Entropic uncertainty relation based on generalized uncertainty principle

We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so-called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.

QUANTUM DYNAMICS FOR DE SITTER RADIATION

We revisit the Hamiltonian formalism for a massive scalar field and study the particle production in a de Sitter space. In the invariant-operator picture the time-dependent annihilation and creation operators are constructed in terms of a complex solution to the classical equation of motion for the field and the Gaussian wave function for each Fourier mode is found which is an exact solution to the Schrödinger equation. The in-out formalism is reformulated by the annihilation and creation operators and the Gaussian wave functions. The de Sitter radiation from the in-out formalism differs from the Gibbons-Hawking radiation in the planar coordinates, and we discuss the discrepancy of the particle production by the two methods.

ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.

Hybrid simulation of speech waveforms utilizing a Gaussian wave function representation

Most of the prior research work concerned with the analysis and synthesis of speech has employed Fourier series and transforms as the mathematical framework for the characterization of live speech. Current studies at UCSB have taken a new approach, namely the time domain analysis of speech waveforms. This work, per formed under the direction of Dr. Glen J. Culler, is based on a Gaussian wave-function approach to the analysis, synthesis and decomposition of speech elements. This paper is concerned with the hybrid simulation of speech waveforms utilizing the wave-function representation. A speech simulator consisting of a hybrid interconnec tion of four TR-20 analog computers is described. Re sults of the simulation of two vowel sounds, the "o" in "on" and the "a" in "at," are presented and compared with the original speech data. The results form an im pressive check on the wave-function approach and have provided the impetus for the realization of a hybrid speech-synthesizer based on this technique.