Nonlinear Realizations of Supersymmetry and Other Symmetries

Simultaneous nonlinear realizations of spontaneously broken supersymmetry in conjunction with other spontaneous and/or explicitly broken symmetries including R symmetry, global chiral symmetry, dilatations and the superconformal symmetries is reviewed.Comment: 15 pages, invited brief review for Mod. Phys. Lett.

A Four-Unit-Cell Periodic Pattern of Quasiparticle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+d

Scanning tunneling microscopy is used to image the additional quasiparticle states generated by quantized vortices in the high-Tc superconductor Bi2Sr2CaCu2O8+d. They exhibit a Cu-O bond oriented 'checkerboard' pattern, with four unit cell (4a0) periodicity and a ~30 angstrom decay length. These electronic modulations may be related to the magnetic field-induced, 8a0 periodic, spin density modulations of decay length ~70 angstroms recently discovered in La1.84Sr0.16CuO4. The proposed explanation is a spin density wave localized surrounding each vortex core. General theoretical principles predict that, in the cuprates, a localized spin modulation of wavelength L should be associated with a corresponding electronic modulation of wavelength L/2, in good agreement with our observations.Comment: 10 pages, 3 figure

Influence of Anomalous Dispersion on Optical Characteristics of Quantum Wells

Frequency dependencies of optical characteristics (reflection, transmission and absorption of light) of a quantum well are investigated in a vicinity of interband resonant transitions in a case of two closely located excited energy levels. A wide quantum well in a quantizing magnetic field directed normally to the quantum-well plane, and monochromatic stimulating light are considered. Distinctions between refraction coefficients of barriers and quantum well, and a spatial dispersion of the light wave are taken into account. It is shown that at large radiative lifetimes of excited states in comparison with nonradiative lifetimes, the frequency dependence of the light reflection coefficient in the vicinity of resonant interband transitions is defined basically by a curve, similar to the curve of the anomalous dispersion of the refraction coefficient. The contribution of this curve weakens at alignment of radiative and nonradiative times, it is practically imperceptible at opposite ratio of lifetimes . It is shown also that the frequency dependencies similar to the anomalous dispersion do not arise in transmission and absorption coefficients.Comment: 10 pages, 6 figure

Temperature- and quantum phonon effects on Holstein-Hubbard bipolarons

The one-dimensional Holstein-Hubbard model with two electrons of opposite spin is studied using an extension of a recently developed quantum Monte Carlo method, and a very simple yet rewarding variational approach, both based on a canonically transformed Hamiltonian. The quantum Monte Carlo method yields very accurate results in the regime of small but finite phonon frequencies, characteristic of many strongly correlated materials such as, e.g., the cuprates and the manganites. The influence of electron-electron repulsion, phonon frequency and temperature on the bipolaron state is investigated. Thermal dissociation of the intersite bipolaron is observed at high temperatures, and its relation to an existing theory of the manganites is discussed.Comment: 12 pages, 7 figures; final version, accepted for publication in Phys. Rev.

Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and Universal Classes

This paper is the first in a series of three, the aim of which is to lay the foundations of algebraic geometry over the free metabelian Lie algebra $F$. In the current paper we introduce the notion of a metabelian Lie $U$-algebra and establish connections between metabelian Lie $U$-algebras and special matrix Lie algebras. We define the $\Delta$-localisation of a metabelian Lie $U$-algebra $A$ and the direct module extension of the Fitting's radical of $A$ and show that these algebras lie in the universal closure of $A$.Comment: 34 page

Resistivity studies under hydrostatic pressure on a low-resistance variant of the quasi-2D organic superconductor kappa-(BEDT-TTF)2Cu[N(CN)2]Br: quest for intrinsic scattering contributions

Resistivity measurements have been performed on a low (LR)- and high (HR)-resistance variant of the kappa-(BEDT-TTF)_2Cu[N(CN)_2]Br superconductor. While the HR sample was synthesized following the standard procedure, the LR crystal is a result of a somewhat modified synthesis route. According to their residual resistivities and residual resistivity ratios, the LR crystal is of distinctly superior quality. He-gas pressure was used to study the effect of hydrostatic pressure on the different transport regimes for both variants. The main results of these comparative investigations are (i) a significant part of the inelastic-scattering contribution, which causes the anomalous rho(T) maximum in standard HR crystals around 90 K, is sample dependent, i.e. extrinsic in nature, (ii) the abrupt change in rho(T) at T* approx. 40 K from a strongly temperature-dependent behavior at T > T* to an only weakly T-dependent rho(T) at T < T* is unaffected by this scattering contribution and thus marks an independent property, most likely a second-order phase transition, (iii) both variants reveal a rho(T) proportional to AT^2 dependence at low temperatures, i.e. for T_c < T < T_0, although with strongly sample-dependent coefficients A and upper bounds for the T^2 behavior measured by T_0. The latter result is inconsistent with the T^2 dependence originating from coherent Fermi-liquid excitations.Comment: 8 pages, 6 figure

Effect of the Spatial Dispersion on the Shape of a Light Pulse in a Quantum Well

Reflectance, transmittance and absorbance of a symmetric light pulse, the carrying frequency of which is close to the frequency of interband transitions in a quantum well, are calculated. Energy levels of the quantum well are assumed discrete, and two closely located excited levels are taken into account. A wide quantum well (the width of which is comparable to the length of the light wave, corresponding to the pulse carrying frequency) is considered, and the dependance of the interband matrix element of the momentum operator on the light wave vector is taken into account. Refractive indices of barriers and quantum well are assumed equal each other. The problem is solved for an arbitrary ratio of radiative and nonradiative lifetimes of electronic excitations. It is shown that the spatial dispersion essentially affects the shapes of reflected and transmitted pulses. The largest changes occur when the radiative broadening is close to the difference of frequencies of interband transitions taken into account.Comment: 7 pages, 5 figure

Superlight small bipolarons

Recent angle-resolved photoemission spectroscopy (ARPES) has identified that a finite-range Fr\"ohlich electron-phonon interaction (EPI) with c-axis polarized optical phonons is important in cuprate superconductors, in agreement with an earlier proposal by Alexandrov and Kornilovitch. The estimated unscreened EPI is so strong that it could easily transform doped holes into mobile lattice bipolarons in narrow-band Mott insulators such as cuprates. Applying a continuous-time quantum Monte-Carlo algorithm (CTQMC) we compute the total energy, effective mass, pair radius, number of phonons and isotope exponent of lattice bipolarons in the region of parameters where any approximation might fail taking into account the Coulomb repulsion and the finite-range EPI. The effects of modifying the interaction range and different lattice geometries are discussed with regards to analytical strong-coupling/non-adiabatic results. We demonstrate that bipolarons can be simultaneously small and light, provided suitable conditions on the electron-phonon and electron-electron interaction are satisfied. Such light small bipolarons are a necessary precursor to high-temperature Bose-Einstein condensation in solids. The light bipolaron mass is shown to be universal in systems made of triangular plaquettes, due to a novel crab-like motion. Another surprising result is that the triplet-singlet exchange energy is of the first order in the hopping integral and triplet bipolarons are heavier than singlets in certain lattice structures at variance with intuitive expectations. Finally, we identify a range of lattices where superlight small bipolarons may be formed, and give estimates for their masses in the anti-adiabatic approximation.Comment: 31 pages. To appear in J. Phys.: Condens. Matter, Special Issue 'Mott's Physics