The magnetic states of the strongly correlated system plutonium dioxide(PuO_(2)) are studied based on the density functional theory(DFT) plus Hubbard U(DFT +U) method with spin–orbit coupling(SOC) included. A series ...The magnetic states of the strongly correlated system plutonium dioxide(PuO_(2)) are studied based on the density functional theory(DFT) plus Hubbard U(DFT +U) method with spin–orbit coupling(SOC) included. A series of typical magnetic structures including the multiple-k types are simulated and compared in the aspect of atomic structure and total energy. We test LDA, PBE, and SCAN exchange–correlation functionals on PuO_(2) and a longitudinal 3k antiferromagnetic(AFM) ground state is theoretically determined. This magnetic structure has been identified to be the most stable one by the former computational work using the hybrid functional. Our DFT +U + SOC calculations for the longitudinal 3k AFM ground state suggest a direct gap which is in good agreement with the experimental value. In addition, a genetic algorithm is employed and proved to be effective in predicting magnetic ground state of PuO2. Finally, a comparison between the results of two extensively used DFT +U approaches to this system is made.展开更多
We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,th...We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.展开更多
In this paper,we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H^(1)(ℝ^(2)).When the nonlinearity satisfies some general 3-superlinear conditions,w...In this paper,we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H^(1)(ℝ^(2)).When the nonlinearity satisfies some general 3-superlinear conditions,we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in[L.Jeanjean,Existence of solutions with prescribed norm for semilinear elliptic equations,Nonlinear Anal.(1997)].展开更多
We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under som...We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.展开更多
In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a ste...In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.展开更多
We report on electromagnetically induced transparency cooling of ^(40)Ca^(+)to sympathetically cool the threedimensional secular modes of motion in a ^(40)Ca^(+)–^(27)Al^(+)two-ion pair near the ground state.We obser...We report on electromagnetically induced transparency cooling of ^(40)Ca^(+)to sympathetically cool the threedimensional secular modes of motion in a ^(40)Ca^(+)–^(27)Al^(+)two-ion pair near the ground state.We observe simultaneous ground state cooling across all radial modes and axial modes of a ^(40)Ca^(+)–^(27)Al^(+)ion pair,occupying a broader cooling range in frequency space over 3 MHz.The cooling time is observed to be less than 1 ms.The mean phonon number and heating rates of all motional modes are measured.This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of ^(27)Al^(+)optical clock,but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.展开更多
In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger...In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.展开更多
In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence ...In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞.展开更多
We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 0<s,t<1,2s+2t>3 and 2s=6/3-2s is the critical ...We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 0<s,t<1,2s+2t>3 and 2s=6/3-2s is the critical Sobolev exponent in 1R3.Under some more general assumptions on f,we prove that(0.1)admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.展开更多
We consider the Schrodinger-Poisson system with nonlinear term Q(x)|u|^p-1u,where the value of |x|→∞ lim Q(x)may not exist and Q may change sign.This means that the problem may have no limit problem.The existence of...We consider the Schrodinger-Poisson system with nonlinear term Q(x)|u|^p-1u,where the value of |x|→∞ lim Q(x)may not exist and Q may change sign.This means that the problem may have no limit problem.The existence of nonnegative ground state solutions is established.Our method relies upon the variational method and some analysis tricks.展开更多
We study the electronic and magnetic properties of an oxygen-deficient perovskite Ca_2 Mn_2 O_5 based on the first principle calculations. The calculations show that the ground state of Ca_2 Mn_2 O_5 is a D-type anti-...We study the electronic and magnetic properties of an oxygen-deficient perovskite Ca_2 Mn_2 O_5 based on the first principle calculations. The calculations show that the ground state of Ca_2 Mn_2 O_5 is a D-type anti-ferromagnetic structure with the anti-ferromagnetic spin coupling along the c-direction. The corresponding electronic structure of the D-type state is investigated, and the results display that Ca_2 Mn_2 O_5 is an insulator with an indirect energy gap of ~2.08 eV. By the partial density-of-state analysis, the valence band maximum is mainly contributed to by the O-2 p orbitals and the conduction band minimum is contributed to by the O-2 p and Mn-3 d orbitals. Due to the Coulomb repulsion interaction between electrons, the density of state of Mn-3 d is pulled to-6--4.5 eV.展开更多
By investigating a harmonically confined and periodically driven particle system with spin-orbit coupling(SOC)and a specific controlled parameter,we demonstrate an exactly solvable two-level model with a complete set ...By investigating a harmonically confined and periodically driven particle system with spin-orbit coupling(SOC)and a specific controlled parameter,we demonstrate an exactly solvable two-level model with a complete set of spin-motion entangled Schrödinger kitten(or cat)states.In the undriven case,application of a modulation resonance results in the exact stationary states.We show a decoherence-averse effect of SOC and implement a transparent coherent control by exchanging positions of the probability-density wavepackets to create transitions between the different degenerate ground states.The expected energy consisting of quantum and continuous parts is derived,and the energy deviations caused by the exchange operations are much less than the quantum gap.The results could be directly extended to a weakly coupled single-particle chain for transparently encoding spin-orbit qubits via the robust spin-motion entangled degenerate ground states.展开更多
In this article,we study the generalized quasilinear Schrodinger equation-div(ε^2g^2(u)▽u)+ε^2g(u)g′(u)|▽u|^2+V(x)u=K(x)|u|^p-2u,x∈R^N where A≥3,e>0,4<p<,22*,g∈C 1(R,R+),V∈C(R^N)∩L∞(R^N)has a posit...In this article,we study the generalized quasilinear Schrodinger equation-div(ε^2g^2(u)▽u)+ε^2g(u)g′(u)|▽u|^2+V(x)u=K(x)|u|^p-2u,x∈R^N where A≥3,e>0,4<p<,22*,g∈C 1(R,R+),V∈C(R^N)∩L∞(R^N)has a positive global minimum,and K∈C(R^N)∩L∞(R^N)has a positive global maximum.By using a change of variable,we obtain the existence and concentration behavior of ground state solutions for this problem and establish a phenomenon of exponential decay.展开更多
In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,...In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,κ∂_(1)A_(0)=e^(2)A_(2)u^(2),κ∂_(2)A_(0)=−e^(2)A_(1)u^(2),where u∈H^(1)(R^(2)),p∈(2,4),Aα:R^(2)→R are the components of the gauge potential(α=0,1,2),N:R^(2)→R is a neutral scalar field,V(x)is a potential function,the parametersκ,q>0 represent the Chern-Simons coupling constant and the Maxwell coupling constant,respectively,and e>0 is the coupling constant.In this paper,the truncation function is used to deal with a neutral scalar field and a gauge field in the Chern-Simons-Schrödinger problem.The ground state solution of the problem(P)is obtained by using the variational method.展开更多
This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. ...This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. Our results here improve some existing results in the literature.展开更多
Complete active space multiconfiguration self-consisten-field (CAS-MCSCF)calculations are carried out on the ground stae() of W2. The spectroscopic properties(Re=2.078A. De=4.224eV and ωe=304.3cm-1) and the poe...Complete active space multiconfiguration self-consisten-field (CAS-MCSCF)calculations are carried out on the ground stae() of W2. The spectroscopic properties(Re=2.078A. De=4.224eV and ωe=304.3cm-1) and the poential energy curve of the state are reported. The calculations predict the W-W bond order of 5.02.展开更多
This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We stud...This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.展开更多
In <span style="font-family:;" "="">the </span><span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of...In <span style="font-family:;" "="">the </span><span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of the lithium atom and l</span><span style="font-family:;" "="">ithium like ions up to <i>Z</i> = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states <img src="Edit_d92f9e9d-e574-4fa3-91fb-a153db020509.png" alt="" /></span><span style="font-family:;" "="">, <span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><img src="data:image/png;base64,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" alt="" /> <img src="Edit_5bf0039b-89f7-4346-a3cb-178f5df359cf.png" width="0" height="0" alt="" /><img src="data:image/png;base64,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" alt="" /><img src="Edit_41f9b122-3fdc-4f01-9470-542944413516.png" alt="" /></span><span style="font-family:;" "="">and <img src="data:image/png;base64,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" alt="" /><span></span></span><span style="font-family:;" "=""><span> <img src="Edit_79f5e8c8-0b24-4dfd-8b9e-080183cc967f.png" alt="" /></span>of the lithium atom in strong magnetic field are also investigated</span><span style="font-family:;" "="">. </span><span style="font-family:;" "="">Simple trial wave functions for lithium are used.</span>展开更多
In this paper,we consider FPU lattices with particles of unit mass.The dynamics of the system is described by the infinite system of second order differential equations qn= U′(q_(n+1)-q_n)-U′(q_n-q_(n-1)),n ∈ Z,whe...In this paper,we consider FPU lattices with particles of unit mass.The dynamics of the system is described by the infinite system of second order differential equations qn= U′(q_(n+1)-q_n)-U′(q_n-q_(n-1)),n ∈ Z,where qndenotes the displacement of the n-th lattice site and U is the potential of interaction between two adjacent particles.Inspired by previous work due to Szulkin and Weth(Ground state solutions for some indefinite variational problems,J.Funct.Anal.,257(2009),3802-3822),we investigate the existence of solitary ground waves,i.e.,nontrivial solutions with least possible energy.展开更多
基金supported by National Natural Science Foundation of China, (Grant No. 12104034)。
文摘The magnetic states of the strongly correlated system plutonium dioxide(PuO_(2)) are studied based on the density functional theory(DFT) plus Hubbard U(DFT +U) method with spin–orbit coupling(SOC) included. A series of typical magnetic structures including the multiple-k types are simulated and compared in the aspect of atomic structure and total energy. We test LDA, PBE, and SCAN exchange–correlation functionals on PuO_(2) and a longitudinal 3k antiferromagnetic(AFM) ground state is theoretically determined. This magnetic structure has been identified to be the most stable one by the former computational work using the hybrid functional. Our DFT +U + SOC calculations for the longitudinal 3k AFM ground state suggest a direct gap which is in good agreement with the experimental value. In addition, a genetic algorithm is employed and proved to be effective in predicting magnetic ground state of PuO2. Finally, a comparison between the results of two extensively used DFT +U approaches to this system is made.
基金supported by NSFC(12075102 and 11971212)the Fundamental Research Funds for the Central Universities(lzujbky-2020-pd01)。
文摘We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.
基金Supported by the National Natural Science Foundation of China (11971393).
文摘In this paper,we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H^(1)(ℝ^(2)).When the nonlinearity satisfies some general 3-superlinear conditions,we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in[L.Jeanjean,Existence of solutions with prescribed norm for semilinear elliptic equations,Nonlinear Anal.(1997)].
基金supported by National Natural Science Foundation of China(11971202)Outstanding Young foundation of Jiangsu Province(BK20200042)。
文摘We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.
基金the National Natural Science Foundation of China (11971393)。
文摘In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.
基金the National Key R&D Program of China(Grant No.2017YFA0304401)the Technical Innovation Program of Hubei Province(Grant No.2018AAA045)the National Natural Science Foundation of China(Grant No.11904387)。
文摘We report on electromagnetically induced transparency cooling of ^(40)Ca^(+)to sympathetically cool the threedimensional secular modes of motion in a ^(40)Ca^(+)–^(27)Al^(+)two-ion pair near the ground state.We observe simultaneous ground state cooling across all radial modes and axial modes of a ^(40)Ca^(+)–^(27)Al^(+)ion pair,occupying a broader cooling range in frequency space over 3 MHz.The cooling time is observed to be less than 1 ms.The mean phonon number and heating rates of all motional modes are measured.This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of ^(27)Al^(+)optical clock,but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.
文摘In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.
基金supported by National Natural Science Foundation of China(11971393)。
文摘In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞.
基金the Science and Technology Project of Education Department in Jiangxi Province(GJJ180357)the second author was supported by NSFC(11701178).
文摘We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 0<s,t<1,2s+2t>3 and 2s=6/3-2s is the critical Sobolev exponent in 1R3.Under some more general assumptions on f,we prove that(0.1)admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.
基金National Natural Science Foundation of China(11471267)the first author was supported by Graduate Student Scientific Research Innovation Projects of Chongqing(CYS17084).
文摘We consider the Schrodinger-Poisson system with nonlinear term Q(x)|u|^p-1u,where the value of |x|→∞ lim Q(x)may not exist and Q may change sign.This means that the problem may have no limit problem.The existence of nonnegative ground state solutions is established.Our method relies upon the variational method and some analysis tricks.
基金Supported by the National Basic Research Program of China under Grant No 2014CB931703the National Natural Science Foundation of China under Grant Nos 11404172,51101088,and 51171082the Fundamental Research Funds for the Central Universities
文摘We study the electronic and magnetic properties of an oxygen-deficient perovskite Ca_2 Mn_2 O_5 based on the first principle calculations. The calculations show that the ground state of Ca_2 Mn_2 O_5 is a D-type anti-ferromagnetic structure with the anti-ferromagnetic spin coupling along the c-direction. The corresponding electronic structure of the D-type state is investigated, and the results display that Ca_2 Mn_2 O_5 is an insulator with an indirect energy gap of ~2.08 eV. By the partial density-of-state analysis, the valence band maximum is mainly contributed to by the O-2 p orbitals and the conduction band minimum is contributed to by the O-2 p and Mn-3 d orbitals. Due to the Coulomb repulsion interaction between electrons, the density of state of Mn-3 d is pulled to-6--4.5 eV.
基金the National Natural Science Foundation of China(Grant Nos.11204077 and 11475060)the Natural Science Foundation of Hunan Province,China(Grant No.2019JJ10002)+1 种基金the Hunan Provincial Hundred People Plan,China(2019)the Science and Technology Plan Project of Hunan Province,China.
文摘By investigating a harmonically confined and periodically driven particle system with spin-orbit coupling(SOC)and a specific controlled parameter,we demonstrate an exactly solvable two-level model with a complete set of spin-motion entangled Schrödinger kitten(or cat)states.In the undriven case,application of a modulation resonance results in the exact stationary states.We show a decoherence-averse effect of SOC and implement a transparent coherent control by exchanging positions of the probability-density wavepackets to create transitions between the different degenerate ground states.The expected energy consisting of quantum and continuous parts is derived,and the energy deviations caused by the exchange operations are much less than the quantum gap.The results could be directly extended to a weakly coupled single-particle chain for transparently encoding spin-orbit qubits via the robust spin-motion entangled degenerate ground states.
基金supported by the National Natural Science Foundation of China(11661053,11771198,11901345,11901276,11961045 and 11971485)partly by the Provincial Natural Science Foundation of Jiangxi,China(20161BAB201009 and 20181BAB201003)+1 种基金the Outstanding Youth Scientist Foundation Plan of Jiangxi(20171BCB23004)the Yunnan Local Colleges Applied Basic Research Projects(2017FH001-011).
文摘In this article,we study the generalized quasilinear Schrodinger equation-div(ε^2g^2(u)▽u)+ε^2g(u)g′(u)|▽u|^2+V(x)u=K(x)|u|^p-2u,x∈R^N where A≥3,e>0,4<p<,22*,g∈C 1(R,R+),V∈C(R^N)∩L∞(R^N)has a positive global minimum,and K∈C(R^N)∩L∞(R^N)has a positive global maximum.By using a change of variable,we obtain the existence and concentration behavior of ground state solutions for this problem and establish a phenomenon of exponential decay.
基金partially supported by NSFC (12161044)Natural Science Foundation of Jiangxi Province (20212BAB211013)+1 种基金Benniao Li was partially supported by NSFC (12101274)Doctoral Research Startup Foundation of Jiangxi Normal University (12020927)
文摘In this paper,we consider the Chern-Simons-Schrodinger system{−Δu+[e^(2)|A|^(2)+(V(x)+2eA_(0))+2(1+κq/2)N]u+q|u|^(p−2)u=0,−ΔN+κ^(2)q^(2)N+q(1+κq2)u^(2)=0,κ(∂_(1)A_(2)−∂_(2)A_(1))=−eu^(2),∂_(1)A_(1)+∂_(2)A_(2)=0,κ∂_(1)A_(0)=e^(2)A_(2)u^(2),κ∂_(2)A_(0)=−e^(2)A_(1)u^(2),where u∈H^(1)(R^(2)),p∈(2,4),Aα:R^(2)→R are the components of the gauge potential(α=0,1,2),N:R^(2)→R is a neutral scalar field,V(x)is a potential function,the parametersκ,q>0 represent the Chern-Simons coupling constant and the Maxwell coupling constant,respectively,and e>0 is the coupling constant.In this paper,the truncation function is used to deal with a neutral scalar field and a gauge field in the Chern-Simons-Schrödinger problem.The ground state solution of the problem(P)is obtained by using the variational method.
文摘This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. Our results here improve some existing results in the literature.
文摘Complete active space multiconfiguration self-consisten-field (CAS-MCSCF)calculations are carried out on the ground stae() of W2. The spectroscopic properties(Re=2.078A. De=4.224eV and ωe=304.3cm-1) and the poential energy curve of the state are reported. The calculations predict the W-W bond order of 5.02.
文摘This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.
文摘In <span style="font-family:;" "="">the </span><span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of the lithium atom and l</span><span style="font-family:;" "="">ithium like ions up to <i>Z</i> = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states <img src="Edit_d92f9e9d-e574-4fa3-91fb-a153db020509.png" alt="" /></span><span style="font-family:;" "="">, <span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><img src="data:image/png;base64,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" alt="" /> <img src="Edit_5bf0039b-89f7-4346-a3cb-178f5df359cf.png" width="0" height="0" alt="" /><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEoAAAAmCAYAAABj5g1QAAACiUlEQVRoBe2Y643sIAyFXVcKoh6qoYb9sR1QwC3DVzzMG2ISImUjRhoNCUxy/HFsQgD3h0UAWKP2INygmCZ4BpQSCADuKxRTyruHrQelJR4Ex7QB8JD63RQY6paD0kphikXLA+GQ2TmGrtcNWQ6qitCk4QZVYalOGEft1KuwlCcUig+4yURVpZ4S61YrJQTy1jyN8vD3tavlgW+r/xFUuqQbsbRylSZhHpuU411CoaBHieKX93+moJvDIii6EAG7o1KJvC4p0YVWr4qpu7iOJPHP/S4HZQMvnAHQC7hXw8hl70nB5aCm5lRLlM0iRq7646BCwQdwKdUNeApbMtiDGqyYmXNpnN8J0PbpTvVIxNjmtKOcwDjTDlo8Lm9w6dgHfB6oS1HznGZ1EDBcn7rToByYtOaY2U+PL6HJ/pQHnXXlB7TwkLOTXqfTOz45f7U5DQpJ3Pl0X9Nk3cQDP4Ix6rsibB4UorP5I28FXG3izYFPr5BuafgvSD0nh1alddY21zUuYO8LR3XsAdezHaWlKLYVoxlNZ5fXnoKEiOWiEu9Ck8hL3/A/C76/KLFBmUDKlHB1YFJQUBYbNujy4ra790DqYTTSzmmqtca7NVrkQJgAFZ5PMhGtWfKOagbYENM5Fe5XPc27TXIzFX3a5e+5SOMkpKDLxMMBRTcvBDuhCqXdzlORXPOG4QwS9IQHB6RvHO5u5LmgAtn3N1alfB7p50B5V2elIQ/52tHXQPkS0axdHUJU4GkPmP2GGvspUFSw+0W3w4px+iOgmoV/afp9BBTDEteHFCt+yMbkivUDZ9K5m5HABhVZDFsb1BBP7NygIotha4Ma4omd8PPvF/f3nMEGxTTKBsUE9R9taPQ6EOddXwAAAABJRU5ErkJggg==" alt="" /><img src="Edit_41f9b122-3fdc-4f01-9470-542944413516.png" alt="" /></span><span style="font-family:;" "="">and <img src="data:image/png;base64,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" alt="" /><span></span></span><span style="font-family:;" "=""><span> <img src="Edit_79f5e8c8-0b24-4dfd-8b9e-080183cc967f.png" alt="" /></span>of the lithium atom in strong magnetic field are also investigated</span><span style="font-family:;" "="">. </span><span style="font-family:;" "="">Simple trial wave functions for lithium are used.</span>
基金supported by the Specialized Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation of China
文摘In this paper,we consider FPU lattices with particles of unit mass.The dynamics of the system is described by the infinite system of second order differential equations qn= U′(q_(n+1)-q_n)-U′(q_n-q_(n-1)),n ∈ Z,where qndenotes the displacement of the n-th lattice site and U is the potential of interaction between two adjacent particles.Inspired by previous work due to Szulkin and Weth(Ground state solutions for some indefinite variational problems,J.Funct.Anal.,257(2009),3802-3822),we investigate the existence of solitary ground waves,i.e.,nontrivial solutions with least possible energy.