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The nanocrystallite have the finite number of the oscillation modes. Their number increases proportionally to a cube of the characteristic size. Thus the oscillation spectrum of nanocrystal becomes discrete, and the separate modes of oscillations does not interact with each other, that considerably strengthens all phonon modulated processes in a crystal. Covering of such a nanocrystallite with the shielding surface of a material with the higher nuclear weight will allow to create the phonon resonant cavity whose oscillation modes will represent the standing waves and, will be amplified by the resonant manner. The composites made of phonon resonant cavities will allow to produce a perspective functional material for the electronics with adjustable structure and properties., Comment: 3 pages

Gap structure in noncentrosymmetric superconductors with spin-orbit band splitting is studied using a microscopic model of pairing mediated by phonons and/or spin fluctuations. The general form of pairing interaction in the band representation is derived, which includes both the intraband and interband pairing terms. In the case of isotropic interaction (in particular, for a BCS-contact interaction), the interband pairing terms vanish identically at any magnitude of the band splitting. The effects of pairing interaction anisotropy are analyzed in detail for a metal of cubic symmetry with strong spin-orbit coupling. It is shown that if phonons are dominant then the gaps in two bands are isotropic, nodeless, and have in general different amplitudes. Applications to the Li_2(Pd_{1-x},Pt_x)_3B family of noncentrosymmetric superconductors are discussed., Comment: 9 pages; minor corrections, published version

Let $X$ be a smooth variety over an algebraically closed field $k$ of positive characteristic, ${\rm D}_X$ the sheaf of PD-differential operators, and ${\bar D}_X$ its central reduction, the sheaf of small differential operators. In this paper we show that if $X$ is a line-hyperplane incidence variety (a partial flag variety of type $(1,n,n+1)$) or a quadric of arbitrary dimension (in this case the characteristic is supposed to be odd) then ${\rm H}^{i}(X,{\bar D}_X)=0$ for $i>0$. Using this vanishing result and the derived localization theorem for crystalline differential operators (\cite{BMR}) we show that the Frobenius pushforward of the structure sheaf is a tilting bundle on these varieties, provided that $p>h$, the Coxeter number of the corresponding group., Comment: Revised version. A vanishing statement added allowing to remove previous restrictions on the characteristic in the case of quadrics. 15 pages

We calculate the spin susceptibility of a superconductor without inversion symmetry, both in the clean and disordered cases. The susceptibility has a large residual value at zero temperature, which is further enhanced in the presence of scalar impurities., Comment: 12 pages, 3 figures

We calculate the relaxation rate of a nuclear spin in s-wave superconductor with nonmagnetic impurities, including the strong-coupling effects. We show that in a weakly disordered three-dimensional system the corrections due to disorder are negligibly small., Comment: 9 pages

In this paper we prove first a general theorem on semiorthogonal decompositions in derived categories of coherent sheaves for flat families over a smooth base. Based on the results of math.AG/0510670, we then show that the derived categories of coherent sheaves on flag varieties of classical type are generated by complete exceptional collections. Finally, we find complete exceptional collections in the derived categories of some homogeneous spaces of the symplectic groups of small rank., Comment: Final version. 14 pages, to appear in Journal Lond. Math. Soc

We microscopically derive the Ginzburg-Landau free energy functional for a noncentrosymmetric superconductor with a large spin-orbit splitting of the electron bands, in the presence of nonmagnetic impurities. The critical temperature is found to be suppressed by disorder, both for conventional and unconventional pairing, in the latter case according to the universal Abrikosov-Gor'kov function. The impurity effect on the upper critical field turns out to be nonuniversal, determined by the pairing symmetry and the band structure. In a BCS-like model, Tc is not affected, while Hc2 increases with disorder. For unconventional pairing, both Tc and Hc2 are suppressed by disorder., Comment: published version, 14 pages, 2 figures

In this paper we prove a cohomology vanishing result for quadrics of low dimension in positive characteristic. This vanishing is a necessary condition for the D-affinity of these varieties., Comment: 6 pages

A new class of generalized solutions related to the essential spectrum of linear Maxwell's equations is presented. The essential modes are given in terms of normalized singular Weyl's sequences, whose square represents Dirac's delta functions in spatial and angular frequency domains. The action integral associated with essential modes is well-defined. We claim that these modes represent the collapsed state of the electromagnetic field and, with some additional assumptions on the conservation of action, are suitable for describing the double-slit experiment in accordance with the orthodox point of view., Comment: 4 pages

We study the effects of dipole interaction on the superfluidity in a homogeneous Fermi gas with population imbalance. We show that the Larkin-Ovchinnikov-Fulde-Ferrell phase is replaced by another nonuniform superfluid phase, in which the order parameter has a nonzero triplet component induced by the dipole interaction., Comment: 4 pages, 1 figure

We derive the essential space-time spectrum of the Maxwell equations in linear isotropic inhomogeneous media together with the corresponding essential modes. These modes represent the collapse of the electromagnetic field into a single point in space at a single angular frequency. The location and frequency of the essential mode are random variables obeying the Born statistical postulate., Comment: 4 pages, no figures

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption., Comment: 14 pages, no figures

We calculate the effect of nonmagnetic impurity scattering on the spin-lattice relaxation rate in two-band superconductors with the s-wave pairing symmetry. It is found that for the interaction parameters appropriate for MgB2 the Hebel-Slichter peak is suppressed by disorder in the limit of small interband impurity scattering rate. In the limit of strong impurity scattering, when the gap functions in the two bands become nearly equal, the single-band behavior is recovered with a well-defined coherence peak just below the transition temperature., Comment: 6 pages, 4 figures

We analyze the nuclear magnetic relaxation rate $(1/T_1)_{orb}$ due to the coupling of nuclear spin to the orbital moment of itinerant electrons in metals. In the clean non--interacting case, contributions from large--distance current fluctuations add up to cause a divergence of $(1/T_1)_{orb}$. When impurity scattering is present, the elastic mean free time $\tau$ cuts off the divergence, and the magnitude of the effect at low temperatures is controlled by the parameter $\ln(\mu \tau)$, where $\mu$ is the chemical potential. The spin--dipolar hyperfine coupling, while has the same spatial variation $1/r^3$ as the orbital hyperfine coupling, does not produce a divergence in the nuclear magnetic relaxation rate., Comment: 11pages; v4: The analysis of the normal state is more compelete now, including a comparison with other hyperfine interactions and a detailed discussion of the effect in representative metals. The superconducting state is excluded from consideration in this paper

We study the superconducting order parameter fluctuations near the phase transition into the Larkin-Ovchinnikov-Fulde-Ferrell state in the clean limit at zero temperature. In contrast to the usual normal metal-to-uniform superconductor phase transition, the fluctuation corrections are dominated by the modes with the wave vectors away from the origin. We find that the superconducting fluctuations lead to a divergent spin susceptibility and a breakdown of the Fermi-liquid behavior at the quantum critical point., Comment: 10 pages, 4 figures

We show how the de Haas-van Alphen effect can be used to directly measure the magnitude of spin-orbit coupling in non-centrosymmetric metals, such as CePt3Si and LaPt3Si., Comment: 3 pages, accepted in Phys. Rev. B

We study the effects of low-energy nodal quasiparticles on the classical phase fluctuations in a two-dimensional d-wave superconductor. The singularities of the phase-only action at T\to 0 are removed in the presence of disorder, which justifies using an extended classical XY-model to describe phase fluctuations at low temperatures., Comment: 14 pages, brief review for Mod. Phys. Lett. B

We present a simple and unified classification of macroscopic electromagnetic resonances in finite arbitrarily inhomogeneous isotropic dielectric 3D structures situated in free space. By observing the complex-plane dynamics of the spatial spectrum of the volume integral operator as a function of angular frequency and constitutive parameters we identify and generalize all the usual resonances, including complex plasmons, real laser resonances in media with gain, and real quasi-static resonances in media with negative permittivity and gain., Comment: 4 pages, 2 figures

Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out at higher ones. The explicit expression of the operator's symbol provides exact outline of the essential spectrum for any inhomogeneous anisotropic scatterer with Holder continuous constitutive parameters. Geometrical bounds on the location of discrete eigenvalues are derived for various physical scenarios. Numerical experiments demonstrate good agreement between the predicted spectrum of the operator and the eigenvalues of its discretized version., Comment: 18 pages, 7 figures

The spin-lattice relaxation rate of nuclear magnetic resonance in a clean superconductor without inversion center is calculated for arbitrary pairing symmetry and band structure, in the presence of strong spin-orbit coupling., Comment: 4 pages

We study the spin-lattice relaxation rate of nuclear magnetic resonance in a two-band superconductor. Both conventional and unconventional pairing symmetries for an arbitrary band structure in the clean limit are considered. The importance of the inter-band interference effects is emphasized. The calculations in the conventional case with two isotropic gaps are performed using a two-band generalization of Eliashberg theory., Comment: 9 pages, 3 figures

We develop a phenomenological model of superconductivity near a domain wall in a ferromagnet. In addition to the electromagnetic interaction of the order parameter with the ferromagnetic magnetization, we take into account the possibility of a local enhancement or suppression of superconducting pairing in the vicinity of the wall, and also a non-perfect transparency of the wall to electrons. It is found that the critical temperature of superconductivity near the domain wall might be substantially higher than in the bulk., Comment: 9 pages, 7 figures

This work presents a quantitative theoretical study of the sound attenuation in the unconventional multiband superconductor Sr2RuO4 below the superconducting transition temperature Tc. Sound attenuation in this material is shown to have the remarkable property of being able to identify different nodal structures on different bands. The nodal structures on the \gamma band on the one hand, and on the \alpha and \beta bands on the other, are both found to be characterized by the existence of point nodes, but are significantly different in their quantitative aspects., Comment: 7 pages, REVTeX

In a non-centrosymmetric crystal, the Zeeman interaction of the band electrons with an external magnetic field is highly anisotropic in the momentum space, vanishing along some high-symmetry planes. One of the consequences is that the paramagnetic susceptibility in superconductors without inversion symmetry, such as CePt3Si, shows an unusual temperature dependence., Comment: 4 pages, REVTeX; discussion of the nodal structure corrected

We study the response of a superconductor with a strong spin-orbit coupling on an external magnetic field. The Ginzburg-Landau free energy functional is derived microscopically for a general crystal structure, both with and without an inversion center, and for an arbitrary symmetry of the superconducting order parameter. As a by-product, we obtain the general expressions for the intrinsic magnetic moment of the Cooper pairs. It is shown that the Ginzburg-Landau gradient energy in a superconductor lacking inversion symmetry has unusual structure. The general formalism is illustrated using as an example CePt$_3$Si, which is the first known heavy-fermion superconductor without an inversion center., Comment: Published version, 14 pages, minor corrections

Most superconducting materials have an inversion center in their crystal lattices. One of few exceptions is the recently discovered heavy-fermion superconductor CePt3Si [E. Bauer et al, Phys. Rev. Lett. 92, 027003 (2004)]. In this paper, we analyze the implications of the lack of inversion symmetry for the superconducting pairing. We show that the order parameter is an odd function of momentum, and that there always are lines of zeros in the excitation energy gap for one-component order parameters, which seems to agree with the experimental data. The superconducting phase can be non-uniform, even without external magnetic field, due to the presence of unusual gradient terms in the Ginzburg-Landau free energy. Also, we performed ab initio electronic structure calculations for CePt3Si, which showed that the spin-orbit coupling in this material is strong, and the degeneracy of the bands is lifted everywhere except along some high symmetry lines in the Brillouin zone., Comment: 10 pages, 3 color figures

We present a variational study of the helicity moduli of an anisotropic quantum three-dimensional (3D) XY-model of YBCO in superconducting state. It is found that both the ab-plane and the c-axis helicity moduli, which are proportional to the inverse square of the corresponding magnetic field penetration depth, vary with temperature T as T to the fourth power in the zero temperature limit. Moreover, the c-axis helicity modulus drops with temperature much faster than the ab-plane helicity modulus because of the weaker Josephson couplings along the c-axis compared to those along the ab-plane. These findings are in disagreement with the experiments on high quality samples of YBCO., Comment: 9 pages, 1 figure

We study the quasiparticle resonance states near strong impurities in the mixed state of a d-wave superconductor. These states give rise to zero-bias peaks in the local density of states, observed in scanning tunneling microscopy experiments. The field dependence of the peaks is obtained by averaging with respect to the spatially non-uniform Doppler shifts in the energy of excitations. The hybridization of the magnetic field-induced nodal quasiparticles with the impurity resonances results in the suppression and broadening of the zero-bias peaks. The height of the peaks is found to scale as \sqrt{Hc2/H}. The magnetic field response of the peaks is shown to be strongly dependent on the field orientation.

We show that the nodal quasiparticles have significant effect on the classical phase fluctuations in a quasi-two-dimensional d-wave superconductor. They give rise to singularities in the temperature behavior of some of the coupling constants in the phase-only effective action. One of the consequences is that the classical XY-model is not adequate for the description of the superconducting fluctuations in d-wave superconductors at low temperatures., Comment: 4 pages

We present a Monte Carlo study of the helicity moduli of an anisotropic classical three-dimensional (3D) XY-model of YBCO in superconducting state. It is found that both the ab-plane and the c-axis helicity moduli, which are proportional to the inverse square of the corresponding magnetic field penetration depth, vary linearly with temperature at low temperatures. The result for the c-axis helicity modulus is in disagreement with the experiments on high quality samples of YBCO. Thus we conclude that purely classical phase fluctuations of the superconducting order parameter cannot account for the observed c-axis electrodynamics of YBCO., Comment: 7 pages, 1 figure