Based on the concept of adiabatic invariant, the perturbation to Noether Mei symmetry and adiabatic invariants for nonholonomie mechanical systems in phase space are studied. The definition of the perturbation to Noet...Based on the concept of adiabatic invariant, the perturbation to Noether Mei symmetry and adiabatic invariants for nonholonomie mechanical systems in phase space are studied. The definition of the perturbation to Noether-Mei symmetry for the system is presented, and the criterion of the perturbation to Noether-Mei symmetry is given. Meanwhile, the Noether adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.展开更多
Abstract Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and adiabatic invariants for nonholonomic mechanical systems in terms of quasi-coordinates are studied. The definition of the pert...Abstract Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and adiabatic invariants for nonholonomic mechanical systems in terms of quasi-coordinates are studied. The definition of the perturbation to Mei symmetry for the system is presented, and the criterion of the perturbation to Mei symmetry is given. Meanwhile, the Mei adiabatic invariants for the perturbed system are obtained.展开更多
Nanosystems play an important role in many applications.Due to their complexity,it is challenging to accurately characterize their structure and properties.An important means to reach such a goal is computational simu...Nanosystems play an important role in many applications.Due to their complexity,it is challenging to accurately characterize their structure and properties.An important means to reach such a goal is computational simulation,which is grounded on ab initio electronic structure calculations.Low scaling and accurate electronic-structure algorithms have been developed in recent years.Especially,the efficiency of hybrid density functional calculations for periodic systems has been significantly improved.With electronic structure information,simulation methods can be developed to directly obtain experimentally comparable data.For example,scanning tunneling microscopy images can be effectively simulated with advanced algorithms.When the system we are interested in is strongly coupled to environment,such as the Kondo effect,solving the hierarchical equations of motion turns out to be an effective way of computational characterization.Furthermore,the first principles simulation on the excited state dynamics rapidly emerges in recent years,and nonadiabatic molecular dynamics method plays an important role.For nanosystem involved chemical processes,such as graphene growth,multiscale simulation methods should be developed to characterize their atomic details.In this review,we review some recent progresses in methodology development for computational characterization of nanosystems.Advanced algorithms and software are essential for us to better understand of the nanoworld.展开更多
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimen...In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.展开更多
文摘Based on the concept of adiabatic invariant, the perturbation to Noether Mei symmetry and adiabatic invariants for nonholonomie mechanical systems in phase space are studied. The definition of the perturbation to Noether-Mei symmetry for the system is presented, and the criterion of the perturbation to Noether-Mei symmetry is given. Meanwhile, the Noether adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.
基金Supported by the Graduate Students' Innovative Foundation of China University of Petroleum (East China) under Grant No.S2009-19
文摘Abstract Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and adiabatic invariants for nonholonomic mechanical systems in terms of quasi-coordinates are studied. The definition of the perturbation to Mei symmetry for the system is presented, and the criterion of the perturbation to Mei symmetry is given. Meanwhile, the Mei adiabatic invariants for the perturbed system are obtained.
基金supported by the Ministry of Science and Technology(No.2016YFA0200604)。
文摘Nanosystems play an important role in many applications.Due to their complexity,it is challenging to accurately characterize their structure and properties.An important means to reach such a goal is computational simulation,which is grounded on ab initio electronic structure calculations.Low scaling and accurate electronic-structure algorithms have been developed in recent years.Especially,the efficiency of hybrid density functional calculations for periodic systems has been significantly improved.With electronic structure information,simulation methods can be developed to directly obtain experimentally comparable data.For example,scanning tunneling microscopy images can be effectively simulated with advanced algorithms.When the system we are interested in is strongly coupled to environment,such as the Kondo effect,solving the hierarchical equations of motion turns out to be an effective way of computational characterization.Furthermore,the first principles simulation on the excited state dynamics rapidly emerges in recent years,and nonadiabatic molecular dynamics method plays an important role.For nanosystem involved chemical processes,such as graphene growth,multiscale simulation methods should be developed to characterize their atomic details.In this review,we review some recent progresses in methodology development for computational characterization of nanosystems.Advanced algorithms and software are essential for us to better understand of the nanoworld.
基金Supported by the National Natural Science Foundation of China under Grant No. 61173050
文摘In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.