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arXiv:1607.06548

The Symmetry of Current of the Coherent State From the View of O(3) sigma-model

Shi, Xu-Guang, Qin, Zhi-Jie

Published Jul 22, 2016• 0 citations
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Abstract

In this paper, we apply the reduced density trajectory, phi-mapping topological current theory and Ginzberg-Landau model to study the current of the coherent state. We give the new expression of the current of the coherent state. Based on this expression, the symmetry of the coherence is studied. We find that the current of the coherent state corresponds to the supercurrent of two-condensate system. The partial wave functions of the coherence carry new charges and their interaction is mediated by new U(1) gauge potential.

DOI
10.48550/arxiv.1607.06548

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In this paper, we apply the reduced density trajectory, phi-mapping topological current theory and Ginzberg-Landau model to study the current of the coherent state. We give the new expression of the current of the coherent state. Based on this expression, the symmetry of the coherence is studied. We find that the current of the coherent state corresponds to the supercurrent of two-condensate system. The partial wave functions of the coherence carry new charges and their interaction is mediated by new U(1) gauge potential.
In this paper, we apply the reduced density trajectory, ϕ-mapping topological current theory and Ginzburg Landau model to study the current of the coherent state.We give the new expression of the current of the coherent state.Based on this expression, the symmetry of the coherence is studied.We nd that the current of the coherent state corresponds to the supercurrent of two-condensate system.The partial wave functions of the coherence carry new charges and their interaction is mediated by new U(1) gauge potential.
We have studied the topological expression of the reduced quantum trajectory using ϕ-mapping topological current theory and reduced density matrix theory. Moreover, we have proposed a new topological expression called the reduced quantum topological trajectory. Ignoring the coefficients of the winding number, we have found that the expression for the reduced quantum topological trajectory is the same for coherence as it is for decoherence. Under certain conditions, the vorticity of the reduced quantum topological trajectory is a topological invariant.
The topological expression of the reduced quantum trajectory is given by using ϕ-mapping topological current theory. The topological expression is used in study of the coherence and the decoherence. We find the expression of vorticity for decoherence has a similar form as that for coherence. A topological reason leading to the decoherence is given and a new parameter is defined to indicate the coherence degree. The parameter is different from the damping factor because it relates to the topological structure of the reduced quantum trajectory.
The topological expression of the reduced quantum trajectory is given by using φ-mapping topologicalcurrent theory.The topological expression is used in study of the coherence and the decoherence.We find the expressionof vorticity for decoherence has a similar form as that for coherence.A topological reason leading to the decoherenceis given and a new parameter is defined to indicate the coherence degree.The parameter is different from the dampingfactor because it relates to the topological structure of the reduced quantum trajectory.
By making use of the ϕϕϕ-mapping topological current theory, a novel expression of ∇×V⃗\nabla \times \vec{V}∇×V in BEC is obtained, which reveals the inner topological structure of vortex lines characterized by Hopf indices and Brouwer degrees. This expression is just that formula Landau and Feynman expected to find out long time ago. In the case of superconductivity, the decomposition theory of U(1) gauge potential in terms of the condensate wave function gives a rigorous proof of London assumption, and shows that each vortex line should carry a quantized flux. The ϕϕϕ-mapping topological current theory of ∇×V⃗\nabla \times \vec{V}∇×V can also gives a precise bifurcation theory of vortex lines in BEC.