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Communications in Theoretical Physics

Topological Effect of Reduced Quantum Trajectory in Coherence and Decoherence

Shi Xu-Guang, Yi-Shi Duan, Qin Zhi-Jie

Published Sep 1, 2010• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/54/3/10

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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.
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 solutions of the De Broglie–Bohm quantum mechanics are presented. Starting from the Schrödinger equation for one particle system and ϕ-mapping topological current theory, the trajectory of the particle is derived explicitly, and can be used as the world line of the particle. The world line is just at the zero point of the wave function and it is shown that the vorticity of the world line can be expressed by Hopf index and Brouwer degree. The evolution of the world line at the bifurcation point is given.
Through the application of ϕ-mapping topological theory, the properties of vortices in quantum Röntgen effect are thoroughly studied. The explicit expression of the vorticity is obtained, in which the δ function indicates that the vortices can only stem from the zero points of ϕ, and the magnetic flux of the consequent monopoles is quantized in terms of the Hopf indices and Brouwer degrees. The evolution of vortex lines is discussed. The reduced dynamic equation and a conserved dynamic quantity on stable vortex lines are obtained.
This paper explores the interplay between topology and quantum coherence, investigating the stability and evolution of quantum systems through the application of quantum entanglement and topological structures. We propose a novel approach to quantum computation, leveraging these principles to develop new methods that offer a fundamentally different understanding of quantum mechanics. The core of this work lies in a detailed analysis of decoherence mechanisms, focusing on how topological properties can mitigate these effects and ultimately enhance the fidelity of quantum operations. The research aims to address limitations inherent in current quantum algorithms and pave the way for more robust and versatile quantum technologies.
Using the phi-mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross-Pitaevskii theory in (3+1)-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the delta function indicates that the vortices can only be generated from the zero points of Phi and are quantized in terms of the Hopf indices and Brouwer degrees. The phi-mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.