P-wave Case Research Articles

Manipulating the Brewster angles by using microscopically coherent dipole quanta and its possible implications

Traditionally, the Brewster angle is a solid property of the material in question with respect to the frequency (or color) of an incident light of proper polarization. For the material in hand, there is a one-to-one correspondence between the Brewster angle and the incident light frequency. However, this paper shows that such Brewster angle can be modified, in a postprocess manner, into a new controllable (even dynamic) variable of the host matter if a microscopic method called "dipole engineering" is employed. It is first demonstrated theoretically how the Brewster angle of the selected host matter may, in principle, be manipulated without having to get involved in the recipe or processes originally leading to the materialization the host matter. Next, numerical experiments for the p-wave case based on the first-principle quantum mechanics simulation further evidence the variation of Brewster angles rendered by the proposed method. Then, some possibilities concerning its untraditional applications are conjectured and discussed, with the null and pump-dependent Brewster angles, and the intensity-wise low-pass filters, in particular, as examples.

Pairing symmetry signatures ofT1in superconducting ferromagnets

We study the nuclear relaxation rate 1/T1 as a function of temperature for a superconducting-ferromagnetic coexistent system using a p-wave triplet model for the superconducting pairing symmetry. This calculation is contrasted with a singlet s-wave one done previously, and we see for the s-wave case that there is a Hebel-Slichter peak, albeit reduced due to the magnetization, and no peak for the p-wave case. We then compare these results to a nuclear relaxation rate experiment on UGe2 to determine the possible pairing symmetry signatures in that material. It is seen that the experimental data is inconclusive to rule out the possibility of s-wave pairing in $UGe_{2}$.

Order-parameter symmetry and mode-coupling effects at dirty superconducting quantum phase transitions

We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an effective long-range interaction between the anomalous density fluctuations which is reflected in singularities in the free energy functional. However, this long-range interaction is not strong enough to suppress disorder fluctuations. The asymptotic critical region is characterized by run-away flow to large disorder. For weak coupling, this asymptotic region is very narrow. It is preempted by a wide crossover regime with mean-field critical behavior and, in the p-wave case, logarithmic corrections to scaling in all dimensions.

Bound and scattering wave functions for a velocity-dependent Kisslinger potential for l > 0

Using formal scattering theory, the scattering wave functions are extrapolated to negative energies corresponding to bound-state poles. It is shown that the ratio of the normalized scattering and the corresponding bound-state wave functions, at a bound-state pole, is uniquely determined by the bound-state binding energy. This simple relation is proved analytically for an arbitrary angular momentum quantum number l > 0, in the presence of a velocity-dependent Kisslinger potential. The extrapolation relation is tested analytically by solving the Schrodinger equation in the p-wave case exactly for the scattering and the corresponding bound-state wave functions when the Kisslinger potential has the form of a square well. A numerical resolution of the Schrodinger equation in the p-wave case and of a square-well Kisslinger potential is carried out to investigate the range of validity of the extrapolated connection. It is found that the derived relation is satisfied best at low energies and short distances.

VORTEX IN CHIRAL SUPERCONDUCTING STATE

We have investigated the vortex in chiral superconductors, especially in p-wave case. In chiral superconductors the Cooper pair has orbital angular momentum hence U(1), parity (P) and time reversal symmetry (T) are broken simultaneously. We have found that the vortex has fractional charge and fractional angular momentum which comes from P- and T-violation. The fractionalization of the angular momentum suggests that the vortex could be an anyon which obeys the fractional statistics. We have also pointed out that the electric field is induced near the vortex core and non-trivial electromagnetic phenomena are expected to occur.

Quasiparticles and vortices in unconventional superconductors

Quasiparticles in the vortex lattice of strongly type-II superconductors are investigated by means of a singular gauge transformation applied to the tight binding lattice Bogoliubov-de Gennes Hamiltonian. We present a detailed derivation of the gauge invariant effective low energy Hamiltonian for the quasiparticle-vortex system and show how the physics of the "Doppler shift" and "Berry phase" can be incorporated at the Hamiltonian level by working in the singular gauge. In particular, we show that the "Berry phase" effect manifests itself in the effective Hamiltonian through a half-flux Aharonov-Bohm scattering of quasiparticles off vortices and stress the important role that this effect plays in the quasiparticle dynamics. Full numerical solutions in the regime of intermediate fields H_c1<<B<<H_c2 are presented for model superconductors with s-, p- and d-wave symmetries and with square and triangular vortex lattices. For s- and p-wave cases we obtain low energy bound states in the core, in agreement with the existing results. For d-wave case only extended quasiparticle states exist. We investigate in detail the nature of these extended states and provide comparison to the previous results within linearized ``Dirac fermion'' model. We also investigate internodal interference effects when vortex and ionic lattices have high degree of commensurability and discuss various specific choices for the singular gauge transformation.

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect

We analyze pairing of fermions in two dimensions for fully gapped cases with broken parity (P) and time reversal (T), especially cases in which the gap function is an orbital angular momentum (l) eigenstate, in particular $l=\ensuremath{-}1$ (p wave, spinless, or spin triplet) and $l=\ensuremath{-}2$ (d wave, spin singlet). For $l\ensuremath{\ne}0,$ these fall into two phases, weak and strong pairing, which may be distinguished topologically. In the cases with conserved spin, we derive explicitly the Hall conductivity for spin as the corresponding topological invariant. For the spinless p-wave case, the weak-pairing phase has a pair wave function that is asympototically the same as that in the Moore-Read (Pfaffian) quantum Hall state, and we argue that its other properties (edge states, quasihole, and toroidal ground states) are also the same, indicating that nonabelian statistics is a generic property of such a paired phase. The strong-pairing phase is an abelian state, and the transition between the two phases involves a bulk Majorana fermion, the mass of which changes sign at the transition. For the d-wave case, we argue that the Haldane-Rezayi state is not the generic behavior of a phase but describes the asymptotics at the critical point between weak and strong pairing, and has gapless fermion excitations in the bulk. In this case the weak-pairing phase is an abelian phase, which has been considered previously. In the p-wave case with an unbroken $U(1)$ symmetry, which can be applied to the double layer quantum Hall problem, the weak-pairing phase has the properties of the 331 state, and with nonzero tunneling there is a transition to the Moore-Read phase. The effects of disorder on noninteracting quasiparticles are considered. The gapped phases survive, but there is an intermediate thermally conducting phase in the spinless p-wave case, in which the quasiparticles are extended.

Photon linear colliders as Aladdin's lamp - novel probes of QCD in tt̄ physics

S-wave and P-wave production cross sections of top quarks in the threshold region are obtained from perturbative QCD in terms of m t, Γ t and α S. S-wave production is described in terms of the Green function for the tt̄ system whereas P-wave production depends on the second space derivatives of the tt̄ Green function. We show by explicit calculation that those relativistic corrections that a priori could affect specifically the non-S-wave production are quite insignificant if top decays mainly like t → bW or t → bH with H denoting a charge Higgs state. A comparison of the S-wave and P-wave case thus provides a novel probe of QCD as it affects top dynamics. Collisions of polarized photons off each other allow us to extract separately the S-wave and P-wave production cross section. Such polarized photon beams can be generated by Compton backscattering laser light off polarized electron and positron beams.

Thin films of anisotropic superconductors.

The effects of boundary scattering in p- and d-wave thin (d\ensuremath{\lesssim}\ensuremath{\xi}) superconducting films are studied. Even for specularly reflecting walls, the transition temperature of anisotropic superconductors is monotonically depressed as the thickness decreases and does not exhibit the oscillations characteristic of an ordinary s-wave (isotropic) superconductor. In the presence of a rough boundary, diffusive scattering dramatically reduces ${T}_{c}$ resulting in a critical thickness below which the film re- mains normal. In the p-wave (odd parity) case there is a critical roughness above which a finite density of states appears at the Fermi level; d-wave (even parity) superconducting films are always gapless.

Ginzburg-Landau free energy in superfluid3He

The Ginzburg-Landau free energy is a basic quantity in the study of BCS-like superfluids. It has been widely used in superconductivity 1 as well as in the theory of superfluid 3He.2 By minimizing this free energy with respect to the variation of the order parameter, one obtains the Ginzburg=Landau equations, which permit one to study the system when the order parameter is slowly varying. Originally introduced for superconductors near the critical temperature, this free energy has been calculated by Werthamer 3 and Eilenberger 4 for all temperatures by solving the Gor'kov equations. This result has been extended to 3He by Cross, 5 who considered the p-wave case and included Fermi liquid effects. Here we wish to present a general kinetic theory derivation for this free energy in the case of superfluid 3He. Kinetic theory has proved to be a very powerful tool in the theory of spin 6 and of orbital dynamics. 7 Therefore it is of interest to show that the free energy, which is of basic importance for static properties, can be derived directly from the kinetic equation. Moreover, as will be seen, this derivation has the advantage o f being conceptually straightforward, as well as easily lending itself to the inclusion 519

Perturbation of relativistic bootstraps

This paper reports the investigation of two problems: (i) the possibility of bootstrapping boundstate scalar and vector mesons from scalar constituents, in an off-shell model, utilizing the direct interaction theory of Bakamjian and Thomas (1953), and then (ii) the effect of applying a linear perturbation procedure to the masses and coupling constants of these solutions. In (i) the Lippmann-Schwinger formalism and an approximate form of crossing symmetry are used to obtain expressions for the bound-state residues, giving solutions to both the scalar and vector cases with properties in excellent agreement with Bethe-Salpeter and N/D dispersion results of other excellent agreement with Bethe-Salpeter and N/D dispersion results of other workers. In (ii) the author calculates the relative contributions of the 'driving-term' and 'feedback' mechanisms. In the S-wave case he finds that the attractive perturbation increases the binding of the bound state, but in the P-wave case, treated with a cut-off, he obtains a 'sign-reversal' of the mass-shift arising from the 'feedback'.

Final State Interaction in Kaon Production

>The final state approach is applied to the reaction pi - + P → K + Y + pi . The pi -Y and K-Y interactions are neglected and only the K- pi interaction is considered in the final state. The matrix elements for the primary interaction are determined by the use of Fermi's statistical model. The secondary interaction is handled by the use of effective range formulae, where the parameters are fitted to the experimental full width at half maximum of 23 Mev and an effective mass of 878 Mev for an I = 1/2 resonance. Both an S-wave and P-wave resonance are considered. The results indicate a κ 0 π+ Σ-/ κ + π0 Σ-- ratio of 1.7 with a small amount of K0 pi - Σ + reaction for both the S- and P-wave cases. This result is in agreement with experimental results. The calculations also indicate a κ + π0 Σ-/ κ 0 π0 Σ0 ratio of 107 for an S-wave resonance and a ratio of 0.7 for a P-wave resonance. Unfortunately, the reaction κ 0π0 Σ0is difficult to determine experimentally and no experimental results have been obtained on them as yet.