[3] **viXra:0909.0059 [pdf]**
*submitted on 28 Sep 2009*

**Authors:** Andrew Beckwith

**Comments:** 23 pages, extension of "NEW S-S' PAIR CREATION RATE EXPRESSION IMPROVING UPON ZENER
CURVES FOR I-E PLOTS; Modern Physics Letters B, Vol. 20, No. 14 (2006) 849-861", as written by
the authors, with a so called 'minimum criterion' for formation of instanton structure in
condensed matter systems. which the author eventually will send to a condensed matter journal.
Has eight figures. Key part of text on pages 21-23, as discussion built about 7th and final
question as to applications of false vacuum hypothesis, and instanton physics for condensed
matter systems.

We present near the end of this document a promising research direction as to how to generalize
a technique initially applied to density wave current calculations to questions of instanton
formation in multi dimensional condensed matter systems. Initially we review prior calculations
done through a numerical simulation that the massive Schwinger model used to formulate solutions
to CDW transport in itself is insufficient for transport of soliton-antisoliton (S S') pairs
through a pinning gap model of CDW transport. Using the Peierls condensation energy permits
formation of CDW S S' pairs in wave functionals. This leads us to conclude that if there is a
small spacing between soliton-antisoliton (S S') charge centers, and an approximate fit between
a tilted washboard potential and the system we are modeling, that instantons are pertinent to
current/transport problems. This requires a very large 'self energy' final value of interaction
energy as calculated between positive and negative charged components of soliton-antisoliton
(S S') pairs with Gaussian wave functionals as modeled for multi dimensional systems along the
lines of Lu's generalization given below. The links to a saddle point treatment of this
instanton formation are make explicit by a comment as to a cosmology variant of instanton
formation in multi dimensions we think is, with slight modifications appropriate for
condensed matter systems

**Category:** Condensed Matter

[2] **viXra:0909.0056 [pdf]**
*submitted on 28 Sep 2009*

**Authors:** Andrew Beckwith

**Comments:** 15 pages. Mathematical / condensed matter joint piece designed to explain
the congruence of the Bogomol’nyi inequality with the fate of the false vacuum hypothesis as given by Sidney Coleman.
Foundational issue involved which was key to up dates as to my PhD dissertation, and subsequent work in terms of the
tunneling Hamiltonian, and I-E curves in laboratory data taking. Note , the Bogomol’nyi inequality is a key work horse
as to PARTICLE/ Astro physics, as is the false vacuum hypothesis

We examine quantum decay of the false vacuum in the driven sine-Gordon
system and show how both together permit construction of a Gaussian wave
functional. This is due to changing a least action integral to be similar with
respect to the WKB approximation. In addition we find that the soliton-antisoliton
(S-S') separation distance obtained from the Bogomol'nyi inequality permits after
rescaling a dominant &phi^{2} contribution to the least action integrand. This is from an
initial scalar potential characterized by a tilted double well potential construction.

**Category:** Condensed Matter

[1] **viXra:0909.0054 [pdf]**
*submitted on 28 Sep 2009*

**Authors:** Andrew Beckwith

**Comments:** 18 pages, Constitutes one fifth of the author's PhD dissertation
at the U. of Houston, in late 2001. Remainder of dissertation used Sidney Coleman's
"fate of the false vacuum" article, plus the Schwinger equation, with chain
couplings to fix short comings evident in the simulations presented in this
document. 6 figures.

We have evidence that the classical random pinning model, if simulated numerically using
a phase evolution scheme pioneered by Littlewood, gives dispersion relationships that are
inconsistent with experimental values near threshold. These results argue for a revision
of contemporary classical models of charge density wave transport phenomena. Classically,
phase evolution equations are in essence driven harmonic oscillator models, with perturbing
terms plus damping. These break down when we are adding more 'energy' into a measured sample
via an applied electric field than is dissipated via a damping coefficient behavior in a
phase evolution equation. We see the consequences of the breakdown of these phase evolution
models in Charge Density Wave conductivity and dielectric functional graphs.

**Category:** Condensed Matter