Quaternion is a division ring.It is shown that planes passing through the origin can be made a field with the quaternion product in R~3.The Hamiltonian operators help us define the homothetic motions on these planes.N...Quaternion is a division ring.It is shown that planes passing through the origin can be made a field with the quaternion product in R~3.The Hamiltonian operators help us define the homothetic motions on these planes.New characterizations for these motions are investigated.展开更多
In this paper, we introduce the class of extended Hamilton operators and study various properties of this class. We examine the decomposability of extended Hamilton operators. In addition, we prove that an extended Ha...In this paper, we introduce the class of extended Hamilton operators and study various properties of this class. We examine the decomposability of extended Hamilton operators. In addition, we prove that an extended Hamilton operator with property （δ） is subscalar. Finally, we consider Weyl type theorems of this class.展开更多
Coarse-graining of some sort is a fundamental and unavoidable step in any attempt to derive the classical mechan- ical behavior from the quantum formalism. We utilize the two-mode Bose-Hubbard model to illustrate how ...Coarse-graining of some sort is a fundamental and unavoidable step in any attempt to derive the classical mechan- ical behavior from the quantum formalism. We utilize the two-mode Bose-Hubbard model to illustrate how different coarse-grained systems can be naturally associated with a fixed quantum system if it is compatible with different dy- namical algebras. Alternative coarse-grained systems generate different evolutions of the same physical quantities, and the difference becomes negligible only in the appropriate macro-limit.展开更多
In this paper, we introduce the class of Hamilton type operators and study various properties of this class. We show that every Hamilton type operator with property（β） or（δ） is decomposable. In addition,we prove...In this paper, we introduce the class of Hamilton type operators and study various properties of this class. We show that every Hamilton type operator with property（β） or（δ） is decomposable. In addition,we prove that a Hamilton type operator T satisfies property（β）, Dunford＇s property（C） and Weyl＇s theorem if and only if its adjoint does.展开更多
文摘Quaternion is a division ring.It is shown that planes passing through the origin can be made a field with the quaternion product in R~3.The Hamiltonian operators help us define the homothetic motions on these planes.New characterizations for these motions are investigated.
基金Supported by the National Natural Science Foundation of China(Grant No.11601130)the Natural Science Foundation of the Department of Education of He’nan Province(Grant Nos.16A110033 and 17A110005)
文摘In this paper, we introduce the class of extended Hamilton operators and study various properties of this class. We examine the decomposability of extended Hamilton operators. In addition, we prove that an extended Hamilton operator with property （δ） is subscalar. Finally, we consider Weyl type theorems of this class.
基金Project supported by the Ministry of Education and Science of the Republic of Serbia(Grant Nos.171017,171028,171038,and III45016)We would like to acknowledge partial support by COST(Action MP1006)
文摘Coarse-graining of some sort is a fundamental and unavoidable step in any attempt to derive the classical mechan- ical behavior from the quantum formalism. We utilize the two-mode Bose-Hubbard model to illustrate how different coarse-grained systems can be naturally associated with a fixed quantum system if it is compatible with different dy- namical algebras. Alternative coarse-grained systems generate different evolutions of the same physical quantities, and the difference becomes negligible only in the appropriate macro-limit.
基金Supported by the National Natural Science Foundation of China under Grant No.11601130 and 11761029the Natural Science Foundation of the Department of Education of Henan Province under Grant No.16A110033and 17A110005Doctoral Foundation of Henan Normal University No.qd15133
文摘In this paper, we introduce the class of Hamilton type operators and study various properties of this class. We show that every Hamilton type operator with property（β） or（δ） is decomposable. In addition,we prove that a Hamilton type operator T satisfies property（β）, Dunford＇s property（C） and Weyl＇s theorem if and only if its adjoint does.
