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Determination of Zeta Potential via Nanoparticle Translocation Velocities through a Tunable Nanopore: Using DNA-modified Particles as an Example

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Ruelle Zeta Function from Field Theory.

Charles Hadfield¹, Santosh Kandel², Michele Schiavina^3,4

¹IBM T.J. Watson Research Center, 1101 Kitchawan Rd, Yorktown Heights, NY 10598 USA.

Annales Henri Poincare

|November 16, 2020

Summary

This summary is machine-generated.

We present a field-theoretic view of the Ruelle zeta function, linking it to BF theory partition functions under specific gauge conditions. This offers a new perspective on the relationship between Ruelle zeta functions and analytic torsion.

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Area of Science:

Mathematical Physics
Number Theory
Differential Geometry

Background:

The Ruelle zeta function is a key object in dynamical systems and number theory.
Analytic torsion is a topological invariant related to the spectrum of the Laplacian on differential forms.
A conjecture by Fried proposes an equivalence between Ruelle zeta functions and analytic torsion.

Purpose of the Study:

To provide a field-theoretic interpretation of the Ruelle zeta function.
To establish a connection between the Ruelle zeta function and BF theory.
To rephrase Fried's conjecture in a new mathematical framework.

Main Methods:

Utilizing field-theoretic techniques to interpret the Ruelle zeta function.
Employing BF theory as a model system.
Imposing a specific gauge-fixing condition on contact manifolds.

Main Results:

The Ruelle zeta function is shown to be equivalent to the partition function of BF theory under a novel gauge-fixing condition.
This interpretation is valid for contact manifolds.
The study suggests a reformulation of Fried's conjecture.

Conclusions:

A novel field-theoretic perspective on the Ruelle zeta function is established.
The connection to BF theory and contact manifolds opens new avenues for research.
The proposed rephrasing of Fried's conjecture offers a geometric interpretation in terms of homotopies of Lagrangian submanifolds.