Collective coordinate analysis for adding a space dependent potential to the double sine-Gordon model is presented. Interaction of solitons with a delta function potential barrier and also delta function potential well is investigated. Most of the features of interaction are derived analytically. We will find that the behaviour of a solitonic solution is like a point particle which moves under the influence of a complicated effective potential. The effective potential is a function of the field initial conditions and also parameters of added external potential.

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Interaction of Double sine-Gordon solitons with a space dependent potential wall and also a potential well has been investigated by employing an analytical model based on the collective coordinate approach. The potential has been added to the model through a suitable nontrivial metric for the background space-time. The model is able to predict most of the features of the soliton-potential interaction. It is shown that a soliton can pass through a potential barrier if its velocity is greater than a critical velocity which is a function of soliton initial conditions and also characters of the potential. It is interesting that the solitons of the double sine-Gordon model can be trapped by a potential barrier and oscillate there. This situation is very important in applied physics. Solitonwell system has been investigated using the presented model too. Analytical results also have been compared with the results of the direct numerical solutions.

The fundamental nature of quantum wave function has been the subject of many discussions since the beginning of the quantum theory. It either corresponds to an element of reality (Ψ − ontic) or it is a subjective state of knowledge about underlying reality (Ψ − epistemic) . Pusey, Barrett, and Rudolph (PBR) showed that epistemic interpretations of the quantum wave function are in contradiction with the predictions of quantum under some assumptions. In this paper, we introduce a laboratory protocol with triple quantum dot as a three-spin interaction system to study the PBR no-go theorem. By this experimental model, we show that the epistemic interpretation of the quantum state is in contradiction with quantum theory, based only on the assumption that measurement settings can be prepared freely and independent of each other.

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