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

On the solutions of the nonlinear Liouville hierarchy

We investigate the initial-value problem of the non-linear Liouville hierarchy. For the general form of the interaction potential we construct an explicit solution in terms of an expansion over particle clusters whose evolution is described by the corresponding-order cumulant of evolution operators of a system of finitely many particles. For the initial data from the space of integrable functions the existence of a strong solution of the Cauchy problem is proved.Comment: 9 page

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.

Effects of Frustrated Surface in Heisenberg Thin Films

We study by extensive Monte Carlo (MC) simulations and analytical Green function (GF) method effects of frustrated surfaces on the properties of thin films made of stacked triangular layers of atoms bearing Heisenberg spins with an Ising-like interaction anisotropy. We suppose that the in-plane surface interaction $J_s$ can be antiferromagnetic or ferromagnetic while all other interactions are ferromagnetic. We show that the ground-state spin configuration is non linear when $J_s$ is lower than a critical value $J_s^c$. The film surfaces are then frustrated. In the frustrated case, there are two phase transitions related to disorderings of surface and interior layers. There is a good agreement between MC and GF results. In addition, we show from MC histogram calculation that the value of the ratio of critical exponents $\gamma/\nu$ of the observed transitions is deviated from the values of two and three Ising universality classes. The origin of this deviation is discussed with general physical arguments.Comment: 9 pages, 16 figure

Can universality of the QCD evolution be checked in W boson decays into hadrons?

Hadron multiplicity from $W$ boson is calculated in pQCD. The agreement of our theoretical predictions with the LEP data says in favor of universality of the QCD evolution in hard processes.Comment: 14 pages, 7 figure

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

Model of collective modes in three-band superconductors with repulsive interband interactions

I consider a simple model of a three-band superconductor with repulsive interband interactions. The frustration, associated with the odd number of bands, leads to the possible existence of an intrinsically complex time-reversal symmetry breaking (TRSB) order parameter. In such state the fluctuations of the different gaps are strongly coupled, and this leads to the development of novel collective modes, which mix phase and amplitude oscillations. I study these fluctuations using a simple microscopic model and derive the dispersion for two physically distinct modes, which are gapped by energy less than twice the gap, and apparently present for all values of interband couplings.Comment: 6 pages, 3 figure

Orbital order and ferrimagnetic properties of the new compound Sr8CaRe3Cu4O24Sr_8 Ca Re_3 Cu_4 O_{24}

By means of the LSDA+U method and the Green function method, we investigate the electronic and magnetic properties of the new material of Sr$_8$CaRe$_3$Cu$_4$O$_{24}$. Our LSDA+U calculation shows that this system is an insulator with a net magnetic moment of 1.01 $\mu_{\rm B}$/f.u., which is in good agreement with the experiment. Magnetic moments are mainly located at Cu atoms, and the magnetic moments of neighboring Cu sites align anti-parallel. It is the non-magnetic Re atoms that induce an orbital order of $d$ electrons of Cu atoms, which is responsible for the strong exchange interaction and the high magnetic transition temperature. Based on the LSDA+U results, we introduce an effective model for the spin degrees of freedom, and investigate the finite-temperature properties by the Green function method. The obtained results are consistent with the experimental results, indicating that the spin-alternating Heisenberg model is suitable for this compound.Comment: 8 pages and 5 figur

Lessons from All Logs Summation in Yukawa Theories

Some features of old results in the total summation of all logarithmic contributions of all diagrams in Yukawa theory are presented. We discuss some lessons from this picture for the description of Pomeron, odderon, etc. in QCD.Comment: 6 pages, 2 figure