Error message
- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: UpdateQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: MergeQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryInterface::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryInterface::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
The system consist of 2 dimensional electron gas inserted into very
strong uniform magnetic field at the temperature near to 0K. In sucha a
system the fractional quantum hall effect (FQHE) is observed. The ground
state proposed by Lauglin: \Psi_N^{\nu}(z_1,..,z_N)=\Pi_{i
where<math> z=x+\text{i}y, is an icompressive liquid and
its elementary collective excitations:
Πi = 1N(zi − z0)ΨNν(z1, .., zN),
behave like anyons placed in z0with the fractional
phase:
θ=2πν
and they have fractional charge eν. In order to see it we remove one electron and the wave
function will be:
\Psi_N^{\nu}(z_2,..,z_N)=\Pi_{i=1}z_i\Pi_{i.
This is an elementary excitation. Removing three electrons would bring
us back to the ground state (with one of the electrons in the origin).
So one quasi particle which in this case is in fact quasi-hole has an
electric charge of <math>-\frac e \nu.
Last modified:
Monday, October 26, 2015 - 17:56
