Spin & Statistics in Nonrelativistic Quantum Mechanics, I

A necessary and sufficient condition for Pauli's spin-statistics relation is given for nonrelativistic anyons, bosons, and fermions in two and three spatial dimensions. For any point particle species in two spatial dimensions, denote by J the total (i.e., spin plus orbital) angular momentum of a single particle, and denote by j the total angular momentum of the corresponding two-particle system with respect to its center of mass. In three spatial dimensions, write J_z and j_z for the z-components of these vector operators. In two spatial dimensions, the spin statistics connection holds if and only if there exists a unitary operator U such that j=2UJU^*. In three dimensions, the analogous relation cannot hold as it stands, but restricting it to an appropriately chosen subspace of the state space yields a sufficient and necessary condition for the spin-statistics connection.Comment: 15 pages, revised and polished versio

Quantum ballistic transport in in-plane-gate transistors showing onset of a novel ferromagnetic phase transition

We study one-dimensional transport in focused-ion-beam written in-plane-gate transistors on III-V heterostructures at moderately low temperatures at zero bias without any external magnetic field applied. In accordance with a recent proposal of A. Gold and L. Calmels, Valley- and spin-occupancy instability in the quasi-one-dimensional electron gas, Phil. Mag. Lett. 74, 33-42 (1996) and earlier experimental data, we observe plateaux in the source-drain conductivity considered as a function of the gate voltage, not only at multliples of 2e^2/h but also clearly at e^2/h, just before the channel closes to zero conductivity. This may be interpreted as a many electron effect, namely as a novel ballistic ferromagnetic ground state evading standard descriptions and theorems.Comment: 19 pages, 9 figures, 22 reference

Parity and the Spin-Statistics Connection

The spin-statistics connection is obtained in a simple and elementary way for general causal fields by using the parity operation to exchange spatial coordinates in the scalar product of a locally commuting field operator, evaluated at position x, with the same field operator evaluated at -x, at equal times.Comment: 6 page

Endogenous life expectancy and R&D-based economic growth

We propose an overlapping generations framework in which life expectancyis determined endogenously by governmental health investments. As a nov-elty, we are able to examine the feedback effects between life expectancy andR&D-driven economic growth for the transitional dynamics. We find that i)higher survival induces economic growth through higher savings and higherlabor force participation; ii) longevity-induced reductions in fertility hampereconomic development; iii) the positive life expectancy effects of larger savingsand higher labor force participation outweigh the negative effect of a reductionin fertility, and iv) there exists a growth-maximizing size of the health caresector that might lie beyond what is observed in most countries. Altogether,the results support a rather optimistic view on the relationship between lifeexpectancy and economic growth and contribute to the debate surroundingrising health shares and economic development

Essays on demographic change and R&D-based economic growth

This dissertation analyzes the economic growth effects of demographic change embedded in a framework of endogenous R&D. Substantial changes in fertility and longevity are the two main demographic features that all industrialized countries have experienced during the twentieth century and are still experiencing until today. Although the individual gains of higher life expectancy and better education, initiated by a quantity-quality tradeoff, are huge, there exist concerns about the macroeconomic effects. To improve the understanding about the aforementioned relationships, this work extends the existing literature on the growth effects of population aging by 1) introducing exogenous longevity into a growth framework with vertical innovations; 2) by endogenizing life expectancy in a growth framework with horizontal innovations; and 3) by examining the growth effects of basic scientific knowledge over the very long run. Chapter two contains the first paper titled Longevity-induced Vertical Innovation and the Tradeoff Between Life and Growth, which is joint work with Annarita Baldanzi and Klaus Prettner. In this paper, the positive effect of a longer retirement period on individual savings is utilized. A higher exogenous probability to survive to old age raises savings, placing a downward pressure on the market interest rate. On the production side, a lower interest rate increases the present value of holding a patent, which, in turn, makes R&D more profitable. As a result, R&D employment increases, leading to a higher frequency of quality improving ideas and, with it, faster economic growth. It is shown that the relationship between life expectancy and economic growth is strictly positive. In a welfare analysis, the utility gains of living longer are disentangled from the longevity-induced utility gains of higher consumption. The analysis concludes that the direct welfare gains of higher life expectancy, usually, outweigh the indirect welfare gains of faster economic growth. Chapter three contains a single-authored paper and is titled Endogenous Life Expectancy and R&D-based Economic Growth. As the title suggests, life expectancy is endogenized and increases in the public resources devoted toward health. Again, the longevity-saving-channel is present. Additionally, a quantity-quality tradeoff is introduced, such that parents have to decide on the number of children to have and on the childrens level of education. Besides the positive saving effect, life expectancy impacts positively on the labor force participation rate and negatively on the fertility rate. The reason is that adults need to work more (at the expense of having fewer children), to compensate for a prolonged retirement period. The feedback effects with production, characterized by horizontal innovation, are then analyzed in a calibrated version of the model. Using U.S. data, the model suggests that the overall effect of life expectancy on economic growth is positive and amounts to 11.9 % of the increases in the real GDP p.c. over the period 1960-2017. From a welfare perspective, the results indicate that the growth-maximizing size of the health care sector might lie beyond what is observed in most industrialized countries, nowadays. The finding that the size of the health care sector that maximizes life expectancy is substantially larger than the growth-maximizing size supports the view to not only consider the growth effects of health care. Chapter four contains the third paper which is co-authored with Klaus Prettner and is titled The Scientific Revolution and Its Role in the Transition to Sustained Economic Growth. Basic scientific knowledge is introduced as a necessary input in applied R&D and increases in the number of tinkerers in the economy and in their education. For low levels of development, fertility is high and educational investments are zero. Once income surpasses a certain threshold, education turns positive. Together with the consequent fertility transition, this marks the takeoff to sustained economic growth. It is shown that the growth rate of as well as the access to basic scientific knowledge is crucial in determining the timing and the magnitude of the takeoff. For low growth rates and low access, the takeoff is delayed by up to one generation because applied R&D takes longer to become profitable. In the extreme case of zero basic scientific knowledge, no takeoff might occur at all. The results improve the understanding of economic growth processes over the very long run and provide one possible explanation why some regions experienced the takeoff to sustained economic growth earlier than others.Diese Dissertation analysiert die ökonomischen Wachstumseffekte des demographischen Wandels im Rahmen endogener Wachstumsmodelle. Substantielle Veränderungen der Fertilität und der Lebenserwartung sind die beiden demographischen Hauptmerkmale, welche alle Industrieländer charakterisieren. Obwohl die individuellen Gewinne aufgrund gestiegener Lebenserwartung und besserer Bildung substantiell sind, bestehen Bedenken hinsichtlich der makroökonomischen Auswirkungen. Um das Verständnis hierüber zu verbessern, erweitert diese Dissertation die bestehende Literatur, indem sie 1) eine exogene Überlebenswahrscheinlichkeit in ein Wachstumsmodell mit vertikalen Innovationen integriert; 2) die Lebenserwartung in einem Wachstumsmodell mit horizontalen Innovationen endogenisiert; und 3) die Wachstumseffekte von Grundlagenforschung innerhalb eines Unified Growth Modells untersucht. Kapitel zwei enthält das erste Papier mit dem Titel "Longevity-induced Vertical Innovation and the Tradeoff between Life and Growth", welches gemeinsam mit Annarita Baldanzi und Klaus Prettner verfasst wurde. In diesem Papier wird der positive Effekt einer steigenden Lebenserwartung auf die individuelle Ersparnisbildung verwendet. Eine höhere exogene Wahrscheinlichkeit, bis ins Rentenalter zu überleben, erhöht die Ersparnisbildung und senkt somit den Marktzins. Auf Produktionsseite erhöht ein niedrigerer Zinssatz den Gegenwartswert eines Patents, was wiederum Forschung profitabler macht. Infolgedessen steigt die Anzahl an Wissenschaftlern, was zu einer höheren Frequenz von qualitätsverbessernden Patenten und somit zu höherem Wirtschaftswachstum führt. Es wird analytisch gezeigt, dass die Beziehung zwischen Lebenserwartung und Wirtschaftswachstum strikt positiv ist. In einer Wohlfahrtsanalyse wird zudem zwischen dem Nutzengewinn eines längeren Lebens und dem Nutzengewinn durch höheren Konsum differenziert. Die Analyse zeigt, dass die direkten Wohlfahrtsgewinne einer höheren Lebenserwartung in der Regel die indirekten Wohlfahrtsgewinne schnelleren Wirtschaftswachstums übersteigen. Kapitel drei enthält das zweite Papier mit dem Titel "Endogenous Life-Expectancy and R&D-based Economic Growth". Die Lebenserwartung wird endogenisiert, indem staatliche Gesundheitsinvestitionen die Überlebenswahrscheinlichkeit erhöhen. Zusätzlich zur individuellen Ersparnisbildung entscheiden Eltern über die Anzahl der Kinder und deren Bildungsgrad. Neben dem Spareffekt wirkt sich die Lebenserwartung positiv auf die Erwerbsquote und negativ auf die Fertilitätsrate aus. Der Grund hierfür ist, dass Arbeitnehmer mehr arbeiten müssen (auf Kosten von weniger Kindern), um eine längere Rentenzeit zu finanzieren. Die Rückkopplungseffekte mit der Produktionsseite werden in einer kalibrierten Version des Modells analysiert. Unter Verwendung von U.S.-Daten legen die Ergebnisse nahe, dass der Gesamteffekt der Lebenserwartung für das Wirtschaftswachstum positiv ist und 11,9 % der Steigerungen des realen BIP p.c. im Zeitraum 1960-2017 ausgemacht hat. Aus Wohlfahrtsperspektive deuten die Ergebnisse darauf hin, dass die Größe des Gesundheitssektors in den meisten Industrieländern unter der wachstumsmaximierenden Größe liegt. Die Feststellung, dass die Größe des Gesundheitssektors, der die Lebenserwartung maximiert, wesentlich größer ist als die wachstumsmaximierende Größe, unterstützt die Ansicht, nicht nur die Wachstumseffekte von Gesundheit zu berücksichtigen. Kapitel vier enthält das dritte Papier, welches gemeinsam mit Klaus Prettner verfasst wurde und den Titel The Scientific Revolution and Its Role in the Transition to Sustained Economic Growth trägt. Wissenschaftliches Grundlagenwissen wird als notwendiger Input für angewandte Forschung integriert und wächst in Abhängigkeit von der Bevölkerungsgröße und den Bildungsinvestitionen. Für einen niedrigen ökonomischen Entwicklungsgrad ist die Fertilität hoch und es gibt keine Bildungsinvestitionen. Sobald das Einkommen einen bestimmten Schwellenwert überschreitet, werden Bildungsinvestitionen positiv. Zusammen mit dem dadurch initiierten Fertilitätsübergang markiert dies den Beginn der Phase anhaltenden Wirtschaftswachstums. Es wird gezeigt, dass die Wachstumsrate von sowie der Zugang zu grundlegenden wissenschaftlichen Kenntnissen entscheidend für den Zeitpunkt und das Ausmaß des ökonomischen Takeoffs sind. Für niedrige Wachstumsraten und einen reduzierten Zugang zu Grundlagenforschung verzögert sich der Takeoff um eine Generation, da angewandte Forschung erst später profitabel wird. Für den Fall, dass gar keine Grundlagenforschung verfügbar ist, stagniert die Ökonomie für immer. Diese Ergebnisse verbessern das Verständnis über langfristige ökonomische Wachstumsprozesse und liefern eine mögliche Erklärung, weshalb einige Regionen den Takeoff zu anhaltendem Wirtschaftswachstum früher als andere erlebt haben

Endogenous life expectancy and R&D-based economic growth

We propose an overlapping generations framework in which life expectancyis determined endogenously by governmental health investments. As a nov-elty, we are able to examine the feedback effects between life expectancy andR&D-driven economic growth for the transitional dynamics. We find that i)higher survival induces economic growth through higher savings and higherlabor force participation; ii) longevity-induced reductions in fertility hampereconomic development; iii) the positive life expectancy effects of larger savingsand higher labor force participation outweigh the negative effect of a reductionin fertility, and iv) there exists a growth-maximizing size of the health caresector that might lie beyond what is observed in most countries. Altogether,the results support a rather optimistic view on the relationship between lifeexpectancy and economic growth and contribute to the debate surroundingrising health shares and economic development

Density functional electronic spectrum of the CuO−6−10Cu O_{-6}^{-10} cluster and possible local Jahn-Teller distorsions in the La-Ba-Cu-O superconductor

We present a density functional theory (DFT) calculation in the generalized gradient approximation to study the possibility for the existence of Jahn-Teller (JT) or pseudo Jahn-Teller (PJT) type local distortions in the La-Ba-Cu-O superconducting system. We performed the calculation and correspondingly group theory classification of the electronic ground state of the CuO${_{6}}^{-10}$ elongated octahedra cluster, immersed in a background simulating the superconductor. Part of the motivation to do this study is that the origin of the apical deformation of the CuO${_{6}}^{-10}$ cluster is not due to a pure JT effect, having therefore a non {\it a priori} condition to remove the degeneracy of the electronic ground state of the parent regular octahedron. We present a comparative analysis of the symmetry classified electron spectrum with previously reported results using unrestricted Hartree-Fock calculations (UHF). Both the DFT and UHF calculations produced a non degenerate electronic ground state, not having therefore the necessary condition for a pure JT effect. However, the appearance of a degenerate E$_{g}$ state near to the highest occupied molecular orbital in the DFT calculation, suggests the possibility for a PJT effect responsible for a local distortion of the oxidized CuO$_{6}^{-9}$ cluster.Comment: 12 pages, 3 figures, submitted to International Journal of Modern Physics B (IJMPB

Bias and temperature dependence of the 0.7 conductance anomaly in Quantum Point Contacts

The 0.7 (2e^2/h) conductance anomaly is studied in strongly confined, etched GaAs/GaAlAs quantum point contacts, by measuring the differential conductance as a function of source-drain and gate bias as well as a function of temperature. We investigate in detail how, for a given gate voltage, the differential conductance depends on the finite bias voltage and find a so-called self-gating effect, which we correct for. The 0.7 anomaly at zero bias is found to evolve smoothly into a conductance plateau at 0.85 (2e^2/h) at finite bias. Varying the gate voltage the transition between the 1.0 and the 0.85 (2e^2/h) plateaus occurs for definite bias voltages, which defines a gate voltage dependent energy difference $\Delta$. This energy difference is compared with the activation temperature T_a extracted from the experimentally observed activated behavior of the 0.7 anomaly at low bias. We find \Delta = k_B T_a which lends support to the idea that the conductance anomaly is due to transmission through two conduction channels, of which the one with its subband edge \Delta below the chemical potential becomes thermally depopulated as the temperature is increased.Comment: 9 pages (RevTex) with 9 figures (some in low resolution

Unusual Thermodynamics on the Fuzzy 2-Sphere

Higher spin Dirac operators on both the continuum sphere($S^2$) and its fuzzy analog($S^2_F$) come paired with anticommuting chirality operators. A consequence of this is seen in the fermion-like spectrum of these operators which is especially true even for the case of integer-spin Dirac operators. Motivated by this feature of the spectrum of a spin 1 Dirac operator on $S_F^2$, we assume the spin 1 particles obey Fermi-Dirac statistics. This choice is inspite of the lack of a well defined spin-statistics relation on a compact surface such as $S^2$. The specific heats are computed in the cases of the spin $\frac{1}{2}$ and spin 1 Dirac operators. Remarkably the specific heat for a system of spin $\frac{1}{2}$ particles is more than that of the spin 1 case, though the number of degrees of freedom is more in the case of spin 1 particles. The reason for this is inferred through a study of the spectrums of the Dirac operators in both the cases. The zero modes of the spin 1 Dirac operator is studied as a function of the cut-off angular momentum $L$ and is found to follow a simple power law. This number is such that the number of states with positive energy for the spin 1 and spin $\frac{1}{2}$ system become comparable. Remarks are made about the spectrums of higher spin Dirac operators as well through a study of their zero-modes and the variation of their spectrum with degeneracy. The mean energy as a function of temperature is studied in both the spin $\frac{1}{2}$ and spin 1 cases. They are found to deviate from the standard ideal gas law in 2+1 dimensions.Comment: 19 pages, 7 figures. The paper has been significantly modified. Main results are unchange