Deformed Density Matrix and Generalized Uncertainty Relation in Thermodynamics

A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the lower limit of inverse temperature. The authors are of the opinion that the approach proposed may lead to proof of these relations. To this end, the statistical mechanics deformation at Planck scale. The statistical mechanics deformation is constructed by analogy to the earlier quantum mechanical results. As previously, the primary object is a density matrix, but now the statistical one. The obtained deformed object is referred to as a statistical density pro-matrix. This object is explicitly described, and it is demonstrated that there is a complete analogy in the construction and properties of quantum mechanics and statistical density matrices at Plank scale (i.e. density pro-matrices). It is shown that an ordinary statistical density matrix occurs in the low-temperature limit at temperatures much lower than the Plank's. The associated deformation of a canonical Gibbs distribution is given explicitly.Comment: 15 pages,no figure

Pure States, Mixed States and Hawking Problem in Generalized Quantum Mechanics

This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As previously, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck remnants of black holes appearing in the assumption of the Generalized Uncertainty Relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the Holographic Principle. Because of this, a conjecture is made about the possibility for obtaining the Generalized Uncertainty Relations from the covariant entropy bound at high energies in the same way as R. Bousso has derived Heisenberg uncertainty principle for the flat space.Comment: 12 pages,no figures,some corrections,new reference

Dynamics for a 2-vertex Quantum Gravity Model

We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N) invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.Comment: 28 pages, v2: typos correcte

Sensitivity of Hawking radiation to superluminal dispersion relations

We analyze the Hawking radiation process due to collapsing configurations in the presence of superluminal modifications of the dispersion relation. With such superluminal dispersion relations, the horizon effectively becomes a frequency-dependent concept. In particular, at every moment of the collapse, there is a critical frequency above which no horizon is experienced. We show that, as a consequence, the late-time radiation suffers strong modifications, both quantitative and qualitative, compared to the standard Hawking picture. Concretely, we show that the radiation spectrum becomes dependent on the measuring time, on the surface gravities associated with different frequencies, and on the critical frequency. Even if the critical frequency is well above the Planck scale, important modifications still show up.Comment: 14 pages, 7 figures. Extensive paragraph added in conclusions to clarify obtained result

The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube II.Simple Cases of Symmetry Breakdown and Restoration

This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and restoration of symmetry in simple quantum-field theories with scalar fields. It is demonstrated that an appropriate deformation opens up new possibilities for symmetry breakdown and restoration. To illustrate, at low energies it offers high-accuracy reproducibility of the same results as with a nondeformed theory. In case of transition from low to higher energies and vice versa it gives description for new types of symmetry breakdown and restoration depending on the rate of the deformation parameter variation in time, and indicates the critical points of the previously described lattice associated with a symmetry restoration. Besides, such a deformation enables one to find important constraints on the initial model parameters having an explicit physical meaning.Comment: 9 pages,Revte

Derivative couplings in gravitational production in the early universe

Gravitational particle production in the early universe is due to the coupling of matter fields to curvature. This coupling may include derivative terms that modify the kinetic term. The most general first order action contains derivative couplings to the curvature scalar and to the traceless Ricci tensor, which can be dominant in the case of (pseudo-)Nambu-Goldstone bosons or disformal scalars, such as branons. In the presence of these derivative couplings, the density of produced particles for the adiabatic regime in the de Sitter phase (which mimics inflation) is constant in time and decays with the inverse effective mass (which in turn depends on the coupling to the curvature scalar). In the reheating phase following inflation, the presence of derivative couplings to the background curvature modifies in a nontrivial way the gravitational production even in the perturbative regime. We also show that the two couplings -- to the curvature scalar and to the traceless Ricci tensor -- are drastically different, specially for large masses. In this regime, the production becomes highly sensitive to the former coupling while it becomes independent of the latter.Comment: 24 pages, 6 figure

Running Coupling with Minimal Length

In models with large additional dimensions, the GUT scale can be lowered to values accessible by future colliders. Due to modification of the loop corrections from particles propagating into the extra dimensions, the logarithmic running of the couplings of the Standard Model is turned into a power law. These loop-correction are divergent and the standard way to achieve finiteness is the introduction of a cut-off. The question remains, whether the results are reliable as they depend on an unphysical parameter. In this paper, we show that this running of the coupling can be calculated within a model including the existence of a minimal length scale. The minimal length acts as a natural regulator and allows us to confirm cut-off computations.Comment: 26 pages, 5 figures, typos corrected, replaced with published versio

\u3cem\u3eHymenachne Amplexicaluis\u3c/em\u3e [(Rudge) Nees] Genetic Resources Collection in México, a Suitable Grass for Flood Plains in Tropical Areas

Hymenachne amplexicaluis [( Rudge ) Nees; 2n= 2x= 24; Azuche, West Indian marsh grass] is a native Central and South America C3 grass that grows well under intermittent flooding conditions. It produces good seed set and stolons to thrive on new areas assuring its survival, combined with an efficient N metabolism to promote vigorous new growing leaves and tillers (Antel et al., 1998). Azuche is a dual attribute species when introduced to new areas; it has valuable forage attributes but also is a potential weed (Hill, 2000). As Azuche is a native species, one must deal with in the best possible way within Tropical Latin America areas (Enríquez et al., 2004). No report has been found to date on living genetic resources collection and evaluation for this species