Nonlinear Bogolyubov-Valatin transformations and quaternions

In introducing second quantization for fermions, Jordan and Wigner (1927/1928) observed that the algebra of a single pair of fermion creation and annihilation operators in quantum mechanics is closely related to the algebra of quaternions H. For the first time, here we exploit this fact to study nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for a single fermionic mode. By means of these transformations, a class of fermionic Hamiltonians in an external field is related to the standard Fermi oscillator.Comment: 6 pages REVTEX (v3: two paragraphs appended, minor stylistic changes, eq. (39) corrected, references [10]-[14], [36], [37], [41], [67]-[69] added; v4: few extensions, references [62], [63] added, final version to be published in J. Phys. A: Math. Gen.

Competition between spin and charge polarized states in nanographene ribbons with zigzag edges

Effects of the nearest neighbor Coulomb interaction on nanographene ribbons with zigzag edges are investigated using the extended Hubbard model within the unrestricted Hartree-Fock approximation. The nearest Coulomb interaction stabilizes a novel electronic state with the opposite electric charges separated and localized along both edges, resulting in a finite electric dipole moment pointing from one edge to the other. This charge-polarized state competes with the peculiar spin-polarized state caused by the on-site Coulomb interaction and is stabilized by an external electric field.Comment: 4 pages; 4 figures; accepted for publication in Phys. Rev. B; related Web site: http://staff.aist.go.jp/k.harigaya/index_E.htm

A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

We present a group theoretical study of the symmetry-broken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N-electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Hueckel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N-electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetry-breaking/symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.Comment: A section VI.B entitled "Quantitative description of the lowest rotational band" has been added. 16 pages. Revtex with 10 EPS figures. A version of the manuscript with high quality figures is available at http://calcite.physics.gatech.edu/~costas/uhf_group.html For related papers, see http://www.prism.gatech.edu/~ph274c

Origin of line broadening in the electronic absorption spectra of conjugated polymers: Three-pulse-echo studies of MEH-PPV in toluene

Integrated three-pulse stimulated echo peak shift data are compared for N,N-bis-dimethylphenyl-1-2,4,6,8-perylenetetracarbonyl diamide and poly[2-(2'-ethylhexyloxy)-5-methoxy-1,4-phenylenevinylene] (MEH-PPV) in toluene solvent. These two molecules represent a model probe of solvation dynamics and a prototypical soluble, electroluminescent conjugated polymer, respectively. The results indicate that it is inappropriate to describe the linear absorption spectrum of MEH-PPV as being primarily inhomogeneously broadened. Conformational disorder along the polymer backbone gives rise to an ensemble of polyene electronic oscillators that are strongly coupled to each other. As a consequence, fluctuations in the electronic energy gap on a time-scale of 50-fs derive primarily from bath-mediated exciton scattering. The data reported here provide an explanation for the broad, structureless electronic absorption of MEH-PPV. This interpretation provides a valuable insight into the nature of the initial photoexcited state, and the efficient population of the emissive state