Malthus to Solow

A unified growth theory is developed that accounts for the roughly constant living standards displayed by world economies prior to 1800 as well as the growing living standards exhibited by modern industrial economies. Our theory also explains the industrial revolution, which is the transition from an era when per capita incomes are stagnant to one with sustained growth. This transition is inevitable given positive rates of total factor productivity growth. We use a standard growth model with one good and two available technologies. The first, denoted the capital as inputs. The second, denoted the does not require land. We show that in the early stages of development, only the Malthus technology is used and, due to population growth, living standards are stagnant despite technological progress. Eventually, technological progress causes the Solow technology to become profitable and both technologies are employed. At this point, living standards improve since population growth has less influence on per capita income growth. In the limit, the economy behaves like a standard Solow growth model.

Compartmentalized PDE4A5 signaling impairs hippocampal synaptic plasticity and long-term memory

Alterations in cAMP signaling are thought to contribute to neurocognitive and neuropsychiatric disorders. Members of the cAMP-specific phosphodiesterase 4 (PDE4) family, which contains >25 different isoforms, play a key role in determining spatial cAMP degradation so as to orchestrate compartmentalized cAMP signaling in cells. Each isoform binds to a different set of protein complexes through its unique N-terminal domain, thereby leading to targeted degradation of cAMP in specific intracellular compartments. However, the functional role of specific compartmentalized PDE4 isoforms has not been examined in vivo. Here, we show that increasing protein levels of the PDE4A5 isoform in mouse hippocampal excitatory neurons impairs a long-lasting form of hippocampal synaptic plasticity and attenuates hippocampus-dependent long-term memories without affecting anxiety. In contrast, viral expression of a truncated version of PDE4A5, which lacks the unique N-terminal targeting domain, does not affect long-term memory. Further, overexpression of the PDE4A1 isoform, which targets a different subset of signalosomes, leaves memory undisturbed. Fluorescence resonance energy transfer sensor-based cAMP measurements reveal that the full-length PDE4A5, in contrast to the truncated form, hampers forskolin-mediated increases in neuronal cAMP levels. Our study indicates that the unique N-terminal localization domain of PDE4A5 is essential for the targeting of specific cAMP-dependent signaling underlying synaptic plasticity and memory. The development of compounds to disrupt the compartmentalization of individual PDE4 isoforms by targeting their unique N-terminal domains may provide a fruitful approach to prevent cognitive deficits in neuropsychiatric and neurocognitive disorders that are associated with alterations in cAMP signaling

Nature of Split Hubbard Bands at Low Densities

We present a numerical scheme for the Hubbard model that throws light on the rather esoteric nature of the Upper and Lower Hubbard bands that have been invoked often in literature. We present a self consistent solution of the ladder diagram equations for the Hubbard model, and show that these provide, at least in the limit of low densities of particles, a vivid picture of the Hubbard split bands. We also address the currently topical problem of decay of the doublon states that are measured in optical trap studies, using the ladder scheme and also by an exact two particle calculation of a relevant Greens function.Comment: 16 pages, 14 figure

Contributions to the optical linewidth of shallow donor - bound excitonic transition in ZnO

We study the donor-bound exciton optical linewidth properties of Al, Ga and In donor ensembles in single-crystal zinc oxide (ZnO). Neutral shallow donors (D$^0$) in ZnO are spin qubits with optical access via the donor-bound exciton (D$^0$X). This spin-photon interface enables applications in quantum networking, memories and transduction. Essential optical parameters which impact the spin-photon interface include radiative lifetime, optical inhomogeneous and homogeneous linewidth and optical depth. The ensemble photoluminescence linewidth ranges from 4-11 GHz, less than two orders of magnitude larger than the expected lifetime-limited linewidth. The ensemble linewidth remains narrow in absorption measurements through the 300 $\mu$m-thick sample, which has an estimated optical depth up to several hundred. Homogeneous broadening of the ensemble line due to phonons is consistent with thermal population relaxation between D$^0$X states. This thermal relaxation mechanism has negligible contribution to the total linewidth at 2 K. We find that inhomogeneous broadening due to the disordered isotopic environment in natural ZnO is significant, ranging from 1.9 GHz - 2.2 GHz. Two-laser spectral anti-hole burning measurements, which can be used to measure the homogeneous linewidth in an ensemble, however, reveal spectral anti-hole linewidths similar to the single laser ensemble linewidth. Despite this broadening, the high homogeneity, large optical depth and potential for isotope purification indicate that the optical properties of the ZnO donor-bound exciton are promising for a wide range of quantum technologies and motivate a need to improve the isotope and chemical purity of ZnO for quantum technologies.Comment: 22 pages, 12 figure