The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invar...The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of are given. The expectation values of in the angular momentum coherent states are calculated as well as the corresponding classical limits.展开更多
A new kind of k-quantum nonlinear coherent states,i.e.,the k eigenstates of the k-th power~k (k≥3) of the generalized annihilation operator=1/f() of f-oscillators,are obtained and their properties are discussed.The c...A new kind of k-quantum nonlinear coherent states,i.e.,the k eigenstates of the k-th power~k (k≥3) of the generalized annihilation operator=1/f() of f-oscillators,are obtained and their properties are discussed.The completeness of the k states is investigated.An alternative method to construct them is proposed.It is shown that these states may form a complete Hilbert space,and all of them can be generated by a linear superposition of k Roy-type nonlinear coherent states.Physically,they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.展开更多
We study the properties of the three-mode Einstein-Podolsky-Rose (EPR) eigenstate and its application in quantum dense coding. Our result shows that the three-mode EPR eigenstate provides a convenient way to realize q...We study the properties of the three-mode Einstein-Podolsky-Rose (EPR) eigenstate and its application in quantum dense coding. Our result shows that the three-mode EPR eigenstate provides a convenient way to realize quantum dense coding when the quantum channel is a three-mode squeezed state.展开更多
The second reference state of the open XYZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz.
Based on an iterative method for solving the groundstate of Schrodinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The res...Based on an iterative method for solving the groundstate of Schrodinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.展开更多
We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris ...We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris approximation is used to deal with centrifugal term.展开更多
We reveal that the common eigenvector of two particles' center-of-mass coordinate and mass-weightedrelative momentum is an entangled state. Its Schmidt decomposition exhibits that the entanglement involves squeezi...We reveal that the common eigenvector of two particles' center-of-mass coordinate and mass-weightedrelative momentum is an entangled state. Its Schmidt decomposition exhibits that the entanglement involves squeezingwhich depends on the ratio of two particles' masses. The corresponding entangling operators are derived.展开更多
Abstract We study dynamics in two mutually coupling multi-quantum-well lasers. We carry out theoretical and numerical analysis of synchronization, anti-synchronization, in-phase locking in the two identical lasers but...Abstract We study dynamics in two mutually coupling multi-quantum-well lasers. We carry out theoretical and numerical analysis of synchronization, anti-synchronization, in-phase locking in the two identical lasers but detuning, in detain. It is proved that the coupling level determines stability of the lasers by analyzing the eigenvalue equation. Critical case of locking is discussed via the phase difference equation. Quasi-period and stable states in the two lasers are investigated via varying the current, detuning and coupling level.展开更多
The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. T...The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.展开更多
The model test of seismic simulation shaking table is an important method to study the seismic design of bridge structure. In order to evaluate the seismic response and dynamic characteristics of pile-water-pier syste...The model test of seismic simulation shaking table is an important method to study the seismic design of bridge structure. In order to evaluate the seismic response and dynamic characteristics of pile-water-pier system for developing more reliable design procedures, shaking table model tests of a submerged bridge pier system, including pile groups-cap-pier and inertia mass, were conducted. Since different similitude laws corresponding to different test objectives affected the validity of test results, the similitude law with the aim to consider the effect of hydrodynamic pressure was proposed and confirmed through an actual example. Based on the test results, the effect of water around model on seismic response under seismic excitation input was analyzed and the failure level was judged by observing the variation of basic frequency. The test results indicate that the transfer function of analytical model with water is different from that without water, the natural frequency without water is always higher than that with water, and the first modal shapes are various. It is also concluded that the similitude law is suitable for practical application and the dynamic characteristics and seismic response of the structure system can be changed because of the existence of the surrounding water, which should be paid much attention in the further investigation.展开更多
Two linear In this letter, we prove the following conclusions by introducing a function Fn(t): (1) If a quantum system S with a time-dependent non-degenerate Hamiltonian H(t) is initially in the n-th eigenstate...Two linear In this letter, we prove the following conclusions by introducing a function Fn(t): (1) If a quantum system S with a time-dependent non-degenerate Hamiltonian H(t) is initially in the n-th eigenstate of H(0), then the state of the system at time t will remain in the n-th eigenstate of H(t) up to a multiplicative phase factor if and only if the values Fn(t) for all t are always on the circle centered at 1 with radius 1; (2) If a quantum system S with a time-dependent Hamiltonian H(t) is initially in the n-th eigenstate of H(0), then the state of the system at time t will remain c-uniformly approximately in the n-th eigenstate of H(t) up to a multiplicative phase factor if and only if the values F,(t) for all t are always outside of the circle centered at 1 with radius 1-ε. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ε-uniformly approximately in the n-th eigenstate of H(t) up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field.展开更多
For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fi...For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ>0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.展开更多
The discovery of neutrino oscillation indicates that neutrinos have masses and each flavor state is actually a superposition of three mass states with masses m1,m2,and m3.However,the neutrino oscillation experiments a...The discovery of neutrino oscillation indicates that neutrinos have masses and each flavor state is actually a superposition of three mass states with masses m1,m2,and m3.However,the neutrino oscillation experiments are not able to measure the absolute masses of neutrinos,but can only measure the squared mass differences between the neutrino mass eigenstates—The solar and reactor experiments gave展开更多
Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures.Here,we point out that discrete synthe...Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures.Here,we point out that discrete synthetic Poincaréhalf-planes and Poincarédisks,which are created by lattices in flat planes,support infinitely degenerate eigenstates for any nonzero eigenenergies.Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces.Furthermore,all eigenstates are exponentially localized in the hyperbolic coordinates,signifying the first example of quantum funneling effects in Hermitian systems.As such,any initial wave packet travels towards the edge of the Poincaréhalf-plane or its equivalent on the Poincarédisk,delivering an efficient scheme to harvest light and atoms in two dimensions.Our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.展开更多
The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation (SE) by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition princi...The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation (SE) by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H(0). Also, we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H(t). On the other hand, any physical experiment may bring errors so that the initial state (input state) may be a superposition of different eigenstates, not just at the desired eigenstate. In this paper, we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t = 0. A generalized adiabatic approximate solution (GAAS) is constructed and an upper bound for the generalized adiabatic approximation error is given. As an application, the fidelity of the exact solution and the GAAS is estimated.展开更多
The Hellmann potential, which is a superposition of an attractive Coulomb potential -air and a Yutmwa potential b e-δr /r , is often used to compute bound-state normalizations and energy levels of neutral atoms. By u...The Hellmann potential, which is a superposition of an attractive Coulomb potential -air and a Yutmwa potential b e-δr /r , is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schr6dinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.展开更多
The operator level proof of factorization theorem exhibited in [ar Xiv:hep-ph/1307.4194] is extended to the semi-inclusive deep inelastic scattering process(SIDIS). Factorization theorem can be proved at operator l...The operator level proof of factorization theorem exhibited in [ar Xiv:hep-ph/1307.4194] is extended to the semi-inclusive deep inelastic scattering process(SIDIS). Factorization theorem can be proved at operator level if there are not detected soft hadrons. The key point is that the initial one-nucleon state is the eigenstate of QCD.展开更多
This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system oper...This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system operator and its quasi-compactness. Some primary reliability indices are discussed with the eigenfunction of system operator and the optimal vacation time to get the maximum system profit is analyzed at the end of paper.展开更多
We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V(τ)= V0(a + exp (λτ))/(b ...We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V(τ)= V0(a + exp (λτ))/(b + exp (λτ)) + V1( d + exp ( λτ) ) / (b + exp (λτ)). We obtain the bound state energy eigenvalue and the corresponding eigenfunction ex- pressed in terms of the Jaeobi polynomials. By choosing appropriate parameter in the potential model, the generalized Hylleraas potential reduces to the well known potentials as special cases.展开更多
文摘The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of are given. The expectation values of in the angular momentum coherent states are calculated as well as the corresponding classical limits.
基金The project supported by National Natural Science Foundation of China under Grant No.10074072the Natural Science Foundation of Shandong Province of China under Grant No.Y2002A05
文摘A new kind of k-quantum nonlinear coherent states,i.e.,the k eigenstates of the k-th power~k (k≥3) of the generalized annihilation operator=1/f() of f-oscillators,are obtained and their properties are discussed.The completeness of the k states is investigated.An alternative method to construct them is proposed.It is shown that these states may form a complete Hilbert space,and all of them can be generated by a linear superposition of k Roy-type nonlinear coherent states.Physically,they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.
文摘We study the properties of the three-mode Einstein-Podolsky-Rose (EPR) eigenstate and its application in quantum dense coding. Our result shows that the three-mode EPR eigenstate provides a convenient way to realize quantum dense coding when the quantum channel is a three-mode squeezed state.
基金Supports by the National Natural Science Foundation of China under Grant Nos. 11075125 and 11031005
文摘The second reference state of the open XYZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz.
文摘Based on an iterative method for solving the groundstate of Schrodinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.
文摘We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris approximation is used to deal with centrifugal term.
文摘We reveal that the common eigenvector of two particles' center-of-mass coordinate and mass-weightedrelative momentum is an entangled state. Its Schmidt decomposition exhibits that the entanglement involves squeezingwhich depends on the ratio of two particles' masses. The corresponding entangling operators are derived.
文摘Abstract We study dynamics in two mutually coupling multi-quantum-well lasers. We carry out theoretical and numerical analysis of synchronization, anti-synchronization, in-phase locking in the two identical lasers but detuning, in detain. It is proved that the coupling level determines stability of the lasers by analyzing the eigenvalue equation. Critical case of locking is discussed via the phase difference equation. Quasi-period and stable states in the two lasers are investigated via varying the current, detuning and coupling level.
文摘The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.
基金National Basic Research Program of China ("973" Program,No.2011CB013605-4)National Natural Science Foundation of China(No.51178079)Major Program of National Natural Science Foundation of China (No.90915011)
文摘The model test of seismic simulation shaking table is an important method to study the seismic design of bridge structure. In order to evaluate the seismic response and dynamic characteristics of pile-water-pier system for developing more reliable design procedures, shaking table model tests of a submerged bridge pier system, including pile groups-cap-pier and inertia mass, were conducted. Since different similitude laws corresponding to different test objectives affected the validity of test results, the similitude law with the aim to consider the effect of hydrodynamic pressure was proposed and confirmed through an actual example. Based on the test results, the effect of water around model on seismic response under seismic excitation input was analyzed and the failure level was judged by observing the variation of basic frequency. The test results indicate that the transfer function of analytical model with water is different from that without water, the natural frequency without water is always higher than that with water, and the first modal shapes are various. It is also concluded that the similitude law is suitable for practical application and the dynamic characteristics and seismic response of the structure system can be changed because of the existence of the surrounding water, which should be paid much attention in the further investigation.
基金supported by the National Natural Science Foundation of China(Grant No. 11171197)the IFGP of Shaanxi Normal University(Grant No. 2011CXB004)the FRF for the Central Universities(Grant No. GK201002006)
文摘Two linear In this letter, we prove the following conclusions by introducing a function Fn(t): (1) If a quantum system S with a time-dependent non-degenerate Hamiltonian H(t) is initially in the n-th eigenstate of H(0), then the state of the system at time t will remain in the n-th eigenstate of H(t) up to a multiplicative phase factor if and only if the values Fn(t) for all t are always on the circle centered at 1 with radius 1; (2) If a quantum system S with a time-dependent Hamiltonian H(t) is initially in the n-th eigenstate of H(0), then the state of the system at time t will remain c-uniformly approximately in the n-th eigenstate of H(t) up to a multiplicative phase factor if and only if the values F,(t) for all t are always outside of the circle centered at 1 with radius 1-ε. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ε-uniformly approximately in the n-th eigenstate of H(t) up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field.
基金supported by the National Natural Science Foundation of China(Nos.11171197,11371012)the Science Foundation of Weinan Normal University(Grant No.14YKS006)+4 种基金the Foundation of Mathematics Subject of Provincial Supporting Subject of Shaanxi Provincethe Civil-Military Integration Research Foundation of Shaanxi Province(No.13JMR12)the Fundamental Research Funds for the Central Universities(Nos.GK201402005,GK201301007)China Postdoctoral Science Foundation(No.2014M552405)the Natural Science Research Program of Shaanxi Province(No.2014JQ1010)
文摘For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ>0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11522540, and 11690021)the Top-Notch Young Talents Program of China, and the Provincial Department of Education of Liaoning (Grant No. L2012087)
文摘The discovery of neutrino oscillation indicates that neutrinos have masses and each flavor state is actually a superposition of three mass states with masses m1,m2,and m3.However,the neutrino oscillation experiments are not able to measure the absolute masses of neutrinos,but can only measure the squared mass differences between the neutrino mass eigenstates—The solar and reactor experiments gave
基金supported by the National Natural Science Foundation of China(11804268)the National Key R&D Program of China(2018YFA0307601)。
文摘Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures.Here,we point out that discrete synthetic Poincaréhalf-planes and Poincarédisks,which are created by lattices in flat planes,support infinitely degenerate eigenstates for any nonzero eigenenergies.Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces.Furthermore,all eigenstates are exponentially localized in the hyperbolic coordinates,signifying the first example of quantum funneling effects in Hermitian systems.As such,any initial wave packet travels towards the edge of the Poincaréhalf-plane or its equivalent on the Poincarédisk,delivering an efficient scheme to harvest light and atoms in two dimensions.Our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.
基金supported by the National Natural Science Foundation of China(Grant Nos.11371012,11171197 and 11401359)the Innovation Fund Project for Graduate Program of Shaanxi Normal University(GrantNo.2013CXB012)+2 种基金the Fundamental Research Funds for the Central Universities(Grant Nos.GK201301007 and GK201404001)the Science Foundation of Weinan Normal University(Grant No.14YKS006)the Foundation of Mathematics Subject of Shaanxi Province(Grant No.14SXZD009)
文摘The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation (SE) by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H(0). Also, we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H(t). On the other hand, any physical experiment may bring errors so that the initial state (input state) may be a superposition of different eigenstates, not just at the desired eigenstate. In this paper, we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t = 0. A generalized adiabatic approximate solution (GAAS) is constructed and an upper bound for the generalized adiabatic approximation error is given. As an application, the fidelity of the exact solution and the GAAS is estimated.
文摘The Hellmann potential, which is a superposition of an attractive Coulomb potential -air and a Yutmwa potential b e-δr /r , is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schr6dinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.
基金Supported by the National Nature Science Foundation of China under Grant No.11275242
文摘The operator level proof of factorization theorem exhibited in [ar Xiv:hep-ph/1307.4194] is extended to the semi-inclusive deep inelastic scattering process(SIDIS). Factorization theorem can be proved at operator level if there are not detected soft hadrons. The key point is that the initial one-nucleon state is the eigenstate of QCD.
基金supported by the National Natural Science Foundation of China under Grant No.11001013
文摘This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectrul distribution of system operator and its quasi-compactness. Some primary reliability indices are discussed with the eigenfunction of system operator and the optimal vacation time to get the maximum system profit is analyzed at the end of paper.
文摘We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V(τ)= V0(a + exp (λτ))/(b + exp (λτ)) + V1( d + exp ( λτ) ) / (b + exp (λτ)). We obtain the bound state energy eigenvalue and the corresponding eigenfunction ex- pressed in terms of the Jaeobi polynomials. By choosing appropriate parameter in the potential model, the generalized Hylleraas potential reduces to the well known potentials as special cases.