[4] **viXra:1304.0075 [pdf]**
*replaced on 2014-06-01 17:45:16*

**Authors:** John Shim

**Comments:** 5 Pages.

This paper notes that the dispersion relation ∇px∇x ≥ ħ/2, when
expressed as an equality, ∇px∇x = ħ/2, defines the relationship
between the ground-state mean kinetic energy of a confined
quantum, and its dimensions of containment. The containment can
occur in two ways: the first by an attractive potential, and the
second by a repulsive potential. If the quantum is bound by an
attractive potential, the ground-state kinetic energy is balanced by
the containing potential in a stable state where the kinetic energy
remains within the bound system. In the second type, which is only
possible by compression, the quantum is contained by collisions
with the bounding potential, which may result in a transfer of
kinetic energy to the boundary. If the boundary is sufficiently
massive, then the energy transfer will have a negligible effect on the
dimensions of containment, and therefore the ground-state kinetic
energy of the contained quantum will not significantly change. This
energy transfer could be large. An electron contained within the
approximate diameter of an iron atom, 250 pm, for example, would
have a minimum velocity very great compared to the dimension of
containment, so that the number of collisions per second with the
boundary would be very high, on the order of 10^15. An exchange of
only 10^-6 ev per collision would produce 10^9 ev per second of
energy transmitted to the boundary.

**Category:** Condensed Matter

[3] **viXra:1304.0059 [pdf]**
*submitted on 2013-04-12 18:20:38*

**Authors:** Renato Vieira dos Santos, Ronald Dickman

**Comments:** 15 Pages. Journal reference: Journal of Statistical Mechanics

Recently a model of intra- and interspecific competition between two species was proposed [Phys. Rev. E 87 (2013) 010101], in which the scarcer species (i.e., with smaller stationary population size) can be more resistant to extinction when it holds a competitive advantage. Here we verify this survival of the scarcer in
space (SSS) phenomenon in models with spatial structure, both analytically and numerically. We find that the conditions for SSS, as obtained applying renormalization group analysis and Monte Carlo simulation to a discrete-space model, differ significantly from those found in the spatially homogeneous case.

**Category:** Condensed Matter

[2] **viXra:1304.0044 [pdf]**
*submitted on 2013-04-09 21:19:41*

**Authors:** P. R. Silva

**Comments:** 09 pages; no figures

Starting from a string with a length equal to the electron mean free path in metals and having a unit cell equal to the Compton length of the electron, we construct a Schwarzschild-like metric. We found that this metric has a surface horizon with radius equal to that of the electron mean free path and its Bekenstein-like entropy is proportional to the number of squared unit cells contained in this spherical surface. The Hawking temperature goes with the inverse of the perimeter of the maximum circle of this sphere. Besides this, interesting analogies are traced out with some features of the particle physics.

**Category:** Condensed Matter

[1] **viXra:1304.0025 [pdf]**
*submitted on 2013-04-04 18:31:34*

**Authors:** P. R. Silva

**Comments:** 06 pages, no figure

A minimization of a free energy inspired in the Landauer’s erasure principle combined with alternatives treatments of the Brownian motion of the free electrons, is used as a means to derive the Fermi energy of metals. The obtained result differs from the usual one by a small discrepancy between the coefficients of the two versions of it, when expressed as a function of the density of free electrons, its mass and the Planck’s constant.

**Category:** Condensed Matter