To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-SchrSdinger scheme with block-matrix implementation on efficient evaluation of nonli...To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-SchrSdinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focusing on the effects of intermolecular transfer coupling and bi-exciton interaction.展开更多
The Schrodinger equation -△u+λ2u=|u|2q-2u has a unique positive radial solution Uλ, which decays exponentially at infinity. Hence it is reasonable that the Schrolinger system -△u1+u1=|u1|2q-1u1-εb(x)|u2...The Schrodinger equation -△u+λ2u=|u|2q-2u has a unique positive radial solution Uλ, which decays exponentially at infinity. Hence it is reasonable that the Schrolinger system -△u1+u1=|u1|2q-1u1-εb(x)|u2|1|u1|q-1u1,-△u2+u2=|u2|2q-2u2-εb(x)|u1|1|u2|q-1u2 has multiple-bump solutions which behave like Uλ in the neighborhood of some points. For u=(u1,u2)∈H1(R3)×H1(R3), a nonlinear functional Iε(u)=I1(u1)+I2(u2)-ε/q∫R3b(x)|u1|q|u2|qdx,is defined,where I1(u1)=1/2||u1||2-1/2q∫R3|u1|2qdx and I2(u2)=1/2||u2||2ω-1/2q∫R3|u2|2qdx. It is proved that the solutions of the system are the critical points of I,. Let Z be the smooth solution manifold of the unperturbed problem and TzZ is the tangent space. The critical point of I is rewritten as the form of z + w, where w ∈ (TzZ)⊥. Using some properties of Iε, it is proved that there exists a critical point of I, close to the form which is a multi-bump solution.展开更多
To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the tim...To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.展开更多
The cubic-quintic nonlinear Schroedinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic sol...The cubic-quintic nonlinear Schroedinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients (vCQNLS) are derived with the aid of a set of subsidiary high-order ordinary differential equations (sub-equations for short). The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.展开更多
The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation...The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system.展开更多
The distributions of the quantum vibrational energy levels of the protein molecular chain are found by the discretely nonlinear Schr?dinger equation appropriate to protein obtained from the Davydov theory. The results...The distributions of the quantum vibrational energy levels of the protein molecular chain are found by the discretely nonlinear Schr?dinger equation appropriate to protein obtained from the Davydov theory. The results calculated by this method are basically consistent with the experimental values. Furthermore, the energy spectra at high excited states have also been obtained for the molecular chain which is helpful in researching the properties of infrared absorption and Raman scattering of the protein molecules.展开更多
In this paper, a new type (or the second type) of transformation which is used to map the variable coefficient nonlinear Schr6dinger (VCNLS) equation to the usual nonlinear Schrodinger (NLS) equation is given. A...In this paper, a new type (or the second type) of transformation which is used to map the variable coefficient nonlinear Schr6dinger (VCNLS) equation to the usual nonlinear Schrodinger (NLS) equation is given. As a special case, a new kind of nonautonomous NLS equation with a t-dependent potential is introduced. Further, by using the new transformation and making full use of the known soliton and rogue wave solutions of the usual NLS equation, the corresponding kinds of solutions of a special model of the new nonautonomous NLS equation are discussed respectively. Additionally, through using the new transformation, a new expression, i.e., the non-rational formula, of the rogue wave of a special VCNLS equation is given analytically. The main differences between the two types of transformation mentioned above are listed by three items.展开更多
We obtain exact spatiotemporal similaritons to a (3+ l)-dimensional inhomogeneous nonlinear Schrodinger equation, which describes the propagation of optical pulses in a cubic-quintic nonlinearity medium with distri...We obtain exact spatiotemporal similaritons to a (3+ l)-dimensional inhomogeneous nonlinear Schrodinger equation, which describes the propagation of optical pulses in a cubic-quintic nonlinearity medium with distributed dispersion and gain. A one-to-one correspondence between such self-similar waves and solutions of the elliptic equation is found when a certain compatibility condition is satisfied. Based on exact solutions, we discuss evolutional behaviors of self-similar cnoidal waves and chirped similaritons in two kind of typicai soliton control systems. Moreover, the comparison between chirped similaritons and chirp-free solitons is given.展开更多
By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-Xi Liu et al. [Phys. Rev. A 63 (2001) 033816]....By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-Xi Liu et al. [Phys. Rev. A 63 (2001) 033816]. The influence of the external laser field on the quantum decoherence of a mesoscopically superposed state of the excitons is investigated. Our result shows that, the classical field can compensate the energy dissipation of the excitons. Although the decoherence rate of the excitonic Schr?dinger cat state does not depend on the external field, the phase of the decoherence factor can be well controlled by adjusting the amplitude of the external field as well as the detuning between the field and the transition frequency of the atom.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
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting (MSS) method to solve the two-dimensional nonlinear Schrodinger equation (2D-NLSE) in this pap...Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting (MSS) method to solve the two-dimensional nonlinear Schrodinger equation (2D-NLSE) in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.展开更多
An improved homogeneous balance principle and self-similar solutions to the cubic-quintic nonlinear Schroedinger and impose constraints on the functions describing dispersion, self-similar waves are presented.
基金This work was supported by the National Natural Science Foundation of China (No.21033008 and No.21073169)the National Basic Research Program of China (No.2010CB923300 and No.2011CB921400)and the Hong Kong RGC (No.604709) and UGC (AoE/P04/08-2) is gratefully acknowledged.
文摘To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-SchrSdinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focusing on the effects of intermolecular transfer coupling and bi-exciton interaction.
基金The National Natural Science Foundation of China(No.11171063)the Natural Science Foundation of Jiangsu Province(No.BK2010404)
文摘The Schrodinger equation -△u+λ2u=|u|2q-2u has a unique positive radial solution Uλ, which decays exponentially at infinity. Hence it is reasonable that the Schrolinger system -△u1+u1=|u1|2q-1u1-εb(x)|u2|1|u1|q-1u1,-△u2+u2=|u2|2q-2u2-εb(x)|u1|1|u2|q-1u2 has multiple-bump solutions which behave like Uλ in the neighborhood of some points. For u=(u1,u2)∈H1(R3)×H1(R3), a nonlinear functional Iε(u)=I1(u1)+I2(u2)-ε/q∫R3b(x)|u1|q|u2|qdx,is defined,where I1(u1)=1/2||u1||2-1/2q∫R3|u1|2qdx and I2(u2)=1/2||u2||2ω-1/2q∫R3|u2|2qdx. It is proved that the solutions of the system are the critical points of I,. Let Z be the smooth solution manifold of the unperturbed problem and TzZ is the tangent space. The critical point of I is rewritten as the form of z + w, where w ∈ (TzZ)⊥. Using some properties of Iε, it is proved that there exists a critical point of I, close to the form which is a multi-bump solution.
文摘To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.
基金The project supported in part by Natural Science Foundation of Henan Province of China under Grant No. 2006110002 and the Science Foundation of Henan University of Science and Technology under Grant No. 2004ZD002
文摘The cubic-quintic nonlinear Schroedinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients (vCQNLS) are derived with the aid of a set of subsidiary high-order ordinary differential equations (sub-equations for short). The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.
基金The project partially supported by the Research Grants Council under Grant Nos, HKU 7123/05E and HKU 7184/04E
文摘The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system.
文摘The distributions of the quantum vibrational energy levels of the protein molecular chain are found by the discretely nonlinear Schr?dinger equation appropriate to protein obtained from the Davydov theory. The results calculated by this method are basically consistent with the experimental values. Furthermore, the energy spectra at high excited states have also been obtained for the molecular chain which is helpful in researching the properties of infrared absorption and Raman scattering of the protein molecules.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10971109 and 10971211supported by Program for New Century Excellent Talents in University under Grant No.NCET-08-0515
文摘In this paper, a new type (or the second type) of transformation which is used to map the variable coefficient nonlinear Schr6dinger (VCNLS) equation to the usual nonlinear Schrodinger (NLS) equation is given. As a special case, a new kind of nonautonomous NLS equation with a t-dependent potential is introduced. Further, by using the new transformation and making full use of the known soliton and rogue wave solutions of the usual NLS equation, the corresponding kinds of solutions of a special model of the new nonautonomous NLS equation are discussed respectively. Additionally, through using the new transformation, a new expression, i.e., the non-rational formula, of the rogue wave of a special VCNLS equation is given analytically. The main differences between the two types of transformation mentioned above are listed by three items.
基金Supported by the National Natural Science Foundation of China under Grant No.10974177by the Ministry of Science and Technology of China under Grant No.2010DFA04690
文摘We obtain exact spatiotemporal similaritons to a (3+ l)-dimensional inhomogeneous nonlinear Schrodinger equation, which describes the propagation of optical pulses in a cubic-quintic nonlinearity medium with distributed dispersion and gain. A one-to-one correspondence between such self-similar waves and solutions of the elliptic equation is found when a certain compatibility condition is satisfied. Based on exact solutions, we discuss evolutional behaviors of self-similar cnoidal waves and chirped similaritons in two kind of typicai soliton control systems. Moreover, the comparison between chirped similaritons and chirp-free solitons is given.
文摘By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-Xi Liu et al. [Phys. Rev. A 63 (2001) 033816]. The influence of the external laser field on the quantum decoherence of a mesoscopically superposed state of the excitons is investigated. Our result shows that, the classical field can compensate the energy dissipation of the excitons. Although the decoherence rate of the excitonic Schr?dinger cat state does not depend on the external field, the phase of the decoherence factor can be well controlled by adjusting the amplitude of the external field as well as the detuning between the field and the transition frequency of the atom.
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Supported by the Natural Science Foundation of China under Grant No.0971226the 973 Project of China under Grant No.2009CB723802+1 种基金the Research Innovation Fund of Hunan Province under Grant No.CX2011B011the Innovation Fund of NUDT under Grant No.B110205
文摘Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting (MSS) method to solve the two-dimensional nonlinear Schrodinger equation (2D-NLSE) in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
基金Supported by Natural Science Foundation of Zhejiang Province of China under Grant Nos.Y604106 and Y606182the Special Foundation of "University Talent Indraught Engineering" of Guangdong Province of China under Grant No.GDU2009109the Key Academic Discipline Foundation of Guangdong Shaoguan University under Gant No.KZ2009001
文摘An improved homogeneous balance principle and self-similar solutions to the cubic-quintic nonlinear Schroedinger and impose constraints on the functions describing dispersion, self-similar waves are presented.