Matches in SemOpenAlex for { <https://semopenalex.org/work/W2091226270> ?p ?o ?g. }
Showing items 1 to 78 of
78
with 100 items per page.
- W2091226270 endingPage "166" @default.
- W2091226270 startingPage "135" @default.
- W2091226270 abstract "The problem of Bloch electrons in a magnetic field in two dimensions can be reduced to a one-dimensional problem with a Hamiltonian Ĥ that is a periodic function of x ^ and p ^ . Wannier functions can be defined for the sub-bands of the spectrum of this effective Hamiltonian. When the Chern class (quantized Hall conductance integer) of the sub-band is zero, the Weyl-Wigner formalism can be used to represent these Wannier functions by a von Neumann lattice. It is shown how this von Neumann lattice of Wannier functions can be defined for irrational as well as rational magnetic fields. An important benefit from using the Weyl-Wigner formalism is that symmetries of the periodic potential are reflected by symmetries of the effective Hamiltonian in phase space. It is shown how the Wannier functions can be defined so that their Wigner functions have the point symmetries of the effective Hamiltonian. An example of how these results can prove useful is given: if we take matrix elements of the Hamiltonian between the Wannier states of a sub-band, we derive a new effective Hamiltonian describing this sub-band, which is again a periodic function of coordinate and momentum operators. Since, by projecting onto a sub-band, we have also reduced the number of degrees of freedom, this operation is a renormalization group transformation. It is shown that the symmetry of the new effective Hamiltonian in phase space is the same as that of the original one. This preservation of symmetry helps to explain some unusual properties of the spectrum when the Hamiltonian has fourfold symmetry." @default.
- W2091226270 created "2016-06-24" @default.
- W2091226270 creator A5089960257 @default.
- W2091226270 date "1986-01-08" @default.
- W2091226270 modified "2023-09-24" @default.
- W2091226270 title "Von Neumann lattices of Wannier functions for Bloch electrons in a magnetic field" @default.
- W2091226270 cites W1511889936 @default.
- W2091226270 cites W1964342816 @default.
- W2091226270 cites W1969558316 @default.
- W2091226270 cites W1979015793 @default.
- W2091226270 cites W1986487433 @default.
- W2091226270 cites W1986508321 @default.
- W2091226270 cites W1988195577 @default.
- W2091226270 cites W2003103790 @default.
- W2091226270 cites W2014846693 @default.
- W2091226270 cites W2026661162 @default.
- W2091226270 cites W2032619826 @default.
- W2091226270 cites W2037807652 @default.
- W2091226270 cites W2042471052 @default.
- W2091226270 cites W2048971077 @default.
- W2091226270 cites W2049138444 @default.
- W2091226270 cites W2050360413 @default.
- W2091226270 cites W2056266391 @default.
- W2091226270 cites W2057752394 @default.
- W2091226270 cites W2059771469 @default.
- W2091226270 cites W2075400961 @default.
- W2091226270 cites W2125792638 @default.
- W2091226270 cites W2127627418 @default.
- W2091226270 cites W3165898261 @default.
- W2091226270 doi "https://doi.org/10.1098/rspa.1986.0006" @default.
- W2091226270 hasPublicationYear "1986" @default.
- W2091226270 type Work @default.
- W2091226270 sameAs 2091226270 @default.
- W2091226270 citedByCount "25" @default.
- W2091226270 countsByYear W20912262702022 @default.
- W2091226270 crossrefType "journal-article" @default.
- W2091226270 hasAuthorship W2091226270A5089960257 @default.
- W2091226270 hasConcept C113603373 @default.
- W2091226270 hasConcept C121332964 @default.
- W2091226270 hasConcept C126255220 @default.
- W2091226270 hasConcept C130787639 @default.
- W2091226270 hasConcept C14022793 @default.
- W2091226270 hasConcept C2524010 @default.
- W2091226270 hasConcept C33923547 @default.
- W2091226270 hasConcept C37914503 @default.
- W2091226270 hasConcept C62520636 @default.
- W2091226270 hasConcept C96469262 @default.
- W2091226270 hasConceptScore W2091226270C113603373 @default.
- W2091226270 hasConceptScore W2091226270C121332964 @default.
- W2091226270 hasConceptScore W2091226270C126255220 @default.
- W2091226270 hasConceptScore W2091226270C130787639 @default.
- W2091226270 hasConceptScore W2091226270C14022793 @default.
- W2091226270 hasConceptScore W2091226270C2524010 @default.
- W2091226270 hasConceptScore W2091226270C33923547 @default.
- W2091226270 hasConceptScore W2091226270C37914503 @default.
- W2091226270 hasConceptScore W2091226270C62520636 @default.
- W2091226270 hasConceptScore W2091226270C96469262 @default.
- W2091226270 hasIssue "1824" @default.
- W2091226270 hasLocation W20912262701 @default.
- W2091226270 hasOpenAccess W2091226270 @default.
- W2091226270 hasPrimaryLocation W20912262701 @default.
- W2091226270 hasRelatedWork W1784384613 @default.
- W2091226270 hasRelatedWork W1985910657 @default.
- W2091226270 hasRelatedWork W1989823215 @default.
- W2091226270 hasRelatedWork W2021568281 @default.
- W2091226270 hasRelatedWork W2045687183 @default.
- W2091226270 hasRelatedWork W2059442511 @default.
- W2091226270 hasRelatedWork W2074254897 @default.
- W2091226270 hasRelatedWork W2127043176 @default.
- W2091226270 hasRelatedWork W2409494313 @default.
- W2091226270 hasRelatedWork W2969727368 @default.
- W2091226270 hasVolume "403" @default.
- W2091226270 isParatext "false" @default.
- W2091226270 isRetracted "false" @default.
- W2091226270 magId "2091226270" @default.
- W2091226270 workType "article" @default.