Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local–global correspondenc...Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local–global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states.We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation.We demonstrate this approach by the non-Hermitian Chern insulator model.We give the consistent topological phases obtained from the Chern number and vorticity.We also find some novel topological invariants embedded in the topological phases of the Chern insulator model,which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity.We also propose a generalized vorticity and its flipping index to understand physics behind this novel local–global correspondence and discuss the relationships between the local–global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane.These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states,which is expected to be applicable in more generic non-Hermitian systems.展开更多
Deviations from the efficient market hypothesis allow us to benefit from risk premium in financial markets.We propose a three-pronged(R,σ,H)theory to generalize the(R,σ)model and present the formulation of a three-p...Deviations from the efficient market hypothesis allow us to benefit from risk premium in financial markets.We propose a three-pronged(R,σ,H)theory to generalize the(R,σ)model and present the formulation of a three-pronged(R,σ,H)model and its Pareto-optimal solution.We define the local-optimal weights(wR,wσ,WH)that construct the triangle of the quasi-optimal investing subspace and further define the centroid or incenter of the triangle as the optimal investing weights that optimize the mean return,risk premium,and volatility risk.By numerically investigating the Chinese stock market,we demonstrate the validity of this formulation method.The proposed theory provides investors of different styles(conservative or aggressive)an efficient way to design portfolios in financial markets to maximize the mean return while minimizing the volatility risk.展开更多
文摘Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local–global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states.We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation.We demonstrate this approach by the non-Hermitian Chern insulator model.We give the consistent topological phases obtained from the Chern number and vorticity.We also find some novel topological invariants embedded in the topological phases of the Chern insulator model,which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity.We also propose a generalized vorticity and its flipping index to understand physics behind this novel local–global correspondence and discuss the relationships between the local–global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane.These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states,which is expected to be applicable in more generic non-Hermitian systems.
基金The authors thank the Natural Science Foundation of Guangdong Province(No.2016A030313313).
文摘Deviations from the efficient market hypothesis allow us to benefit from risk premium in financial markets.We propose a three-pronged(R,σ,H)theory to generalize the(R,σ)model and present the formulation of a three-pronged(R,σ,H)model and its Pareto-optimal solution.We define the local-optimal weights(wR,wσ,WH)that construct the triangle of the quasi-optimal investing subspace and further define the centroid or incenter of the triangle as the optimal investing weights that optimize the mean return,risk premium,and volatility risk.By numerically investigating the Chinese stock market,we demonstrate the validity of this formulation method.The proposed theory provides investors of different styles(conservative or aggressive)an efficient way to design portfolios in financial markets to maximize the mean return while minimizing the volatility risk.
