Quantaloids Describing Causation and Propagation of Physical Properties

A general principle of causal duality for physical systems, lying at the base of representation theorems for both compound and evolving systems, is proved; formally it is encoded in a quantaloidal setting. Other particular examples of quantaloids and quantaloidal morphisms appear naturally within this setting; as in the case of causal duality, they originate from primitive physical reasonings on the lattices of properties of physical systems. Furthermore, an essentially dynamical operational foundation for studying physical systems is outlined; complementary as it is to the existing static operational foundation, it leads to the natural axiomatization of causal duality in operational quantum logic.     

Thermodynamic and critical properties of an antiferromagnetically stacked triangular Ising antiferromagnet in a field

We study a stacked triangular lattice Ising model with both intra- and inter-plane antiferromagnetic interactions in a field, by Monte Carlo simulation. We find only one phase transition from a paramagnetic to a partially disordered phase, which is of second order and 3D XY universality class. At low temperatures we identify two highly degenerate phases: at smaller (larger) fields the system shows long-range ordering in the stacking direction (within planes) but not in the planes (stacking direction). Nevertheless, crossovers to these phases do not have a character of conventional phase transitions but rather linear-chain-like excitations.     

Hearing loss from interrupted, intermittent, and time varying Gaussian noise exposures: the applicability of the equal energy hypothesis

Eight groups of chinchillas (N=74) were exposed to various equivalent energy [100 or 106 dB(A) sound pressure level (SPL)] noise exposure paradigms. Six groups received an interrupted, intermittent, time varying (IITV) Gaussian noise exposure that lasted 8 h/d, 5 d/week for 3 weeks. The exposures modeled an idealized workweek. At each level, three different temporal patterns of Gaussian IITV noise were used. The 100 dB(A) IITV exposure had a dB range of 90-108 dB SPL while the range of the 106 dB(A) IITV exposure was 80-115 dB SPL. Two reference groups were exposed to a uniform 100 or 106 dB(A) SPL noise, 24 h/d for 5 days. Each reference group and the three corresponding IITV groups comprised a set of equivalent energy exposures. Evoked potentials were used to estimate hearing thresholds and surface preparation histology quantified sensory cell populations. All six groups exposed to the IITV noise showed threshold toughening effects of up to 40 dB. All IITV exposures produced hearing and sensory cell loss that was similar to their respective equivalent energy reference group. These results indicate that for Gaussian noise the equal energy hypothesis for noise-induced hearing loss is an acceptable unifying principle.     

Symmetry and Resonance in Periodic FPU Chains

The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This “Birkhoff–Gustavson normal form” retains the symmetries of the original system and we show that in most cases this allows us to view the periodic FPU Hamiltonian as a perturbation of a nondegenerate Liouville integrable Hamiltonian. According to the KAM theorem this proves the existence of many invariant tori on which motion is quasiperiodic. Experiments confirm this qualitative behaviour. We note that one can not expect this in lower-order resonant Hamiltonian systems. So the periodic FPU chain is an exception and its special features are caused by a combination of special resonances and symmetries. Received: 25 July 2000 / Accepted: 20 December 2000     

Thermal degradation of trimethylolpropane/adipic acid hyperbranched poly(ester)s

Hyperbranched poly(ester)s offer attractive features for applications in a number of areas, particularly as platforms for the support of controlled release actives in the agricultural and biomedical fields. Such materials have been generated from trimethylolpropane and adipic acid, and fully characterized using chromatographic, spectroscopic, and thermal methods. The thermal stability of these polymers has been assessed using thermogravimetry and infrared spectroscopy. The degradation characteristics of these materials have been compared to those of two linear adipic acid polymers. The prominent feature of the thermal degradation of the hyperbranched poly(ester)s is ether formation while that for the comparable linear poly(ester)s is ester pyrolysis resulting in chain scission.     

The Sasaki Hook Is Not a [Static] Implicative Connective but Induces a Backward [in Time] Dynamic One That Assigns Causes

The Sasaki adjunction, which formally encodes the logicality that different authors tried to attach to the Sasaki hook as a ‘quantum implicative connective,’ has a fundamental dynamic nature and encodes the so-called ‘causal duality’ (Coecke et al., 2001) for the particular case of a quantum measurement with a projector as corresponding self-adjoint operator. The action of the Sasaki hook ( $a\xrightarrow{S} - $ ) for fixed antecedent a assigns to some property “the weakest cause before the measurement of actuality of that property after the measurement,” i.e., ( $a\xrightarrow{S}b$ ) is the weakest property that guarantees actuality of b after performing the measurement represented by the projector that has the ‘subspace a’ as eigenstates for eigenvalue 1, say, the measurement that ‘tests’ a. The logicality attributable to quantum systems contains a fundamentally dynamic ingredient: Causal duality actually provides a new dynamic interpretation of orthomodularity. We also reconsider the status of the Sasaki hook within ‘dynamic (operational) quantum logic,’ what leads us to the claim made in the title of this paper. The Sasaki adjunction has a physical significance in terms of causal duality. The labeled dynamic hooks (forwardly and backwardly) that encode quantum measurements, act on properties as $(a_1 \xrightarrow{{\varphi _a }}a_2 ): = (a_1 \to _L (a\xrightarrow{S}a_2 ))$ and $(a_1 \xleftarrow{{\varphi _a }}a_2 ): = ((a\xrightarrow{S}a_2 ) \to _L a_1 )$ , taking values in the ‘disjunctive extension’ $DI(L)$ of the property lattice L, where $a \in L$ is the tested property and $( - \to _L - )$ is the Heyting implication that lives on DI(L). Since these hooks $( - \xrightarrow{{\varphi _a }} - )$ and $( - \xleftarrow{{\varphi _a }} - )$ extend to DI(L)×DI(L) they constitute internal operations. The transition from either classical or constructive/intuitionistic logic to quantum logic entails besides the introduction of an additional unary connective ‘operational resolution’ (Coecke, 2002a) the shift from a binary connective implication to a ternary connective where two of the arguments refer to qualities of the system and the third, the new one, to an obtained outcome (in a measurement)     

Hearing loss from interrupted, intermittent, and time varying non-Gaussian noise exposure: The applicability of the equal energy hypothesis

Sixteen groups of chinchillas (N=140) were exposed to various equivalent energy noise paradigms at 100 dB(A) or 103 dB(A) SPL. Eleven groups received an interrupted, intermittent, and time varying (IITV) non-Gaussian exposure quantified by the kurtosis statistic. The IITV exposures, which lasted for 8 hday, 5 daysweek for 3 weeks, were designed to model some of the essential features of an industrial workweek. Five equivalent energy reference groups were exposed to either a Gaussian or non-Gaussian 5 days, 24 hday continuous noise. Evoked potentials were used to estimate hearing thresholds and surface preparations of the organ of Corti quantified the sensory cell population. For IITV exposures at an equivalent energy and kurtosis, the temporal variations in level did not alter trauma and in some cases the IITV exposures produced results similar to those found for the 5 day continuous exposures. Any increase in kurtosis at a fixed energy was accompanied by an increase in noise-induced trauma. These results suggest that the equal energy hypothesis is an acceptable approach to evaluating noise exposures for hearing conservation purposes provided that the kurtosis of the amplitude distribution is taken into consideration. Temporal variations in noise levels seem to have little effect on trauma.