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Modern Physics Letters A

REDUCED QUANTUM TOPOLOGICAL TRAJECTORY IN COHERENCE AND DECOHERENCE

Xuguang Shi, Yi-Shi Duan

Published May 30, 2011• 3 citations
Publisher

Abstract

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.

DOI
10.1142/s0217732311035821

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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.
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.
We show how to define a dynamical topological invariant for one-dimensional two-band topological systems after a quantum quench. By analyzing general two-band models of topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifolds S2{S}^{2}S2, and thus we are able to define a dynamical topological invariant on each of the spheres. We also unveil the intrinsic relation between the dynamical topological invariant and the difference in the topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.
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.