2,302 research outputs found
Exact ground and excited states of frustrated antiferromagnets on the CaV_4O_9 lattice
The experimental observation of a spin-gap in the antiferromagnetic spin-1/2
compound has been attributed to the formation of a plaquette
resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square
lattice. We construct a spin-1/2 model on the 1/5-depleted lattice for which
the PRVB state can be shown to be the exact ground state in a particular
parameter regime. In a subspace of this parameter regime, the first excited
state can be calculated exactly. In a different parameter regime, the dimer
state is shown to be the exact ground state.Comment: 13 pages, LaTeX, 4 figures, to appear in Phys. Rev.
Origins of Binary Gene Expression in Post-transcriptional Regulation by MicroRNAs
MicroRNA-mediated regulation of gene expression is characterised by some
distinctive features that set it apart from unregulated and transcription
factor-regulated gene expression. Recently, a mathematical model has been
proposed to describe the dynamics of post-transcriptional regulation by
microRNAs. The model explains the observations made in single cell experiments
quite well. In this paper, we introduce some additional features into the model
and consider two specific cases. In the first case, a non-cooperative positive
feedback loop is included in the transcriptional regulation of the target gene
expression. In the second case, a stochastic version of the original model is
considered in which there are random transitions between the inactive and
active expression states of the gene. In the first case we show that
bistability is possible in a parameter regime, due to the presence of a
non-linear protein decay term in the gene expression dynamics. In the second
case, we derive the conditions for obtaining stochastic binary gene expression.
We find that this type of gene expression is more favourable in the case of
regulation by microRNAs as compared to the case of unregulated gene expression.
The theoretical predictions relating to binary gene expression are
experimentally testable.Comment: 10 Pages, 5 Figure
Exact ground and excited states of a t-J ladder doped with two holes
A two chain ladder model is considered described by the strong coupling
Hamiltonian. For the case of two holes moving in a
background of antiferromagnetically interacting spins, exact, analytical
results are derived for the ground state energy and low-lying excitation
spectrum. The ground state is a bound state of two holes with total spin S=0.
The charge excitation is gapless and the spin excitation has a gap. The
corresponding wavefunctions are also exactly determined. The bound hole pair is
found to have symmetry of the d-wave type. In the limit of strong rung
coupling, the model maps onto an effective hard core boson model which exhibits
dominant superconducting pairing correlations.Comment: LaTeX, 15 pages, 5 PS figures, accepted in Journal of Physics:
Condensed Matte
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