Quantum Mechanics as a Framework for Dealing with Uncertainty

Quantum uncertainty is described here in two guises: indeterminacy with its concomitant indeterminism of measurement outcomes, and fuzziness, or unsharpness. Both features were long seen as obstructions of experimental possibilities that were available in the realm of classical physics. The birth of quantum information science was due to the realization that such obstructions can be turned into powerful resources. Here we review how the utilization of quantum fuzziness makes room for a notion of approximate joint measurement of noncommuting observables. We also show how from a classical perspective quantum uncertainty is due to a limitation of measurability reflected in a fuzzy event structure -- all quantum events are fundamentally unsharp.Comment: Plenary Lecture, Central European Workshop on Quantum Optics, Turku 2009

The kinetic glass transition of the Zr46.75Ti8.25Cu7.5Ni10Be27.5 bulk metallic glass former-supercooled liquids on a long time scale

Viscosity and enthalpy relaxation from the amorphous state into the supercooled liquid state was investigated in the bulk metallic glass forming Zr46.75Ti8.25Cu7.5Ni10Be27.5 alloy below the calorimetric glass transition. At different temperatures, the viscosities relax into states that obey the same Vogel–Fulcher–Tammann relation as the data obtained at higher temperatures in the supercooled liquid. Enthalpy recovery experiments after relaxation in the same temperature range show that the enthalpy of the material reaches values that also corresponds to the supercooled liquid state. The glass relaxes into a metastable supercooled liquid state, if it is observed on a long time scale. Equilibration is possible far below the calorimetric glass transition and very likely even below the isentropic temperature

Thermodynamics and kinetics of the Mg65Cu25Y10 bulk metallic glass forming liquid

The thermodynamics and kinetics of the bulk metallic glass forming Mg65Cu25Y10 liquid were investigated using differential scanning calorimetry and three-point beam bending. The experiments lead to the determination of the thermodynamic functions as well as the viscosity of the supercooled liquid. The viscosity shows a temperature dependence, which is consistent with that of a strong glass similar to Zr–Ti–Cu–Ni–Be bulk metallic glasses or sodium silicate glasses. This contrasts with more fragile conventional metallic glass formers or pure metals. The relatively weak temperature dependence of the thermodynamic functions of the supercooled liquid is related to these sluggish kinetics in the supercooled liquid. Entropy, viscosity, and kinetic glass transition are compared in the frameworks of the fragility concept and the Adam–Gibbs theory. Strong liquid behavior retards the formation of crystals kinetically and thermodynamically

Crystallization kinetics of the bulk-glass-forming Pd43Ni10Cu27P20 melt

The crystallization of undercooled Pd43Ni10Cu27P20 melts is studied under isothermal conditions and at constant heating and cooling rates. Investigations are carried out by fluxing the melt with B2O3 and without any fluxing material. The isothermal experiments allow us to determine the complete time–temperature-transformation diagram with a minimum crystallization time of about 200 s for the fluxed melt and about 130 s for the unfluxed Pd43Ni10Cu27P20 melt. The results of the experiments at constant cooling and heating rates are summarized in a continuous heating and cooling diagram. The critical cooling rate for the fluxed alloy is determined to be 0.09 K/s, whereas the critical heating rate is 6 K/s. For the unfluxed Pd43Ni10 Cu27P20, 0.4 and 9 K/s are found, respectively. This alloy exhibits the most sluggish crystallization kinetics of all metallic systems known so far

Change of Compressiblity at the Glass Transition and Prigogine-Defay Ratio in ZrTiCuNiBe Alloys

The change of the compressibility at the glass transition Tg is evaluated from pressure experiments in the liquid and the glassy state of the ZrTiCuNiBe bulk metallic glass forming system. Via the enthalpy recovery method, we derive an increase of Tg with pressure of 3.6 K/GPa. Comparing the changes of the compressibility, the specific heat capacity, and the thermal expansion coefficient at Tg, we estimate for the first time a Prigogine-Defay ratio in metallic systems. This ratio is about 2.4 for the present alloy and compares well with known nonmetallic glass forming systems

Repeated crystallization in undercooled Zr41Ti14Cu12Ni10Be23 liquids

Isothermal crystallization studies are performed on Zr41Ti14Cu12Ni10Be23 melts. Undercooling experiments are carried out repeatedly at 907, 860, and 750 K. The scattering of the time to reach the onset of crystallization is investigated. Results from experiments performed at 907 K show a large scatter of the onset time of crystallization. For the experiments carried out at 860 and 750 K, scattering of the onset time is two orders of magnitude smaller. These results indicate that, at high temperatures, the crystallization is governed by the time scale of the statistical nucleation events. At low temperatures, the crystallization is controlled by diffusion, resulting in a well-defined onset time for crystallization

Power and Inefficient Institutions

This paper is concerned with the persistence of inefficient institutions. Why are they not replaced by more effcient ones? What and/or who prevents such change? We provide an answer to these questions based on two key ideas. The principal idea is that institutional change on an issue may adversely affect the bargaining power of some agents on different issues. The second is that certain kinds of frictions (or transaction costs) are present, which do not allow for this deteriorating bargaining power to be compensated for. A key insight obtained from our analysis is that, the greater is the degree of inequality in the players� bargaining powers the more likely it is that ineffcient institutions will persist.

Thermodynamics and kinetics of the undercooled liquid and the glass transition of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy

Differential scanning calorimetry (DSC) was used to determine the thermodynamic functions of the undercooled liquid and the amorphous phase with respect to the crystalline state of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5bulk metallic glass forming alloy. The specific heat capacities of this alloy in the undercooled liquid, the amorphous state and the crystal were determined. The differences in enthalpy, ∆H, entropy, ∆S, and Gibbs free energy, ∆G, between crystal and the undercooled liquid were calculated using the measured specific heat capacity data as well as the heat of fusion. The results indicate that the Gibbs free energy difference between metastable undercooled liquid and crystalline solid, ∆G, stays small compared to conventional metallic glass forming alloys even for large undercoolings. Furthermore, the Kauzmann temperature, TK, where the entropy of the undercooled liquid equals to that of the crystal, was determined to be 560 K. The Kauzmann temperature is compared with the experimentally observed rate-dependent glass transition temperature, Tg. Both onset and end temperatures of the glass transition depend linearly on the logarithm of the heating rate based on the DSC experiments. Those characteristic temperatures for the kinetically observed glass transition become equal close to the Kauzmann temperature in this alloy, which suggests an underlying thermodynamic glass transition as a lower bound for the kinetically observed freezing process

The effect of silicon on the glass forming ability of the Cu47Ti34Zr11Ni8 bulk metallic glass forming alloy during processing of composites

Composites of the Cu47Ti34Zr11Ni8 bulk metallic glass, reinforced with up to 30 vol % SiC particles are synthesized and characterized. Results based on x-ray diffraction, optical microscopy, scanning Auger microscopy, and differential scanning calorimetry (DSC) are presented. During processing of the composites, a TiC layer forms around the SiC particles and Si diffuses into the Cu47Ti34Zr11Ni8 matrix stabilizing the supercooled liquid against crystallization. The small Si addition between 0.5 and 1 at. % increases the attainable maximum thickness of glassy ingots from 4 mm for Cu–Ti–Zr–Ni alloys to 7 mm for Cu–Ti–Zr–Ni–Si alloys. DSC analyses show that neither the thermodynamics nor the kinetics of the alloy are affected significantly by the Si addition. This suggests that Si enhances the glass forming ability by chemically passivating impurities such as oxygen and carbon that cause heterogeneous nucleation in the melt