## 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.

**Download:** **PDF**

### Submission history

[v1] 28 Sep 2009

**Unique-IP document downloads:** 95 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*