633 research outputs found
Phase Transitions in Quantum Dots
We perform Hartree-Fock calculations to show that quantum dots (i.e. two
dimensional systems of up to twenty interacting electrons in an external
parabolic potential) undergo a gradual transition to a spin-polarized Wigner
crystal with increasing magnetic field strength. The phase diagram and ground
state energies have been determined. We tried to improve the ground state of
the Wigner crystal by introducing a Jastrow ansatz for the wavefunction and
performing a variational Monte Carlo calculation. The existence of so called
magic numbers was also investigated. Finally, we also calculated the heat
capacity associated with the rotational degree of freedom of deformed many-body
states.Comment: 14 pages, 7 postscript figure
Penguins leaving the pole: bound-state effects in B decaying to K* + photon
Applying perturbative QCD methods recently seen to give a good description of
the two body hadronic decays of the B meson, we address the question of
bound-state effects on the decay B into K* + gamma. Consistent with most
analyses, we demonstrate that gluonic penguins, with photonic bremsstrahlung
off a quark, change the decay rate by only a few percent. However, explicit
off-shell b-quark effects normally discarded are found to be large in
amplitude, although in the standard model accidents of phase minimize the
effect on the rate. Using an asymptotic distribution amplitude for the K* and
just the standard model, we can obtain a branching ratio of a few times
10^{-5}, consistent with the observed rate.Comment: 12 pages. U. of MD PP \#94-129; DOE/ER/40762-033; WM-94-104. LaTeX,
One figure, available by fax or pos
Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries
At special loci in their moduli spaces, Calabi-Yau manifolds are endowed with
discrete symmetries. Over the years, such spaces have been intensely studied
and have found a variety of important applications. As string compactifications
they are phenomenologically favored, and considerably simplify many important
calculations. Mathematically, they provided the framework for the first
construction of mirror manifolds, and the resulting rational curve counts.
Thus, it is of significant interest to investigate such manifolds further. In
this paper, we consider several unexplored loci within familiar families of
Calabi-Yau hypersurfaces that have large but unexpected discrete symmetry
groups. By deriving, correcting, and generalizing a technique similar to that
of Candelas, de la Ossa and Rodriguez-Villegas, we find a calculationally
tractable means of finding the Picard-Fuchs equations satisfied by the periods
of all 3-forms in these families. To provide a modest point of comparison, we
then briefly investigate the relation between the size of the symmetry group
along these loci and the number of nonzero Yukawa couplings. We include an
introductory exposition of the mathematics involved, intended to be accessible
to physicists, in order to make the discussion self-contained.Comment: 54 pages, 3 figure
The BCS Functional for General Pair Interactions
The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed
attention as a description of fermionic gases interacting with local pairwise
interactions. We present here a rigorous analysis of the BCS functional for
general pair interaction potentials. For both zero and positive temperature, we
show that the existence of a non-trivial solution of the nonlinear BCS gap
equation is equivalent to the existence of a negative eigenvalue of a certain
linear operator. From this we conclude the existence of a critical temperature
below which the BCS pairing wave function does not vanish identically. For
attractive potentials, we prove that the critical temperature is non-zero and
exponentially small in the strength of the potential.Comment: Revised Version. To appear in Commun. Math. Phys
Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree
Recently it has been proved that any arithmetically Cohen-Macaulay (ACM)
bundle of rank two on a general, smooth hypersurface of degree at least three
and dimension at least four is a sum of line bundles. When the dimension of the
hypersurface is three, a similar result is true provided the degree of the
hypersurface is at least six. We extend these results to complete intersection
subvarieties by proving that any ACM bundle of rank two on a general, smooth
complete intersection subvariety of sufficiently high multi-degree and
dimension at least four splits. We also obtain partial results in the case of
threefolds.Comment: 15 page
Low energy collective modes, Ginzburg-Landau theory, and pseudogap behavior in superconductors with long-range pairing interactions
We study the superconducting instability in systems with long but finite
ranged, attractive, pairing interactions. We show that such long-ranged
superconductors exhibit a new class of fluctuations in which the internal
structure of the Cooper pair wave function is soft, and thus lead to
"pseudogap" behavior in which the actual transition temperature is greatly
depressed from its mean field value. These fluctuations are {\it not} phase
fluctuations of the standard superconducting order parameter, and lead to a
highly unusual Ginzburg-Landau description. We suggest that the crossover
between the BCS limit of a short-ranged attraction and our problem is of
interest in the context of superconductivity in the underdoped cuprates.Comment: 20 pages with one embedded ps figure. Minor revisions to the text and
references. Final version to appear in PRB on Nov. 1st, 200
The low-energy phase-only action in a superconductor: a comparison with the XY model
The derivation of the effective theory for the phase degrees of freedom in a
superconductor is still, to some extent, an open issue. It is commonly assumed
that the classical XY model and its quantum generalizations can be exploited as
effective phase-only models. In the quantum regime, however, this assumption
leads to spurious results, such as the violation of the Galilean invariance in
the continuum model. Starting from a general microscopic model, in this paper
we explicitly derive the effective low-energy theory for the phase, up to
fourth-order terms. This expansion allows us to properly take into account
dynamic effects beyond the Gaussian level, both in the continuum and in the
lattice model. After evaluating the one-loop correction to the superfluid
density we critically discuss the qualitative and quantitative differences
between the results obtained within the quantum XY model and within the correct
low-energy theory, both in the case of s-wave and d-wave symmetry of the
superconducting order parameter. Specifically, we find dynamic anharmonic
vertices, which are absent in the quantum XY model, and are crucial to restore
Galilean invariance in the continuum model. As far as the more realistic
lattice model is concerned, in the weak-to-intermediate-coupling regime we find
that the phase-fluctuation effects are quantitatively reduced with respect to
the XY model. On the other hand, in the strong-coupling regime we show that the
correspondence between the microscopically derived action and the quantum XY
model is recovered, except for the low-density regime.Comment: 29 pages, 11 figures. Slightly revised presentation, accepted for
publication in Phys. Rev.
Phase fluctuations, dissipation and superfluid stiffness in d-wave superconductors
We study the effect of dissipation on quantum phase fluctuations in d-wave
superconductors. Dissipation, arising from a nonzero low frequency optical
conductivity which has been measured in experiments below , has two
effects: (1) a reduction of zero point phase fluctuations, and (2) a reduction
of the temperature at which one crosses over to classical thermal fluctuations.
For parameter values relevant to the cuprates, we show that the crossover
temperature is still too large for classical phase fluctuations to play a
significant role at low temperature. Quasiparticles are thus crucial in
determining the linear temperature dependence of the in-plane superfluid
stiffness. Thermal phase fluctuations become important at higher temperatures
and play a role near .Comment: Presentation improved, new references added (10 latex pages, 3 eps
figures). submitted to PR
Experimental implications of quantum phase fluctuations in layered superconductors
I study the effect of quantum and thermal phase fluctuations on the in-plane
and c-axis superfluid stiffness of layered d-wave superconductors. First, I
show that quantum phase fluctuations in the superconductor can be damped in the
presence of external screening of Coulomb interactions, and suggest an
experiment to test the importance of these fluctuations, by placing a metal in
close proximity to the superconductor to induce such screening. Second, I show
that a combination of quantum phase fluctuations and the linear temperature
dependence of the in-plane superfluid stiffness leads to a linear temperature
dependence of the c-axis penetration depth, below a temperature scale
determined by the magnitude of in-plane dissipation.Comment: 6 pgs, 1 figure, minor changes in comparison with c-axis expt, final
published versio
Avalanches and the Renormalization Group for Pinned Charge-Density Waves
The critical behavior of charge-density waves (CDWs) in the pinned phase is
studied for applied fields increasing toward the threshold field, using
recently developed renormalization group techniques and simulations of
automaton models. Despite the existence of many metastable states in the pinned
state of the CDW, the renormalization group treatment can be used successfully
to find the divergences in the polarization and the correlation length, and, to
first order in an expansion, the diverging time scale. The
automaton models studied are a charge-density wave model and a ``sandpile''
model with periodic boundary conditions; these models are found to have the
same critical behavior, associated with diverging avalanche sizes. The
numerical results for the polarization and the diverging length and time scales
in dimensions are in agreement with the analytical treatment. These
results clarify the connections between the behaviour above and below
threshold: the characteristic correlation lengths on both sides of the
transition diverge with different exponents. The scaling of the distribution of
avalanches on the approach to threshold is found to be different for automaton
and continuous-variable models.Comment: 29 pages, 11 postscript figures included, REVTEX v3.0 (dvi and PS
files also available by anonymous ftp from external.nj.nec.com in directory
/pub/alan/cdwfigs
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