Different Clusters of Text from Ancient China, Different Mathematical Ontologies

Sources attesting to mathematical activities in ancient China form at least four distinct clusters of texts, bespeaking at least four different—though overlapping—ways of practicing mathematics. I will focus on two such sets of documents: the canons that in the seventh century constituted one of the two curricula taught in the Imperial “School of Mathematics,” and manuscripts recently excavated from tombs sealed in the last centuries BCE. I will argue that these two sets of documents testify to two different ways of practicing mathematics, which related to different material practices. Accordingly, we can perceive that mathematical objects were shaped and explored in different ways, with significant consequences for the knowledge produced

Ultrafast Enhancement of Ferromagnetism via Photoexcited Holes in GaMnAs

We report on the observation of ultrafast photo-enhanced ferromagnetism in GaMnAs. It is manifested as a transient magnetization increase on a 100-ps time scale, after an initial sub-ps demagnetization. The dynamic magnetization enhancement exhibits a maximum below the Curie temperature Tc and dominates the demagnetization component when approaching Tc. We attribute the observed ultrafast collective ordering to the p-d exchange interaction between photoexcited holes and Mn spins, leading to a correlation-induced peak around 20K and a transient increase in Tc.Comment: 4 page

Observation of inter-Landau-level quantum coherence in semiconductor quantum wells

Using three-pulse four-wave-mixing femtosecond spectroscopy, we excite a non-radiative coherence between the discrete Landau levels of an undoped quantum well and study its dynamics. We observe quantum beats that reflect the time evolution of the coherence between the two lowest Landau level magnetoexcitons. We interpret our observations using a many-body theory and find that the inter Landau level coherence decays with a new time constant, substantially longer than the corresponding interband magnetoexciton dephasing times. Our results indicate a new intraband excitation dynamics that cannot be described in terms of uncorrelated interband excitations.Comment: 5 pages, 5 figures, to appear in Phys. Rev. B Rapid Communication

Ultrafast dynamics of coherences in the quantum Hall system

Using three-pulse four-wave-mixing optical spectroscopy, we study the ultrafast dynamics of the quantum Hall system. We observe striking differences as compared to an undoped system, where the 2D electron gas is absent. In particular, we observe a large off-resonant signal with strong oscillations. Using a microscopic theory, we show that these are due to many-particle coherences created by interactions between photoexcited carriers and collective excitations of the 2D electron gas. We extract quantitative information about the dephasing and interference of these coherences.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Let

Photonic crystals of coated metallic spheres

It is shown that simple face-centered-cubic (fcc) structures of both metallic and coated metallic spheres are ideal candidates to achieve a tunable complete photonic bandgap (CPBG) for optical wavelengths using currently available experimental techniques. For coated microspheres with the coating width to plasma wavelength ratio $l_c/\lambda_p \leq 10$ and the coating and host refractive indices $n_c$ and $n_h$, respectively, between 1 and 1.47, one can always find a sphere radius $r_s$ such that the relative gap width $g_w$ (gap width to the midgap frequency ratio) is larger than 5% and, in some cases, $g_w$ can exceed 9%. Using different coatings and supporting liquids, the width and midgap frequency of a CPBG can be tuned considerably.Comment: 14 pages, plain latex, 3 ps figures, to appear in Europhys. Lett. For more info on this subject see http://www.amolf.nl/research/photonic_materials_theory/moroz/moroz.htm

Photocarrier relaxation in the quantum kinetics regime

We present a study of carrier relaxation in GaAs in the quantum- kinetics regime. The results cannot be explained by Bolzmann kinetics. They are in satisfactory agreement with quantum-kinetic theory calculation of the occupation number in k-space

Proportional Relations Between Systolic, Diastolic and Mean Pulmonary Artery Pressure are Explained by Vascular Properties

Recently, it was shown that proportional relationships exist between systolic, diastolic and mean pulmonary artery pressure (Psys, Pdia and Pmean) and that they are maintained under various conditions in both health and disease. An arterial-ventricular interaction model was used to study the contribution of model parameters to the ratios Psys/Pmean, and Pdia/Pmean. The heart was modeled by a time-varying elastance function, and the arterial system by a three-element windkessel model consisting of peripheral resistance, Rp, arterial compliance Ca, and pulmonary artery characteristic impedance Z0. Baseline model parameters were estimated in control subjects and compared to values estimated in patients with pulmonary hypertension. Results indicate that experimentally derived ratios Psys/Pmean and Pdia/Pmean could be accurately reproduced using our model (1.59 and 0.61 vs. 1.55 and 0.64, respectively). Sensitivity analysis showed that the (empirical) constancy of Psys/Pmean and Pdia/Pmean was primarily based on the inverse hyperbolic relation between total vascular resistance (RT; calculated as Rp + Z0) and Ca, (i.e. constant RTCa product). Of the cardiac parameters, only heart rate affected the pressure ratios, but the contribution was small. Therefore, we conclude that proportional relations between systolic, diastolic and mean pulmonary artery pressure result from the constancy of RTCa thus from pulmonary arterial properties, with only little influence of heart rate

Theory of exciton-exciton correlation in nonlinear optical response

We present a systematic theory of Coulomb interaction effects in the nonlinear optical processes in semiconductors using a perturbation series in the exciting laser field. The third-order dynamical response consists of phase-space filling correction, mean-field exciton-exciton interaction, and two-exciton correlation effects expressed as a force-force correlation function. The theory provides a unified description of effects of bound and unbound biexcitons, including memory-effects beyond the Markovian approximation. Approximations for the correlation function are presented.Comment: RevTex, 35 pages, 10 PostScript figs, shorter version submitted to Physical Review

Giant Superfluorescent Bursts from a Semiconductor Magnetoplasma

Currently, considerable resurgent interest exists in the concept of superradiance (SR), i.e., accelerated relaxation of excited dipoles due to cooperative spontaneous emission, first proposed by Dicke in 1954. Recent authors have discussed SR in diverse contexts, including cavity quantum electrodynamics, quantum phase transitions, and plasmonics. At the heart of these various experiments lies the coherent coupling of constituent particles to each other via their radiation field that cooperatively governs the dynamics of the whole system. In the most exciting form of SR, called superfluorescence (SF), macroscopic coherence spontaneously builds up out of an initially incoherent ensemble of excited dipoles and then decays abruptly. Here, we demonstrate the emergence of this photon-mediated, cooperative, many-body state in a very unlikely system: an ultradense electron-hole plasma in a semiconductor. We observe intense, delayed pulses, or bursts, of coherent radiation from highly photo-excited semiconductor quantum wells with a concomitant sudden decrease in population from total inversion to zero. Unlike previously reported SF in atomic and molecular systems that occur on nanosecond time scales, these intense SF bursts have picosecond pulse-widths and are delayed in time by tens of picoseconds with respect to the excitation pulse. They appear only at sufficiently high excitation powers and magnetic fields and sufficiently low temperatures - where various interactions causing decoherence are suppressed. We present theoretical simulations based on the relaxation and recombination dynamics of ultrahigh-density electron-hole pairs in a quantizing magnetic field, which successfully capture the salient features of the experimental observations.Comment: 21 pages, 4 figure