We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and cons...We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ｜〉=[f＋∑^tφk1σ1hk2σ2ck3σ3hk4σ4 ∏exp（ρck1σ1 hk2σ2）]｜〉0,where φ and ρ are the coupling constants. Our results are then compared to those of varlational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method （VMC） as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.展开更多
This paper studies an investment and consumption problem with stochastic interest rate,where interest rate is governed by the Vasicek model.The financial market is composed of one riskfree asset and one risky asset,in...This paper studies an investment and consumption problem with stochastic interest rate,where interest rate is governed by the Vasicek model.The financial market is composed of one riskfree asset and one risky asset,in which stock price dynamics is assumed to be generally correlated with interest rate dynamics.The aim is to maximize expected utility of consumption and terminal wealth in the finite horizon.Legendre transform is used to deal with this investment and consumption problem and the explicit solutions of the optimal investment and consumption strategies with power and logarithm preference are achieved.Finally,the authors add a numerical example to analyze the effect of market parameters on the optimal investment and consumption strategy and provide some economic implications.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10575087 We gratefully acknowledge Dr. H. Jeshker at Freie Universitgt Berlin for his valuable discussions. Thanks are also given to the center 0f Nonlinear Science for providing the powerful sG~ 02000 Computer.
文摘We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ｜〉=[f＋∑^tφk1σ1hk2σ2ck3σ3hk4σ4 ∏exp（ρck1σ1 hk2σ2）]｜〉0,where φ and ρ are the coupling constants. Our results are then compared to those of varlational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method （VMC） as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.
基金supported by the Humanities and Social Science Research Youth Foundation of Ministry of Education of China under Grant No.11YJC790006Center for Research of Regulation and Policy of Zhejiang Province of China under Grant No.13JDGZ03YB+1 种基金the project of National Statistical Science of China under Grant No.2013LY125the Higher School Science and Technology Development Foundation of Tianjin of China under Grant No.20100821
文摘This paper studies an investment and consumption problem with stochastic interest rate,where interest rate is governed by the Vasicek model.The financial market is composed of one riskfree asset and one risky asset,in which stock price dynamics is assumed to be generally correlated with interest rate dynamics.The aim is to maximize expected utility of consumption and terminal wealth in the finite horizon.Legendre transform is used to deal with this investment and consumption problem and the explicit solutions of the optimal investment and consumption strategies with power and logarithm preference are achieved.Finally,the authors add a numerical example to analyze the effect of market parameters on the optimal investment and consumption strategy and provide some economic implications.
