# Landau electron in a rotating environment: A general factorization of time evolution

## Abstract

For the Landau problem with a rotating magnetic field and a confining potential in the (changing) direction of the field, we derive a general factorization of the time evolution operator that includes the adiabatic factorization as a special case. The confining potential is assumed to be of a general form and it can correspond to nonlinear Heisenberg equations of motion. The rotation operator associated with the solid angle Berry phase is used to transform the problem to a rotating reference frame. In the rotating reference frame, we derive a natural factorization of the time evolution operator by recognizing the crucial role played by a gauge transformation. The major complexity of the problem arises from the coupling between motion in the direction of the magnetic field and motion perpendicular to the field. In the factorization, this complexity is consolidated into a single operator which approaches the identity operator when the potential confines the particle sufficiently close to a rotating plane perpendicular to the magnetic field. The structure of this operator is clarified by deriving an expression for its generating Hamiltonian. The adiabatic limit and non-adiabatic effects follow as consequences of the general factorization which are clarified using the magnetic translation concept.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22157012

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 327; Journal Issue: 11; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COUPLING; EIGENSTATES; ELECTRONS; EQUATIONS OF MOTION; FACTORIZATION; GAUGE INVARIANCE; HAMILTONIANS; MAGNETIC FIELDS; NONLINEAR PROBLEMS; POTENTIALS; QUANTUM OPERATORS; ROTATION; SYMMETRY

### Citation Formats

```
Chee, J.
```*Landau electron in a rotating environment: A general factorization of time evolution*. United States: N. p., 2012.
Web. doi:10.1016/J.AOP.2012.07.007.

```
Chee, J.
```*Landau electron in a rotating environment: A general factorization of time evolution*. United States. doi:10.1016/J.AOP.2012.07.007.

```
Chee, J. Thu .
"Landau electron in a rotating environment: A general factorization of time evolution". United States. doi:10.1016/J.AOP.2012.07.007.
```

```
@article{osti_22157012,
```

title = {Landau electron in a rotating environment: A general factorization of time evolution},

author = {Chee, J.},

abstractNote = {For the Landau problem with a rotating magnetic field and a confining potential in the (changing) direction of the field, we derive a general factorization of the time evolution operator that includes the adiabatic factorization as a special case. The confining potential is assumed to be of a general form and it can correspond to nonlinear Heisenberg equations of motion. The rotation operator associated with the solid angle Berry phase is used to transform the problem to a rotating reference frame. In the rotating reference frame, we derive a natural factorization of the time evolution operator by recognizing the crucial role played by a gauge transformation. The major complexity of the problem arises from the coupling between motion in the direction of the magnetic field and motion perpendicular to the field. In the factorization, this complexity is consolidated into a single operator which approaches the identity operator when the potential confines the particle sufficiently close to a rotating plane perpendicular to the magnetic field. The structure of this operator is clarified by deriving an expression for its generating Hamiltonian. The adiabatic limit and non-adiabatic effects follow as consequences of the general factorization which are clarified using the magnetic translation concept.},

doi = {10.1016/J.AOP.2012.07.007},

journal = {Annals of Physics (New York)},

issn = {0003-4916},

number = 11,

volume = 327,

place = {United States},

year = {2012},

month = {11}

}