## Toward a Mininum Criteria of Multi Dimensional Instanton Formation for Condensed Matter Systems?

**Authors:** Andrew Beckwith

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

**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.

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### Submission history

[v1] 28 Sep 2009

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