34,181 research outputs found
Mathematical Models and Biological Meaning: Taking Trees Seriously
We compare three basic kinds of discrete mathematical models used to portray
phylogenetic relationships among species and higher taxa: phylogenetic trees,
Hennig trees and Nelson cladograms. All three models are trees, as that term is
commonly used in mathematics; the difference between them lies in the
biological interpretation of their vertices and edges. Phylogenetic trees and
Hennig trees carry exactly the same information, and translation between these
two kinds of trees can be accomplished by a simple algorithm. On the other
hand, evolutionary concepts such as monophyly are represented as different
mathematical substructures are represented differently in the two models. For
each phylogenetic or Hennig tree, there is a Nelson cladogram carrying the same
information, but the requirement that all taxa be represented by leaves
necessarily makes the representation less efficient. Moreover, we claim that it
is necessary to give some interpretation to the edges and internal vertices of
a Nelson cladogram in order to make it useful as a biological model. One
possibility is to interpret internal vertices as sets of characters and the
edges as statements of inclusion; however, this interpretation carries little
more than incomplete phenetic information. We assert that from the standpoint
of phylogenetics, one is forced to regard each internal vertex of a Nelson
cladogram as an actual (albeit unsampled) species simply to justify the use of
synapomorphies rather than symplesiomorphies.Comment: 15 pages including 6 figures [5 pdf, 1 jpg]. Converted from original
MS Word manuscript to PDFLaTe
Magnetic field effects in few-level quantum dots: theory, and application to experiment
We examine several effects of an applied magnetic field on Anderson-type
models for both single- and two-level quantum dots, and make direct comparison
between numerical renormalization group (NRG) calculations and recent
conductance measurements. On the theoretical side the focus is on
magnetization, single-particle dynamics and zero-bias conductance, with
emphasis on the universality arising in strongly correlated regimes; including
a method to obtain the scaling behavior of field-induced Kondo resonance shifts
over a very wide field range. NRG is also used to interpret recent experiments
on spin-1/2 and spin-1 quantum dots in a magnetic field, which we argue do not
wholly probe universal regimes of behavior; and the calculations are shown to
yield good qualitative agreement with essentially all features seen in
experiment. The results capture in particular the observed field-dependence of
the Kondo conductance peak in a spin-1/2 dot, with quantitative deviations from
experiment occurring at fields in excess of 5 T, indicating the eventual
inadequacy of using the equilibrium single-particle spectrum to calculate the
conductance at finite bias.Comment: 15 pages, 12 figures. Version as published in PR
A local moment approach to the degenerate Anderson impurity model
The local moment approach is extended to the orbitally-degenerate [SU(2N)]
Anderson impurity model (AIM). Single-particle dynamics are obtained over the
full range of energy scales, focussing here on particle-hole symmetry in the
strongly correlated regime where the onsite Coulomb interaction leads to
many-body Kondo physics with entangled spin and orbital degrees of freedom. The
approach captures many-body broadening of the Hubbard satellites, recovers the
correct exponential vanishing of the Kondo scale for all N, and its universal
scaling spectra are found to be in very good agreement with numerical
renormalization group (NRG) results. In particular the high-frequency
logarithmic decays of the scaling spectra, obtained here in closed form for
arbitrary N, coincide essentially perfectly with available numerics from the
NRG. A particular case of an anisotropic Coulomb interaction, in which the
model represents a system of N `capacitively-coupled' SU(2) AIMs, is also
discussed. Here the model is generally characterised by two low-energy scales,
the crossover between which is seen directly in its dynamics.Comment: 23 pages, 7 figure
Correlated electron physics in multilevel quantum dots: phase transitions, transport, and experiment
We study correlated two-level quantum dots, coupled in effective 1-channel
fashion to metallic leads; with electron interactions including on-level and
inter-level Coulomb repulsions, as well as the inter-orbital Hund's rule
exchange favoring the spin-1 state in the relevant sector of the free dot. For
arbitrary dot occupancy, the underlying phases, quantum phase transitions
(QPTs), thermodynamics, single-particle dynamics and electronic transport
properties are considered; and direct comparison is made to conductance
experiments on lateral quantum dots. Two distinct phases arise generically, one
characterised by a normal Fermi liquid fixed point (FP), the other by an
underscreened (USC) spin-1 FP. Associated QPTs, which occur in general in a
mixed valent regime of non-integral dot charge, are found to consist of
continuous lines of Kosterlitz-Thouless transitions, separated by first order
level-crossing transitions at high symmetry points. A `Friedel-Luttinger sum
rule' is derived and, together with a deduced generalization of Luttinger's
theorem to the USC phase (a singular Fermi liquid), is used to obtain a general
result for the T=0 zero-bias conductance, expressed solely in terms of the dot
occupancy and applicable to both phases. Relatedly, dynamical signatures of the
QPT show two broad classes of behavior, corresponding to the collapse of either
a Kondo resonance, or antiresonance, as the transition is approached from the
Fermi liquid phase; the latter behavior being apparent in experimental
differential conductance maps. The problem is studied using the numerical
renormalization group method, combined with analytical arguments.Comment: 22 pages, 18 figures, submitted for publicatio
Quantum phase transition in capacitively coupled double quantum dots
We investigate two equivalent, capacitively coupled semiconducting quantum
dots, each coupled to its own lead, in a regime where there are two electrons
on the double dot. With increasing interdot coupling a rich range of behavior
is uncovered: first a crossover from spin- to charge-Kondo physics, via an
intermediate SU(4) state with entangled spin and charge degrees of freedom;
followed by a quantum phase transition of Kosterlitz-Thouless type to a
non-Fermi liquid `charge-ordered' phase with finite residual entropy and
anomalous transport properties. Physical arguments and numerical
renormalization group methods are employed to obtain a detailed understanding
of the problem.Comment: 4 pages, 3 figure
Two-channel Kondo physics in tunnel-coupled double quantum dots
We investigate theoretically the possibility of observing two-channel Kondo
(2CK) physics in tunnel-coupled double quantum dots (TCDQDs), at both zero and
finite magnetic fields; taking the two-impurity Anderson model (2AIM) as the
basic TCDQD model, together with effective low-energy models arising from it by
Schrieffer-Wolff transformations to second and third order in the tunnel
couplings. The models are studied primarily using Wilson's numerical
renormalization group. At zero-field our basic conclusion is that while 2CK
physics arises in principle provided the system is sufficiently
strongly-correlated, the temperature window over which it could be observed is
much lower than is experimentally feasible. This finding disagrees with recent
work on the problem, and we explain why. At finite field, we show that the
quantum phase transition known to arise at zero-field in the two-impurity Kondo
model (2IKM), with an essentially 2CK quantum critical point, persists at
finite fields. This raises the prospect of access to 2CK physics by tuning a
magnetic field, although preliminary investigation suggests this to be even
less feasible than at zero field.Comment: 10 pages, 8 figures. Version as published in PR
- …