carnot engine, the law for adiabatic processes and the heat capacity at
constant volume. There is a region at which an interesting behavior of the
thermodynamic potentials arise, maxima and minima appear for the BBR
system at very high temperatures and low dimensionality, suggesting a possible
application to cosmology. Finally we propose that an optimality criterion in a
thermodynamic framework could have to do with the nature of the universe.Comment: 9 pages, 8 figure
Well-posedness and stability results for the Gardner equation
In this article we present local well-posedness results in the classical
Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner
equation, overcoming the problem of the loss of the scaling property of this
equation. We also cover the energy space H^1(R) where global well-posedness
follows from the conservation laws of the system. Moreover, we construct
solitons of the Gardner equation explicitly and prove that, under certain
conditions, this family is orbitally stable in the energy space.Comment: 1 figure. Accepted for publication in Nonlin.Diff Eq.and App
Can ultrastrong coupling change ground state chemical reactions?
Recent advancements on the fabrication of organic micro- and nanostructures
have permitted the strong collective light-matter coupling regime to be reached
with molecular materials. Pioneering works in this direction have shown the
effects of this regime in the excited state reactivity of molecular systems and
at the same time has opened up the question of whether it is possible to
introduce any modifications in the electronic ground energy landscape which
could affect chemical thermodynamics and/or kinetics. In this work, we use a
model system of many molecules coupled to a surface-plasmon field to gain
insight on the key parameters which govern the modifications of the
ground-state Potential Energy Surface (PES). Our findings confirm that the
energetic changes per molecule are determined by single-molecule-light
couplings which are essentially local, in contrast with those of the
electronically excited states, for which energetic corrections are of a
collective nature. Still, we reveal some intriguing quantum-coherent effects
associated with pathways of concerted reactions, where two or more molecules
undergo reactions simultaneously, and which can be of relevance in low-barrier
reactions. Finally, we also explore modifications to nonadiabatic dynamics and
conclude that, for this particular model, the presence of a large number of
dark states yields negligible changes. Our study reveals new possibilities as
well as limitations for the emerging field of polariton chemistry
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