336 research outputs found
Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms
We exhibit scarring for certain nonlinear ergodic toral automorphisms. There
are perturbed quantized hyperbolic toral automorphisms preserving certain
co-isotropic submanifolds. The classical dynamics is ergodic, hence in the
semiclassical limit almost all eigenstates converge to the volume measure of
the torus. Nevertheless, we show that for each of the invariant submanifolds,
there are also eigenstates which localize and converge to the volume measure of
the corresponding submanifold.Comment: 17 page
Solitonic excitations in the Haldane phase of a S=1 chain
We study low-lying excitations in the 1D antiferromagnetic
valence-bond-solid (VBS) model. In a numerical calculation on finite systems
the lowest excitations are found to form a discrete triplet branch, separated
from the higher-lying continuum. The dispersion of these triplet excitations
can be satisfactorily reproduced by assuming approximate wave functions. These
wave functions are shown to correspond to moving hidden domain walls, i.e. to
one-soliton excitations.Comment: RevTex 3.0, 24 pages, 2 figures on request by fax or mai
Quantum spin models with exact dimer ground states
Inspired by the exact solution of the Majumdar-Ghosh model, a family of
one-dimensional, translationally invariant spin hamiltonians is constructed.
The exchange coupling in these models is antiferromagnetic, and decreases
linearly with the separation between the spins. The coupling becomes
identically zero beyond a certain distance. It is rigorously proved that the
dimer configuration is an exact, superstable ground state configuration of all
the members of the family on a periodic chain. The ground state is two-fold
degenerate, and there exists an energy gap above the ground state. The
Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just
the first member of the family.
The scheme of construction is generalized to two and three dimensions, and
illustrated with the help of some concrete examples. The first member in two
dimensions is the Shastry-Sutherland model. Many of these models have
exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.
On the multiplicativity of quantum cat maps
The quantum mechanical propagators of the linear automorphisms of the
two-torus (cat maps) determine a projective unitary representation of the theta
group, known as Weil's representation. We prove that there exists an
appropriate choice of phases in the propagators that defines a proper
representation of the theta group. We also give explicit formulae for the
propagators in this representation.Comment: Revised version: proof of the main theorem simplified. 21 page
Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation
A generalized approach to the quantization of a large class of maps on a
torus, i.e. quantization via the von Neumann Equation, is described and a
number of issues related to the quantization of model systems are discussed.
The approach yields well behaved mixed quantum states for tori for which the
corresponding Schrodinger equation has no solutions, as well as an extended
spectrum for tori where the Schrodinger equation can be solved.
Quantum-classical correspondence is demonstrated for the class of mappings
considered, with the Wigner-Weyl density going to the correct
classical limit. An application to the cat map yields, in a direct manner,
nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the
correspondence limit.Comment: 36 pages, RevTex preprint forma
Analysis of Clock-Regulated Genes in Neurospora Reveals Widespread Posttranscriptional Control of Metabolic Potential
Neurospora crassa has been for decades a principal model for filamentous fungal genetics and physiology as well as for understanding the mechanism of circadian clocks. Eukaryotic fungal and animal clocks comprise transcription-translation-based feedback loops that control rhythmic transcription of a substantial fraction of these transcriptomes, yielding the changes in protein abundance that mediate circadian regulation of physiology and metabolism: Understanding circadian control of gene expression is key to understanding eukaryotic, including fungal, physiology. Indeed, the isolation of clock-controlled genes (ccgs) was pioneered in Neurospora where circadian output begins with binding of the core circadian transcription factor WCC to a subset of ccg promoters, including those of many transcription factors. High temporal resolution (2-h) sampling over 48 h using RNA sequencing (RNA-Seq) identified circadianly expressed genes in Neurospora, revealing that from ∼10% to as much 40% of the transcriptome can be expressed under circadian control. Functional classifications of these genes revealed strong enrichment in pathways involving metabolism, protein synthesis, and stress responses; in broad terms, daytime metabolic potential favors catabolism, energy production, and precursor assembly, whereas night activities favor biosynthesis of cellular components and growth. Discriminative regular expression motif elicitation (DREME) identified key promoter motifs highly correlated with the temporal regulation of ccgs. Correlations between ccg abundance from RNA-Seq, the degree of ccg-promoter activation as reported by ccg-promoter-luciferase fusions, and binding of WCC as measured by ChIP-Seq, are not strong. Therefore, although circadian activation is critical to ccg rhythmicity, posttranscriptional regulation plays a major role in determining rhythmicity at the mRNA level
Apoptosis and proliferation in the trigeminal placode
The neurogenic trigeminal placode develops from the crescent-shaped panplacodal primordium which delineates the neural plate anteriorly. We show that, in Tupaia belangeri, the trigeminal placode is represented by a field of focal ectodermal thickenings which over time changes positions from as far rostral as the level of the forebrain to as far caudal as opposite rhombomere 3. Delamination proceeds rostrocaudally from the ectoderm adjacent to the rostral midbrain, and contributes neurons to the trigeminal ganglion as well as to the ciliary ganglion/oculomotor complex. Proliferative events are centered on the field prior to the peak of delamination. They are preceded, paralleled and, finally, outnumbered by apoptotic events which proceed rostrocaudally from non-delaminating to delaminating parts of the field. Apoptosis persists upon regression of the placode, thereby exhibiting a massive “wedge” of apoptotic cells which includes the postulated position of the “ventrolateral postoptic placode” (Lee et al. in Dev Biol 263:176–190, 2003), merges with groups of lens-associated apoptotic cells, and disappears upon lens detachment. In conjunction with earlier work (Washausen et al. in Dev Biol 278:86–102, 2005) our findings suggest that apoptosis contributes repeatedly to the disintegration of the panplacodal primordium, to the elimination of subsets of premigratory placodal neuroblasts, and to the regression of placodes
Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map
We rationalize the somewhat surprising efficacy of the Hadamard transform in
simplifying the eigenstates of the quantum baker's map, a paradigmatic model of
quantum chaos. This allows us to construct closely related, but new, transforms
that do significantly better, thus nearly solving for many states of the
quantum baker's map. These new transforms, which combine the standard Fourier
and Hadamard transforms in an interesting manner, are constructed from
eigenvectors of the shift permutation operator that are also simultaneous
eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal)
symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title;
corrected minor error
Excitation Spectrum of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain:
The natural explanation of the excitation spectrum of the spin-1
antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2
ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy
spectrum of the latter is calculated with fixed momentum by numerical
diagonalization of finite size systems. It consists of a branch of propagating
triplet pair (triplet wave) and the continuum of multiple triplet waves for
weak ferromagnetic coupling. As the ferromagnetic coupling increases, the
triplet wave branch is absorbed in the continuum for small , reproducing the
characteristics of the spin-1 antiferromagnetic Heisenberg chain.Comment: 12 Pages REVTEX, Postscript file for the figures included.
SKPH-94-C00
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