# Zero modes in a system of Aharonov–Bohm solenoids on the Lobachevsky plane

@article{Geyler2005ZeroMI, title={Zero modes in a system of Aharonov–Bohm solenoids on the Lobachevsky plane}, author={Vladimir A. Geyler and Pavel {\vS}ťov{\'i}{\vc}ek}, journal={Journal of Physics A}, year={2005}, volume={39}, pages={1375-1384} }

We consider a spin 1/2 charged particle on the Lobachevsky plane subjected to a magnetic field corresponding to a discrete system of Aharonov–Bohm solenoids. Let H+ and H− be the two components of the Pauli operator for spin-up and -down, respectively. We show that neither H+ nor H− has a zero mode if the number of solenoids is finite. On the other hand, a construction is described of an infinite periodic system of solenoids for which either H+ or H− has zero modes depending on the value of the…

## One Citation

### PERIODIC AHARONOV–BOHM SOLENOIDS IN A CONSTANT MAGNETIC FIELD

- Physics, Mathematics
- 2006

We consider the magnetic Schrodinger operator on R2. The magnetic field is the sum of a homogeneous magnetic field and periodically varying pointlike magnetic fields on a lattice. We shall give a…

### Landau levels on the hyperbolic plane in the presence of Aharonov–Bohm fields

- Physics, Mathematics
- 2012

### On the harmonic oscillator on the Lobachevsky plane

- Mathematics, Physics
- 2007

We introduce the harmonic oscillator on the Lobachevsky plane with the aid of the potential V (ϱ) = (a2ω2/4) sinh(ϱ/a)2, where a is the curvature radius and ϱ is the geodesic distance from a chosen…

### A quantum ring in a nanosphere

- PhysicsInternational Journal of Geometric Methods in Modern Physics
- 2019

In this paper, we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential. Suggesting…

## References

SHOWING 1-10 OF 22 REFERENCES

### Zero modes in a periodic system of Aharonov-Bohm solenoids

- Physics
- 2002

The existence of infinitely degenerate zero modes is proved for a quantum-mechanical two-dimensional charged particle with spin 1/2 moving in the field of an infinite system of Aharonov-Bohm…

### ZERO MODES IN A SYSTEM OF AHARONOV–BOHM FLUXES

- Physics
- 2004

We study zero modes of two-dimensional Pauli operators with Aharonov–Bohm fluxes in the case when the solenoids are arranged in periodic structures like chains or lattices. We also consider…

### Infiniteness of zero modes for the Pauli operator with singular magnetic field

- Physics, Mathematics
- 2005

### Properties of the Dirac-Weyl operator with a strongly singular gauge potential

- Physics
- 1992

Considered is a quantum system of a charged particle moving in the plane R2 under the influence of a perpendicular magnetic field concentrated on some fixed isolated points in R2. Such a magnetic…

### Ground state of a spin-½ charged particle in a two-dimensional magnetic field

- Physics, Mathematics
- 1979

We prove that a spin-\textonehalf{} charged particle moving in a plane under the influence of a perpendicular magnetic field has ($N\ensuremath{-}1$) zero-energy states, where $N$ is the closest…

### Geometric Phase Related to Point-Interaction Transport on a Magnetic Lobachevsky Plane

- Physics
- 2000

AbstractWe consider a charged quantum particle living in the Lobachevsky plane and interacting with a homogeneous magnetic field perpendicular to the plane and a point interaction which is…

### Quantum Hall Effect on the Hyperbolic Plane in the Presence of Disorder

- Mathematics, Physics
- 1998

We study both the continuous model and the discrete model of the quantum Hall effect (QHE) on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper. Here we…

### Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field

- Physics
- 2001

It is investigated that the structure of the kernel of the Dirac–Weyl operator D of a charged particle in the magnetic-field B=B0+B1, given by the sum of a strongly singular magnetic field…

### Zero modes and the quantized Hall conductance of the two-dimensional lattice in a magnetic field.

- PhysicsPhysical review. B, Condensed matter
- 1989

Several properties of the tight-binding electrons in two dimensions with a uniform magnetic field perpendicular to the plane are discussed. The existence of zero-energy states is explicitly shown.…