Fuzzification of Feynman Path Integral and Its Effect on Field Theory and Quantum Gravity—Reformation and Redevelopment of Quantum Theory

The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory reforms quantum mechanics, making the later become its special case. This theory breaks unitarity, gauge invariance, probability conservation and information conservation, making these principles become approximate ones under certain conditions. This new theory, which needs no renormalization and can naturally give meaningful results which are in accordance with the experiments, is the proper theory to describe microscopic high-speed phenomenon, whereas quantum mechanics is only a proper theory to describe microscopic low-speed phenomenon. This theory is not divergent under the condition of there being no renormalization and infinitely many offsetting terms, thereby it can become the theoretical framework required for the quantization of gravity.

There Also Can Be Fuzziness in Quantum States Itself—Breaking through the Framework and the Principle of Quantum Mechanics

In this paper, an attempt is made to synthesize fuzzy mathematics and quantum mechanics. By using the method of fuzzy mathematics to blur the probability (wave) of quantum mechanics, the concept of fuzzy wave function is put forward to describe the fuzzy quantum probability. By applying the non-fuzzy formula of fuzzy quantity and Schrödinger wave equation of quantum mechanics, the membership function equation is established to describe the evolution of the fuzzy wave function. The concept of membership degree amplitude is introduced to calculate fuzzy probability amplitude. Some important concepts in fuzzy mathematics are also illustrated.

Phase Transitions Governed by the Fifth Power of the Golden Mean and Beyond

In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio φ respectively its fifth power φ5. The research fields cover model calculations of statistical physics associated with phase transitions, the quantum probability of two particles, new physics of everything suggested by the information relativity theory (IRT) including explanations of cosmological relevance, the ε-infinity theory, superconductivity, and the Tammes problem of the largest diameter of N non-overlapping circles on the surface of a sphere with its connection to viral morphology and crystallography. Finally, Fibonacci anyons proposed for topological quantum computation (TQC) were briefly described in comparison to the recently formulated reverse Fibonacci approach using the Janičko number sequence. An architecture applicable for a quantum computer is proposed consisting of 13-step twisted microtubules similar to tubulin microtubules of living matter. Most topics point to the omnipresence of the golden mean as the numerical dominator of our world.

The properties of an asymmetric Gaussian potential quantum well qubit in RbCl crystal

With the circumstance of the electron strongly coupled to LO-phonon and using the variational method of Pekar type（VMPT）,we study the eigenenergies and the eigenfunctions（EE） of the ground and the first excited states（GFES） in a RbCl crystal asymmetric Gaussian potential quantum well（AGPQW）.It concludes：（i） Twoenergy-level of the AGPQW may be seen as a qubit.（ii） When the electron located in the superposition state of the two-energy-level system,the time evolution and the coordinate changes of the electron probability density oscillated periodically in the AGPQW with every certain period T0=22.475 fs.（iii） Due to the confinement that is a two dimensional x-y plane symmetric structure in the AGPQW and the asymmetrical Gaussian potential（AGP） in the AGPQW growth direction,the electron probability density presents only one peak configuration located in the coordinate of z 〉 0,whereas it is zero in the range of z 〈 0.（iv） The oscillatory period is a decreasing function of the AGPQW height and the polaron radius,（v） The oscillating period is a decreasing one in the confinement potential R 〈 0.24 nm,whereas it is an increasing one in the confinement potential R 〉 0.24 nm and it takes a minimum value in R = 0.24 nm.