Theory of Raman scattering from Leggett's collective mode in a multiband superconductor: Application to MgB2_2

In 1966 Leggett used a two-band superconductor to show that a new collective mode could exist at low temperatures, corresponding to a counter-flow of the superconducting condensates in each band. Here, the theory of electronic Raman scattering in a superconductor by Klein and Dierker (1984) is extended to a multiband superconductor. Raman scattering creates particle/hole pairs. In the relevant $A_{1g}$\ symmetry, the attraction that produces pairing necessarily couples excitations of superconducting pairs to these p/h excitations. In the Appendix it is shown that for zero wave vector transfer $$ this coupling modifies the Raman response and makes the long-range Coulomb correction null. The 2-band result is applied to MgB$_{2}$ where this coupling activates Leggett's collective mode. His simple limiting case is obtained when the interband attractive potential is decreased to a value well below that given by LDA theory. The peak from Leggett's mode is studied as the potential is increased through the theoretical value: With realistic MgB$_{2}$\ parameters, the peak broadens through decay into the continuum above the smaller ($\pi$ band) superconducting gap. Finite $q$ effects are also taken into account, yielding a Raman peak that agrees well in energy with the experimental result by Blumberg \textit{et el.} (2007). This approach is also applied to the $q=0$, 2-band model of the Fe-pnictides considered by Chubukov \textit{et al.}(2009).Comment: 10 pages, 3 figures. To appear in Physical Review

Quantum Breathing Mode of Interacting Particles in a One-dimensional Harmonic Trap

Extending our previous work, we explore the breathing mode---the [uniform] radial expansion and contraction of a spatially confined system. We study the breathing mode across the transition from the ideal quantum to the classical regime and confirm that it is not independent of the pair interaction strength (coupling parameter). We present the results of time-dependent Hartree-Fock simulations for 2 to 20 fermions with Coulomb interaction and show how the quantum breathing mode depends on the particle number. We validate the accuracy of our results, comparing them to exact Configuration Interaction results for up to 8 particles

Phase transition in the Higgs model of scalar dyons

In the present paper we investigate the phase transition "Coulomb--confinement" in the Higgs model of abelian scalar dyons -- particles having both, electric $e$ and magnetic $g$, charges. It is shown that by dual symmetry this theory is equivalent to scalar fields with the effective squared electric charge e^{*2}=e^2+g^2. But the Dirac relation distinguishes the electric and magnetic charges of dyons. The following phase transition couplings are obtained in the one--loop approximation: \alpha_{crit}=e^2_{crit}/4\pi\approx 0.19, \tilde\alpha_{crit}=g^2_{crit}/4\pi\approx 1.29 and \alpha^*_{crit}\approx 1.48.Comment: 16 pages, 2 figure

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.

Heavy-to-light form factors: sum rules on the light cone and beyond

We report the first systematic analysis of the off-light-cone effects in sum rules for heavy-to-light form factors. These effects are investigated in a model based on scalar constituents, which allows a technically rather simple analysis but has the essential features of the analogous QCD calculation. The correlator relevant for the extraction of the heavy-to-light form factor is calculated in two different ways: first, by adopting the full Bethe-Salpeter amplitude of the light meson and, second, by performing the expansion of this amplitude near the light cone $x^2=0$. We demonstrate that the contributions to the correlator from the light-cone term $x^2=0$ and the off-light-cone terms $x^2\ne 0$ have the same order in the $1/m_Q$ expansion. The light-cone correlator, corresponding to $x^2=0$, is shown to systematically overestimate the full correlator, the difference being $\sim \Lambda_{\rm QCD}/\delta$, with $\delta$ the continuum subtraction parameter of order 1 GeV. Numerically, this difference is found to be 10-20%.Comment: revtex 14 pages, version to be published in Phys. Rev. D (discussion in Sect. 3 extended, example in Sect. 4 added

Anderson Localization of Bogolyubov Quasiparticles in Interacting Bose-Einstein Condensates

We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with healing length \xi) subjected to a random potential (with finite correlation length \sigma_R). We derive analytically the Lyapunov exponent as a function of the quasiparticle momentum k and we study the localization maximum k_{max}. For 1D speckle potentials, we find that k_{max} is proportional to 1/\xi when \xi is much larger than \sigma_R while k_{max} is proportional to 1/\sigma_R when \xi is much smaller than \sigma_R, and that the localization is strongest when \xi is of the order of \sigma_R. Numerical calculations support our analysis and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in current experiments with ultracold atoms.Comment: published version (no significant changes compared to last version

Renormalization and additional degrees of freedom within the chiral effective theory for spin-1 resonances

We study in detail various aspects of the renormalization of the spin-1 resonance propagator in the effective field theory framework. First, we briefly review the formalisms for the description of spin-1 resonances in the path integral formulation with the stress on the issue of propagating degrees of freedom. Then we calculate the one-loop 1-- meson self-energy within the Resonance chiral theory in the chiral limit using different methods for the description of spin-one particles, namely the Proca field, antisymmetric tensor field and the first order formalisms. We discuss in detail technical aspects of the renormalization procedure which are inherent to the power-counting non-renormalizable theory and give a formal prescription for the organization of both the counterterms and one-particle irreducible graphs. We also construct the corresponding propagators and investigate their properties. We show that the additional poles corresponding to the additional one-particle states are generated by loop corrections, some of which are negative norm ghosts or tachyons. We count the number of such additional poles and briefly discuss their physical meaning.Comment: 65 pages, 12 figure

Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

We study the Anderson localization of Bogoliubov quasiparticles (elementary many-body excitations) in a weakly interacting Bose gas of chemical potential $\mu$ subjected to a disordered potential $V$. We introduce a general mapping (valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov-de Gennes equations onto a single-particle Schr\"odinger-like equation with an effective potential. For disordered potentials, the Schr\"odinger-like equation accounts for the scattering and localization properties of the Bogoliubov quasiparticles. We derive analytically the localization lengths for correlated disordered potentials in the one-dimensional geometry. Our approach relies on a perturbative expansion in $V/\mu$, which we develop up to third order, and we discuss the impact of the various perturbation orders. Our predictions are shown to be in very good agreement with direct numerical calculations. We identify different localization regimes: For low energy, the effective disordered potential exhibits a strong screening by the quasicondensate density background, and localization is suppressed. For high-energy excitations, the effective disordered potential reduces to the bare disordered potential, and the localization properties of quasiparticles are the same as for free particles. The maximum of localization is found at intermediate energy when the quasicondensate healing length is of the order of the disorder correlation length. Possible extensions of our work to higher dimensions are also discussed.Comment: Published versio

Electronic Orbital Currents and Polarization in Mott Insulators

The standard view is that at low energies Mott insulators exhibit only magnetic properties while charge degrees of freedom are frozen out as the electrons become localized by a strong Coulomb repulsion. We demonstrate that this is in general not true: for certain spin textures {\it spontaneous circular electric currents} or {\it nonuniform charge distribution} exist in the ground state of Mott insulators. In addition, low-energy ``magnetic'' states contribute comparably to the dielectric and magnetic functions $\epsilon_{ik}(\omega)$ and $\mu_{ik}(\omega)$ leading to interesting phenomena such as rotation the electric field polarization and resonances which may be common for both functions producing a negative refraction index in a window of frequencies

Light Scalar Mesons as Manifestation of Spontaneously Broken Chiral Symmetry

Attention is paid to the production mechanisms of light scalars that reveal their nature. We reveal the chiral shielding of the \sigma(600) meson. We show that the kaon loop mechanism of the \phi radiative decays, ratified by experiment, points to the four-quark nature of light scalars. We show also that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor q\bar q mesons that are produced via two-quark transitions $\gamma\gamma\to q\bar q$. The history of spontaneous breaking of symmetry in quantum physics is discussed in Appendix.Comment: Talk at The International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" devoted to the 100th anniversary of N.N.Bogolyubov's birth that was held from August 21 to August 22,2009 in Moscow at the Russian Academy of Sciences (RAS) and from August 23 to August 27, 2009 in Dubna at the Joint Institute for Nuclear Research (JINR