Condensed Matter


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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