# First Order Vortex Dynamics

@inproceedings{NSManton1997FirstOV, title={First Order Vortex Dynamics}, author={N.S.Manton}, year={1997} }

A non-dissipative model for vortex motion in thin superconductors is considered. The Lagrangian is a Galilean invariant version of the Ginzburg–Landau model for time-dependent ﬁelds, with kinetic terms linear in the ﬁrst time derivatives of the ﬁelds. It is shown how, for certain values of the coupling constants, the ﬁeld dynamics can be reduced to ﬁrst order diﬀerential equations for the vortex positions. Two vortices circle around one another at constant speed and separation in this model.

## 5 Citations

### Vortex counting and the quantum Hall effect

- PhysicsJournal of High Energy Physics
- 2022

Abstract
We provide evidence for conjectural dualities between nonrelativistic Chern-Simons-matter theories and theories of (fractional, nonAbelian) quantum Hall fluids in 2 + 1 dimensions. At low…

### Nonlinearity, Geometry and Field Theory Solitons

- Physics
- 2020

Topological solitons occur in many types of nonlinear field theory. Their motion and interactions can be simulated classically, and can be well approximated by a finite-dimensional dynamics on a…

### Vortices and magnetic impurities

- PhysicsPhysical Review D
- 2020

Ginzburg-Landau vortices in superconductors attract or repel depending on whether the value of the coupling constant λ is less than 1 or larger than 1. At critical coupling λ=1,it was previously…

### Kähler quantization of vortex moduli

- MathematicsLetters in Mathematical Physics
- 2019

We discuss the Kähler quantization of moduli spaces of vortices in line bundles over compact surfaces $$\Sigma $$ Σ . This furnishes a semiclassical framework for the study of quantum vortex dynamics…

## References

SHOWING 1-9 OF 9 REFERENCES

### Gradient flow of the superconducting Ginzburg–Landau functional on the plane

- Mathematics
- 1997

First we prove the existence of global smooth solutions of the gradient flow of the superconducting Ginzburg Landau (or Abelian Higgs) functional on M. It is then proved that in the case of critical…

### Cosmic Strings and Other Topological Defects

- Physics
- 1985

Preface 1. Introduction 2. Phase transitions in the early universe 3. Topological defects 4. String field theory 5. Superconducting strings 6. String dynamics 7. String gravity 8. String interactions…

### FARACH AND R.J. CRESWICK, “Superconductivity

- TILLEY AND J. TILLEY, “Superfluidity and Superconductivity (3rd ed.)”, Inst. of Phys. Publishing,
- 1995

### GENNES, “Superconductivity in Metals and Alloys”, Benjamin

- New York,
- 1966

### Phys

- Rev. Lett. 72 (1994)

### Phys

- Rev. B51 (1995) 6531; M. STONE, Int. J. Mod. Phys. B9 (1995)

### Phys

- Rev. D52 (1995)

### BELLAC AND J.-M. LÉVY-LEBLOND

- Nuovo Cim
- 1973