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.     

Dissipative tunneling through a parabolic potential in the Lindblad theory of open quantum systems

By using the Lindblad theory for open quantum systems, an analytical expression of the tunneling probability through an inverted parabola is obtained. This penetration probability depends on the environment coefficients. It is shown that the tunneling probability increases with the dissipation and the temperature of the thermal bath. Received 15 October 1999 and Received in final form 5 January 2000     

Statistical Optimization for Succinic Acid Production from E. Coli in a Cost-Effective Medium

Response surface methodology (RSM) was employed for optimization of medium components and cultural parameters in cost effective cane molasses based medium for attaining high yield of succinic acid. The important factors obtained by “one-variable-at-a-time-approach” (cane molasses, corn steep liquor, sodium carbonate, and inoculum density) were further optimized by RSM. The optimum values of the parameters obtained through RSM (cane molasses 12.5%, corn steep liquor 7.5%, and sodium carbonate 25 mM) led to almost double yield of succinic acid (15.2 g/l in 36 h) as against “one-variable-at-a-time-approach” (7.1 g/l in 36 h) in 500-ml anaerobic bottles containing 300-ml cane molasses based medium. Subsequently, in 10-l bioreactor succinic acid production from Escherichia coli was further improved to 26.2 g/l in 30 h under conditions optimized through RSM. This fermentation-derived succinic acid will definitely help in replacing existing environmentally hazardous and cost-intensive chemical methods for the production of succinic acid.     

Quantum fidelity of Gaussian states in open systems

Using the expression of the fidelity for the most general Gaussian quantum states, the behaviour of the quantum fidelity is described for the states of a harmonic oscillator interacting with an environment, in particular with a thermal bath. By taking a correlated squeezed Gaussian state as initial state, we calculate the quantum fidelity for both kinds of undisplaced and displaced states, and for different values of the squeezing and correlation parameters and of the environment temperature.     

Exponentiable Functors Between Quantaloid-Enriched Categories

Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey some lax commutativity; this, in turn, is precisely what is needed to prove the existence of partial products with that functor; so that the functor’s exponentiability follows from the works of Niefield (J. Pure Appl. Algebra 23:147–167, 1982) and Dyckhoff and Tholen (J. Pure Appl. Algebra 49:103–116, 1987).      

Wigner Functions and Spin Tomograms for Qubit States

We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel connecting Wigner symbols on the discrete phase space with the tomographic symbols.