29 research outputs found
Effect of Anisotropic Reactivity on the Rate of Diffusion-Controlled Reactions: Comparative Analysis of the Models of Patches and Hemispheres
AbstractA comparative analysis of two models of anisotropic reactivity in bimolecular diffusion-controlled reaction kinetics is presented. One is the conventional model of reactive patches (MRP), where the surface of a molecule is assumed to be reactive over a certain region (circular patch) with the rest of the surface being inert. Another one is the model of reactive hemispheres (MRH), assuming that a molecule is reactive within a certain distance from a point on its surface. The accuracy of the known and newly derived simple analytical expressions for the reaction rate is tested by comparison with the simulation results obtained by the original Brownian dynamics method. These formulas prove to be quite accurate in the practically important limit of strong anisotropy corresponding to small size of the reactive patches or hemispheres. Numerical calculations confirm earlier predictions that the MRP rates are much smaller than the MRH rates for the same radii of the reactive regions, especially in the case where both reacting molecules are anisotropic
Effect of nodes, ellipticity and impurities on the spin resonance in Iron-based superconductors
We analyze doping dependence of the spin resonance of an s+- superconductor
and its sensitivity to the ellipticity of electron pockets, to magnetic and
non-magnetic impurities, and to the angle dependence of the superconducting gap
along electron Fermi surfaces. We show that the maximum intensity of the
resonance shifts from commensurate to incommensurate momentum above some
critical doping which decreases with increasing ellipticity. Angle dependence
of the gap and particularly the presence of accidental nodes lowers the overall
intensity of the resonance peak and shifts its position towards the onset of
the particle-hole continuum. Still, however, the resonance remains a true
\delta-function in the clean limit. When non-magnetic or magnetic impurities
are present, the resonance broadens and its position shifts. The shift depends
on the type of impurities and on the ratio of intraband and interband
scattering components. The ratio Omega_{res}/T_c increases almost linearly with
the strength of the interband impurity scattering, in agreement with the
experimental data. We also compare spin response of s+- and s++
superconductors. We show that there is no resonance for s++ gap, even when
there is a finite mismatch between electron and hole Fermi surfaces shifted by
the antiferromagnetic momentum.Comment: 12 pages, 10 figures, submitted to PR
Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions
We consider two-dimensional Fermi liquids in the vicinity of a quantum
transition to a phase with commensurate, antiferromagnetic long-range order.
Depending upon the Fermi surface topology, mean-field spin-density-wave theory
predicts two different types of such transitions, with mean-field dynamic
critical exponents (when the Fermi surface does not cross the magnetic
zone boundary, type ) and (when the Fermi surface crosses the magnetic
zone boundary, type ). The type system only displays behavior at
all energies and its scaling properties are similar (though not identical) to
those of an insulating Heisenberg antiferromagnet. Under suitable conditions
precisely stated in this paper, the type system displays a crossover from
relaxational behavior at low energies to type behavior at high energies. A
scaling hypothesis is proposed to describe this crossover: we postulate a
universal scaling function which determines the entire, temperature-,
wavevector-, and frequency-dependent, dynamic, staggered spin susceptibility in
terms of 4 measurable, , parameters (determining the distance, energy, and
order parameter scales, plus one crossover parameter). The scaling function
contains the full scaling behavior in all regimes for both type and
systems. The crossover behavior of the uniform susceptibility and the specific
heat is somewhat more complicated and is also discussed. Explicit computation
of the crossover functions is carried out in a large expansion on a
mean-field model. Some new results for the critical properties on the ordered
side of the transition are also obtained in a spin-density wave formalism. The
possible relevance of our results to the doped cuprate compounds is briefly
discussed.Comment: 20 pages, REVTeX, 6 figures (uuencoded compressed PostScript file for
figures is appended
Effect of point-contact transparency on coherent mixing of Josephson and transport supercurrents
The influence of electron reflection on dc Josephson effect in a ballistic
point contact with transport current in the banks is considered theoretically.
The effect of finite transparency on the vortex-like currents near the contact
and at the phase difference which has been predicted recently
\cite{KOSh}, is investigated. We show that at low temperatures even a small
reflection on the contact destroys the mentioned vortex-like current states,
which can be restored by increasing of the temperature.Comment: 6 pages, 8 Figures, Latex Fil
Quasiparticle spectrum in a nearly antiferromagnetic Fermi liquid: shadow and flat bands
We consider a two-dimensional Fermi liquid in the vicinity of a
spin-density-wave transition to a phase with commensurate antiferromagnetic
long-range order. We assume that near the transition, the Fermi surface is
large and crosses the magnetic Brillouin zone boundary. We show that under
these conditions, the self-energy corrections to the dynamical spin
susceptibility, , and to the quasiparticle spectral function
function, , are divergent near the transition. We identify and
sum the series of most singular diagrams, and obtain a solution for and an approximate solution for . We show that (i)
at a given, small has an extra peak at (`shadow
band'), and (ii) the dispersion near the crossing points is much flatter than
for free electrons. The relevance of these results to recent photoemission
experiments in and systems is discussed.Comment: a sign and amplitude of the vertex renormalization and few typos are
correcte
Microscopic theory of weak pseudogap behavior in the underdoped cuprate superconductors I: General theory and quasiparticle properties
We derive in detail a novel solution of the spin fermion model which is valid
in the quasi-static limit pi T<<omega_sf, found in the intermediate
(pseudoscaling) regime of the magnetic phase diagram of cuprate
superconductors, and use it to obtain results for the temperature and doping
dependence of the single particle spectral density, the electron-spin
fluctuation vertex function, and the low frequency dynamical spin
susceptibility. The resulting strong anisotropy of the spectral density and the
vertex function lead to the qualitatively different behavior of_hot_ (around
k=(pi,0)) and_cold_ (around k=(pi/2,pi/2)) quasiparticles seen in ARPES
experiments. We find that the broad high energy features found in ARPES
measurements of the spectral density of the underdoped cuprate superconductors
are determined by strong antiferromagnetic (AF) correlations and incoherent
precursor effects of an SDW state, with reduced renormalized effective coupling
constant. The electron spin-fluctuation vertex function, i.e. the effective
interaction of low energy quasiparticles and spin degrees of freedom, is found
to be strongly anisotropic and enhanced for hot quasiparticles; the
corresponding charge-fluctuation vertex is considerably diminished. We thus
demonstrate that, once established, strong AF correlations act to reduce
substantially the effective electron-phonon coupling constant in cuprate
superconductors.Comment: REVTEX with EPS figures, uses multicol.sty, epsfig,sty, psfig.st
Charge and spin density wave ordering transitions in strongly correlated metals
We study the quantum transition from a strongly correlated metal, with heavy
fermionic quasiparticles, to a metal with commensurate charge or spin density
wave order. To this end, we introduce and numerically analyze a large
dimensionality model of Ising spins in a transverse field, coupled to two
species of fermions; the analysis borrows heavily from recent progress in the
solution of the Hubbard model in large dimensions. At low energies, the Ising
order parameter fluctuations are characterized by the critical exponent , while above an energy scale, , there is a crossover to criticality. We show that is of the order of the width of the
heavy quasiparticle band, and can be made arbitrarily small for a correlated
metal close to a Mott-Hubbard insulator. Therefore, such a correlated metal has
a significant intermediate energy range of behavior, a single
particle spectrum with a narrow quasiparticle band, and well-formed analogs of
the lower and upper Hubbard bands; we suggest that these features are
intimately related in general.Comment: 14 pages, REVTEX 3.0, 2 postscript figure
Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps
The problem of a diffusing particle moving among diffusing traps is analyzed
in general space dimension d. We consider the case where the traps are
initially randomly distributed in space, with uniform density rho, and derive
upper and lower bounds for the probability Q(t) (averaged over all particle and
trap trajectories) that the particle survives up to time t. We show that, for
1<=d<2, the bounds converge asymptotically to give where and D
is the diffusion constant of the traps, and that for d=2. For d>2 bounds can still be derived, but they no longer
converge for large t. For 1<=d<=2, these asymptotic form are independent of the
diffusion constant of the particle. The results are compared with simulation
results obtained using a new algorithm [V. Mehra and P. Grassberger, Phys. Rev.
E v65 050101 (2002)] which is described in detail. Deviations from the
predicted asymptotic forms are found to be large even for very small values of
Q(t), indicating slowly decaying corrections whose form is consistent with the
bounds. We also present results in d=1 for the case where the trap densities on
either side of the particle are different. For this case we can still obtain
exact bounds but they no longer converge.Comment: 13 pages, RevTeX4, 6 figures. Figures and references updated;
equations corrected; discussion clarifie
Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
We propose that underdoped high superconductors are described by an
algebraic spin liquid (ASL) at high energies, which undergoes a spin-charge
recombination transition at low energies. The spin correlation in the ASL is
calculated via its effective theory - a system of massless Dirac fermions
coupled to a U(1) gauge field. We find that without fine tuning any parameters
the gauge interaction strongly enhances the staggered spin correlation even in
the presence of a large single particle pseudo-gap. This allows us to show that
the ASL plus spin-charge recombination picture can explain many highly unusual
properties of underdoped high superconductors.Comment: 22 pages, 18 figures, submitted to PR
Quantum Disordered Regime and Spin Gap in the Cuprate Superconductors
We discuss the crossover from the quantum critical, , to the quantum
disordered regime in high-T materials in relation to the experimental data
on the nuclear relaxation, bulk susceptibility, and inelastic neutron
scattering. In our scenario, the spin excitations develop a gap
well above T, which is supplemented by the
quasiparticle gap below T. The above experiments yield consistent estimates
for the value of the spin gap, which increases as the correlation length
decreases.Comment: 14 pages, REVTeX v3.0, PostScript file for 3 figures is attached,
UIUC-P-93-07-06