We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free ferm...We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.展开更多
Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversati...Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversation with the Lagrangian approach, the dynamic equation of a robot is established. Based on the above results, the free-floating dual-arm space robot system is modeled with RBF neural networks, the GL matrix and its product operator. With all uncertain inertial system parameters, an adaptive RBF neural network control scheme is developed for coordinated motion between the base attitude and the arm joints. The proposed scheme does not need linear parameterization of the dynamic equation of the system and any accurate prior-knowledge of the actual inertial parameters. Also it does not need to train the neural network offline so that it would present real-time and online applications. A planar free-floating dual-arm space robot is simulated to show feasibility of the proposed scheme.展开更多
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB30000000)the National Natural Science Foundation of China(Grant Nos.11774398 and T2121001)。
文摘We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.
基金the National Natural Science Foundation of China (Nos. 10672040 and10372022)the Natural Science Foundation of Fujian Province of China (No. E0410008)
文摘Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversation with the Lagrangian approach, the dynamic equation of a robot is established. Based on the above results, the free-floating dual-arm space robot system is modeled with RBF neural networks, the GL matrix and its product operator. With all uncertain inertial system parameters, an adaptive RBF neural network control scheme is developed for coordinated motion between the base attitude and the arm joints. The proposed scheme does not need linear parameterization of the dynamic equation of the system and any accurate prior-knowledge of the actual inertial parameters. Also it does not need to train the neural network offline so that it would present real-time and online applications. A planar free-floating dual-arm space robot is simulated to show feasibility of the proposed scheme.
