The Origin of the Non-Classical Character of the Quantum Probability Model

Alexandru I. Lupascu

We present a discrete model for the motion of a beam of classical particles propagating across a rectangular lattice. These particles are represented by their classical probabilities to be found in different cells of the lattice. We consider two kinds of interactions between the particles and the intmvening substance. In free space the particles slightly deviate fiom a pure forward movement. When they collide with an obstacle, they are elastically reflected. Rather surprisingly, our simple model predicts a wavy character for the probability profile of this non-quantum particle beam. We observe maxima and minima under very general conditions. Specifically, particles experience difgaction around obstacles. These fiinges are not the result of interference of certain waves, but rather of the particle reflections on obstacles, as well as of the deviations from a pure advancing movement. We study the influence of the dimensions of the source, of the obstacles and of the interaction between the beam and the screens.

Hairong Yin

Andrei Yu. Khrennikov

Yannic Rath, Florian Mintert

This paper discusses the dynamics of interference structures in the Anderson model with decoherence. Due to an intricate interplay of interference, disorder, and decoherence there is a rise and decay of interference peaks on transient time scales, that is the transition from a quantum mechanical interference pattern to a classical probability distribution is of non-monotonic character. An analytic solution in the limit of weak dephasing supplemented with a numerical analysis beyond this limiting case provides an intuitive understanding for the observed phenomena.

Yaochen Liu, Qiuchi Li, Benyou Wang +2 more

Quantum theory, originally proposed as a physical theory to describe the motions of microscopic particles, has been applied to various non-physics domains involving human cognition and decision-making that are inherently uncertain and exhibit certain non-classical, quantum-like characteristics. Sentiment analysis is a typical example of such domains. In the last few years, by leveraging the modeling power of quantum probability (a non-classical probability stemming from quantum mechanics methodology) and deep neural networks, a range of novel quantum-cognitively inspired models for sentiment analysis have emerged and performed well. This survey presents a timely overview of the latest developments in this fascinating cross-disciplinary area. We first provide a background of quantum probability and quantum cognition at a theoretical level, analyzing their advantages over classical theories in modeling the cognitive aspects of sentiment analysis. Then, recent quantum-cognitively inspired models are introduced and discussed in detail, focusing on how they approach the key challenges of the sentiment analysis task. Finally, we discuss the limitations of the current research and highlight future research directions.

Nicola Cufaro Petroni