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
We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion ...We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and O, the hyperbolic function solutions （including the solitary wave solutions） and trigonometric solutions are also given respectively.展开更多
Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing...Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.展开更多
Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋ 1）-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd ...Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋ 1）-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.展开更多
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt d...We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.展开更多
An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explic...An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.展开更多
The simplest spin-orbital model can host a nematic spin-orbital liquid state on the triangular lattice.We provide clear evidence that the ground state of the SU(4)Kugel-Khomskii model on the triangular lattice can be ...The simplest spin-orbital model can host a nematic spin-orbital liquid state on the triangular lattice.We provide clear evidence that the ground state of the SU(4)Kugel-Khomskii model on the triangular lattice can be well described by a‘‘single”Gutzwiller projected wave function with an emergent parton Fermi surface,despite it exhibits strong finite-size effect in quasi-one-dimensional cylinders.The finite-size effect can be resolved by the fact that the parton Fermi surface consists of open orbits in the reciprocal space.Thereby,a stripy liquid state is expected in the two-dimensional limit,which preserves the SU(4)symmetry while breaks the translational symmetry by doubling the unit cell along one of the lattice vector directions.It is indicative that these stripes are critical and the central charge is c=3,in agreement with the SU(4)1Wess-Zumino-Witten conformal field theory.All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.展开更多
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.
基金河南省自然科学基金，河南省教育厅自然科学基金，the Science Foundation of Henan University of Science and Technology
文摘We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and O, the hyperbolic function solutions （including the solitary wave solutions） and trigonometric solutions are also given respectively.
文摘Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.
基金The project supported by the National Natural Science Foundation of China under Grant No. 10272071, the Natural Science Foundation of Zhejiang Province of China under Grant No. Y504111, and the Science Research Foundation of Huzhou University
文摘Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋ 1）-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We invest/gate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.
文摘We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.
基金Supported by the Natural Science Foundation of China under the grant 11026165 and 11072053Doctaral Fund of Ministry of Education of China under the grant 20100041120037the Fundamental Research Funds for the Central Universities
文摘An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.
基金supported by the National Natural Science Foundation of China(12034004 and 11774306)the K.C.Wong Education Foundation(GJTD2020–01)+3 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(XDB28000000)funded by the European Research Council(ERC)under the European Unions Horizon 2020 Research and Innovation Program(771537)supported by the Deutsche Forschungsgemeinschaft through project A06 of SFB 1143(247310070)The numerical simulations in this work are based on the GraceQ project(www.gracequantum.org)。
文摘The simplest spin-orbital model can host a nematic spin-orbital liquid state on the triangular lattice.We provide clear evidence that the ground state of the SU(4)Kugel-Khomskii model on the triangular lattice can be well described by a‘‘single”Gutzwiller projected wave function with an emergent parton Fermi surface,despite it exhibits strong finite-size effect in quasi-one-dimensional cylinders.The finite-size effect can be resolved by the fact that the parton Fermi surface consists of open orbits in the reciprocal space.Thereby,a stripy liquid state is expected in the two-dimensional limit,which preserves the SU(4)symmetry while breaks the translational symmetry by doubling the unit cell along one of the lattice vector directions.It is indicative that these stripes are critical and the central charge is c=3,in agreement with the SU(4)1Wess-Zumino-Witten conformal field theory.All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.
