445 research outputs found
Analytical solution of generalized Burton--Cabrera--Frank equations for growth and post--growth equilibration on vicinal surfaces
We investigate growth on vicinal surfaces by molecular beam epitaxy making
use of a generalized Burton--Cabrera--Frank model. Our primary aim is to
propose and implement a novel analytical program based on a perturbative
solution of the non--linear equations describing the coupled adatom and dimer
kinetics. These equations are considered as originating from a fully
microscopic description that allows the step boundary conditions to be directly
formulated in terms of the sticking coefficients at each step. As an example,
we study the importance of diffusion barriers for adatoms hopping down
descending steps (Schwoebel effect) during growth and post-growth equilibration
of the surface.Comment: 16 pages, REVTeX 3.0, IC-DDV-94-00
Magnetotransport Mechanisms in Strongly Underdoped YBa_2Cu_3O_x Single Crystals
We report magnetoresistivity measurements on strongly underdoped YBa_2Cu_3O_x
(x=6.25, 6.36) single crystals in applied magnetic fields H || c-axis. We
identify two different contributions to both in-plane and out-of-plane
magnetoresistivities. The first contribution has the same sign as the
temperature coefficient of the resistivity \partial ln(\rho_i)/\partial T
(i={c,ab}). This contribution reflects the incoherent nature of the
out-of-plane transport. The second contribution is positive, quadratic in
field, with an onset temperature that correlates to the antiferromagnetic
ordering.Comment: 4 pages, 3 figure
Decay of the metastable phase in d=1 and d=2 Ising models
We calculate perturbatively the tunneling decay rate of the
metastable phase in the quantum d=1 Ising model in a skew magnetic field near
the coexistence line at T=0. It is shown that
oscillates in the magnetic field due to discreteness of the excitation
energy spectrum. After mapping of the obtained results onto the extreme
anisotropic d=2 Ising model at , we verify in the latter model the
droplet theory predictions for the free energy analytically continued to the
metastable phase. We find also evidence for the discrete-lattice corrections in
this metastable phase free energy.Comment: 4 pages, REVTe
The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets
The spin-half XXZ model on the linear chain and the square lattice are
examined with the extended coupled cluster method (ECCM) of quantum many-body
theory. We are able to describe both the Ising-Heisenberg phase and the
XY-Heisenberg phase, starting from known wave functions in the Ising limit and
at the phase transition point between the XY-Heisenberg and ferromagnetic
phases, respectively, and by systematically incorporating correlations on top
of them. The ECCM yields good numerical results via a diagrammatic approach,
which makes the numerical implementation of higher-order truncation schemes
feasible. In particular, the best non-extrapolated coupled cluster result for
the sublattice magnetization is obtained, which indicates the employment of an
improved wave function. Furthermore, the ECCM finds the expected qualitatively
different behaviours of the linear chain and the square lattice cases.Comment: 22 pages, 3 tables, and 15 figure
A Gravitational Aharonov-Bohm Effect, and its Connection to Parametric Oscillators and Gravitational Radiation
A thought experiment is proposed to demonstrate the existence of a
gravitational, vector Aharonov-Bohm effect. A connection is made between the
gravitational, vector Aharonov-Bohm effect and the principle of local gauge
invariance for nonrelativistic quantum matter interacting with weak
gravitational fields. The compensating vector fields that are necessitated by
this local gauge principle are shown to be incorporated by the DeWitt minimal
coupling rule. The nonrelativistic Hamiltonian for weak, time-independent
fields interacting with quantum matter is then extended to time-dependent
fields, and applied to problem of the interaction of radiation with
macroscopically coherent quantum systems, including the problem of
gravitational radiation interacting with superconductors. But first we examine
the interaction of EM radiation with superconductors in a parametric oscillator
consisting of a superconducting wire placed at the center of a high Q
superconducting cavity driven by pump microwaves. We find that the threshold
for parametric oscillation for EM microwave generation is much lower for the
separated configuration than the unseparated one, which then leads to an
observable dynamical Casimir effect. We speculate that a separated parametric
oscillator for generating coherent GR microwaves could also be built.Comment: 25 pages, 5 figures, YA80 conference (Chapman University, 2012
The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems
There are numerous examples of morphogen gradients controlling long range signalling in developmental and cellular systems. The prospect of two such interacting morphogens instigating long range self-organisation in biological systems via a Turing bifurcation has been explored, postulated, or implicated in the context of numerous developmental processes. However, modelling investigations of cellular systems typically neglect the influence of gene expression on such dynamics, even though transcription and translation are observed to be important in morphogenetic systems. In particular, the influence of gene expression on a large class of Turing bifurcation models, namely those with pure kinetics such as the Gierer–Meinhardt system, is unexplored. Our investigations demonstrate that the behaviour of the Gierer–Meinhardt model profoundly changes on the inclusion of gene expression dynamics and is sensitive to the sub-cellular details of gene expression. Features such as concentration blow up, morphogen oscillations and radical sensitivities to the duration of gene expression are observed and, at best, severely restrict the possible parameter spaces for feasible biological behaviour. These results also indicate that the behaviour of Turing pattern formation systems on the inclusion of gene expression time delays may provide a means of distinguishing between possible forms of interaction kinetics. Finally, this study also emphasises that sub-cellular and gene expression dynamics should not be simply neglected in models of long range biological pattern formation via morphogens
Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays
Turing’s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing’s model has received limited attention. Here, we novelly focus on the Gierer–Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing’s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99–130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing’s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing’s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing’s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning
The anomalous Higgs-top couplings in the MSSM
The anomalous couplings of the top quark and the Higgs boson has been studied
in an effective theory resulting in the framework of the minimal supersymmetric
extension of the standard model (MSSM) when the heavy fields are integrated
out. Constraints on the parameters of the model from the experimental data on
the ratio are derived.Comment: Latex, 26 pages + 13 ps figures, final version in PR
Hidden Order in the Cuprates
We propose that the enigmatic pseudogap phase of cuprate superconductors is
characterized by a hidden broken symmetry of d(x^2-y^2)-type. The transition to
this state is rounded by disorder, but in the limit that the disorder is made
sufficiently small, the pseudogap crossover should reveal itself to be such a
transition. The ordered state breaks time-reversal, translational, and
rotational symmetries, but it is invariant under the combination of any two. We
discuss these ideas in the context of ten specific experimental properties of
the cuprates, and make several predictions, including the existence of an
as-yet undetected metal-metal transition under the superconducting dome.Comment: 12 pages of RevTeX, 9 eps figure
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