一种新型的两态叠加多模Schrödinger猫态光场的等阶N次方Y压缩

本文根据量子力学的线性叠加原理,构造了由多模(即q模)相干态的相反态|{-Z_j}〉q及多模虚相干态|{Z_j}〉q这两者的线性叠加所组成的一种新型的多模Schrdinger猫态光场|Ψ⁽²⁾〉q,利用新近建立的多模压缩态理论,研究了态|Ψ⁽²⁾〉q的N次方Y压缩效应。结果发现:①当压缩阶数N=2p且p=2m(m=1,2,3,…,…)时,态|Ψ⁽²⁾〉q总是恒处于N-Y最小测不准态;②当压缩阶数N=2p且p=2m+1(m=0,1,2,3,…,…)时,如果各模的初始相位φ_j,态间的初始相位差θ_pq^(I)-θ_nq^(R)以及各单模相干态光场的平均光子数之总和 等满足一定的量子化条件,则态|Ψ⁽²⁾〉q可呈现出周期性变化的、任意阶的N次方Y压缩效应;③当压缩阶数N=2p′+1时,无论p′=2m(m=0,1,2,…,…)还是p′=2m+1(m=0,1,2,3,…,…),只要各模的初始相位φ_j满足一定的量子条件,则当两态叠加几率幅满足r_pq^(I)=r_nq^(R)时,态|Ψ⁽²⁾〉q就恒处于N-Y测不准态,始终不呈现N-Y最小测不准态和N次方Y压缩;而当r_pq^(I)≠r_nq^(R)时,态|Ψ⁽²⁾〉q始终不呈现N-Y测不准态、N-Y最小测不准态和N次方Y压缩效应。     

多模叠加态光场|ψ5(3)〉q中广义磁场4m次方Y压缩

构造了由多模复共轭相干态|{Z_j^*}〉_q、多模复共轭相干态的相反态|{-Z_j^*}〉_q以及多模虚相干态|{iZ_j^*}〉_q的线性叠加所组成的第Ⅴ类三态叠加多模叠加态光场|ψ₅⁽³⁾〉_q.利用多模压缩态理论研究了态|ψ₅⁽³⁾〉_q中广义磁场分量的等幂次N次方Y压缩特性.结果发现:当压缩次数N=2p且p=2m(m=1,2,3,…,…)时,只要各模的初始相位φ_j(j=1,2,…,…,q)、态间的初始相位差(θ₁-θ₂)、(θ₁-θ₃)和(θ₂-θ₃)以及受各模的初始相位φ_j调制的各单模相干态光场的平均光子数之和 等分别满足一定的取值条件,则态|ψ₅⁽³⁾〉_q的广义磁场分量就可呈现出周期性变化的广义非线性等幂次4m次方Y压缩效应.     

MuSR method and tomographic-probability representation of spin states

The muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. The time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. The entanglement phenomenon of a bipartite muon–electron system is investigated, in view of the tomographic analogs of the Bell number and the positive partial transpose (PPT) criterion. Reconstruction of the muon–electron spin state as well as the total spin tomography of the composed system is discussed.     

Nonlinear magnetic phenomena in atomic bose gas

Optically confined (j=1, j=2)-Bose gas is studied. The spin Hamiltonian and the ground state of a set of particles with spins j=1 and j=2 are obtained. Nonlinear magnetic phenomena in the set of particles with j=1 are considered.     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩1腔模总数与压缩阶数两者之积取偶数的情形

利用多模压缩态理论研究了第种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)〉q的等阶N次方H压缩特性.结果发现:1)当腔模总数q与压缩阶数N的乘积取偶数,亦即qN=2p时,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要各模的初始相位差(φ_j^(a)-φ_j^(b))、态间的初始相位差(θ_nq^(aR)-θ_nq^(bR))及光子干涉项的幅度 1R_j^(a)R_j^(b)等分别满足一定的条件,则态|Ψ_||^(ab)〉q的第一和第二正交分量总可分别呈现出周期性变化的等阶N次方H压缩效应.2)当qN=2p且p=2m+1(m=0,1,2,3,…,…)时,若构成态|Ψ_Ⅱ^(ab)〉q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位相等,亦即R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),则态|Ψ_Ⅱ^(ab)〉q可呈现出“等阶N次方H压缩简并”现象.     

Probability representation and quantumness tests for qudits and two-mode light states

Using the tomographic-probability representation of spin states, the quantum behavior of qudits is examined. For a general j-qudit state, we propose an explicit formula for quantumness witness whose negative average value is incompatible with classical statistical model. The probability representations of quantum and classical (2j + 1)-level systems are compared within the framework of quantumness tests. In view of the Jordan–Schwinger map, the method is extended for checking the quantumness of two-mode light states.     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩——2腔模总数与压缩阶数两者之积取奇数的情形

构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}〉q和多模虚共轭相干态的相反态|{-Z_j^(b)*}〉q的线性叠加所组成的第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ(ab)Ⅱ〉q.利用多模压缩态理论,研究了态|Ψ(ab)Ⅱ〉q的等阶N次方H压缩特性.结果发现,在腔模总数与压缩阶数这两者之积取奇数,则当各对应模的初始相位、各对应模的初始相位差,态间的初始相位差、以及光子干涉项的幅度之和等分别满足一定的量子化条件时,态|Ψ(ab)Ⅱ〉q的第一及第二正交分量可分别呈现出周期性变化的等阶N次方H压缩效应.这与现有报道的结果截然不同.     

Evolution Equation for a Joint Tomographic Probability Distribution of Spin-1 Particles

The nine-component positive vector optical tomographic probability portrait of quantum state of spin-1 particles containing full spatial and spin information about the state without redundancy is constructed. Also the suggested approach is expanded to symplectic tomography representation and to representations with quasidistributions like Wigner function, Husimi Q?function, and Glauber-Sudarshan P?function. The evolution equations for constructed vector optical and symplectic tomograms and vector quasidistributions for arbitrary Hamiltonian are found. The evolution equations are also obtained in special case of the quantum system of charged spin-1 particle in arbitrary electro-magnetic field, which are analogs of non-relativistic Proca equation in appropriate representations. The generalization of proposed approach to the cases of arbitrary spin is discussed. The possibility of formulation of quantum mechanics of the systems with spins in terms of joint probability distributions without the use of wave functions or density matrices is explicitly demonstrated.     

Co3+离子自旋态对六方相LaCoO3的低指数晶面稳定性影响的密度泛函理论研究

By the first-principles calculations,most studies indicated that the (11102)-CoO₂ termination of LaCoO₃ cannot be stabilized,which disagrees with the experimental observation.Besides the crystal structure,we found that the spin states of Co³⁺ ions could affect surface stability,which previously were not well considered.By examining the different states of Co³⁺ ions in hexagonal-phase LaCoO₃,including low spin,intermediate spin,and high spin states,the surface grand potentials of these facets are calculated and compared.The results show that the spin states of Co³⁺ ions have an important influence on stability of the LaCoO₃ facets.Different from the previous results,the stability diagrams demonstrate that the (11102)-CoO₂ termination can stably exist under O-rich condition,which can get an agreement with the experimental ones.Furthermore,the surface oxygen vacancy formation energies (E_Ov) of stable facets are computed in different spin states.The E_Ov of these possible exposed terminations strongly depend on the spin state of Co³⁺ ions:in particular,the E_Ov of the HS states is lower than that of other spin states.This indicates that one can tune the properties of LaCoO₃ by directly tuning the spin states of Co³⁺ ions.     

受量子相位调制的两态叠加多模叠加态光场的广义非线性等阶N次方Y压缩

本文根据量子力学中的线性叠加原理,构造了由受量子相位调制的多模(即q模)虚相干态|{i^m₁Z_j}〉q及其相反态|{-i^m₂Z_j}〉q这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场|ψ_m1,m2⁽²⁾〉q.利用新近建立的多模压缩态理论,详细研究了态|ψ_m1,m2⁽²⁾〉q的广义非线性等阶N次方Y压缩特性.结果发现:1)无论态间的初始相位差(θ_m2-θm₁)、各模的初始相位φ_j、腔模总数q、压缩参量R_j以及两态叠加的几率幅r_m1和r_m2等取何值,无论压缩阶数N取奇还是取偶,只要相位调制因子m1和m2与压缩阶数N的关系满足一定的量子化条件,态|ψ_m1,m2⁽²⁾〉q就恒处于等阶N-Y最小测不准态.2)当态间的初始相位差(θ_m2-θm₁)在态间压缩区[2kθπ-π/2+ {R_j²[(m₂-m₁)π/2]},2kθπ+π/2+ {R_j²[(m₂-m₁)π/2]}]内取值时,无论压缩阶数N取奇还是取偶,只要相位调制因子m₁和m₂与N的关系式以及各模的初始相位φ_j等满足一定的量子化条件,态|ψ_m1,m2〉q就可呈现出周期性变化的,任意阶的等阶N次方Y压缩效应.3)利用相位调制因子m₁、m₂与压缩阶数N之间的解析关系式,可直接确定出|ψ_m1,m2〉q呈现等阶N次方Y压缩效应时的压缩阶数N.4)文献2、11、15关于等阶N次方Y压缩的研究结果,仅仅是本文所得普遍性结果在相位调制因子m₁和m₂取不同值时的特例.     

第Ⅱ种强度不等的非对称两态叠加多模叠加态光场的偶数阶等阶N次方Y压缩

本文构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}>_q与多模虚共轭相干态的相反态|{-iZ_j^(b)*}>_q这两者的线性叠加所组成的第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)>_q,利用多模压缩态理论研究了态|Ψ_Ⅱ^(ab)>_q的任意偶数阶等阶N次方Y压缩特性.结果发现:1)在压缩阶数N取偶数,即N=2p的条件下,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要构成态|Ψ_Ⅱ^(ab)>_q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位都不相等,亦即R_j^(a)≠R_j^(b)和φ_j^(a)≠φ_j^(b)(j=1,2,3,…,q),并且 ,则当满足一定的量子化条件(或者在一些闭区间内连续取值)时,态|Ψ_Ⅱ^(ab)>_q总可呈现出周期性变化的、任意偶数阶的等阶N次方Y压缩效应.2)在N=2p且p=2m+1(m=0,1,2,3,…,…)的条件下,若R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),态|Ψ_Ⅱ^(ab)>_q则可呈现出等阶N次方Y压缩简并现象.     

四态叠加多模叠加态光场|Ψe(4),Ⅲ〉q的等阶N次方Y压缩

根据量子力学的线性叠加原理,构造了由多模偶相干态与多模虚偶相干态组成的第Ⅲ种四态叠加多模叠加态光场态|Ψ_e⁽⁴⁾,Ⅲ〉_q的等阶N次方Y压缩特性.结果发现:1) 当压缩阶数N=4m,(m=1,2,3,…)时,态|Ψ_e⁽⁴⁾,Ⅲ〉_q恒处于等阶数N-Y最小测不准态;2) 当压缩阶数N=4m′+2,(m′=0,1,2,…)时,在(θ₁-θ₂),q,R_j,r₁,r₂等取不同的组合定值下,态|Ψ_e⁽⁴⁾,Ⅲ〉_q可分别呈现出等阶N次方Y压缩效应与"半相干态"效应;3) 当压缩阶数N为奇数时,在(θ₁-θ₂),q,R_j,r₁,r₂等取不同的组合定值下,态|Ψ_e⁽⁴⁾,Ⅲ〉_q可呈现出等阶N次方Y压缩效应.     

Metastates in Finite-type Mean-field Models: Visibility,Invisibility, and Random Restoration of Symmetry

We consider a general class of disordered mean-field models where both the spin variables and disorder variables η take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate describing the probabilities to find a large system close to a particular convex combination of the pure infinite-volume states. We show that, under a non-degeneracy assumption, only pure states j are seen, with non-random probability weights w _j for which we derive explicit expressions in terms of interactions and distributions of the disorder variables. We provide a geometric construction distinguishing invisible states (having w _j =0) from visible ones. As a further consequence we show that, in the case where precisely two pure states are available, these must necessarily occur with the same weight, even if the model has no obvious symmetry relating the two.     

Maximal entanglement of bipartite spin states in the context of quantum algebra

In the framework of the U _q (su(2)) quantum algebra, we investigate the entanglement properties of two-spin systems, of arbitrary spins j ₁ and j ₂, defined in an entanglement of deformed spin coherent states of each of the spins. We derive the amount of entanglement and we give conditions under which bipartite entangled states become maximally entangled. Using these conditions, we construct a large class of Bell states for any choices of the parameters that specify the spin coherent states.     

态|ψ5(3)〉q中广义电场的2(2m+1)次方Y压缩特性

利用多模压缩态理论,研究了由多模复共轭相干态|{Z_j^*}〉_q(j =1,2,3,…,…,q)、多模复共轭相干态的相反态|{-Z_j^*}〉_q和多模虚相干态|{iZ_{j}〉q的线性叠加所组成的第Ⅴ类三态叠加多模叠加态光场|ψ5⁽³⁾〉q中广义电场分量的等幂次N次方Y压缩特性 .结果发现 :当压缩次数N=2 p且p=2m+1(m=0,1,2,…,…)时,在一定的条件下,态|ψ5⁽³⁾〉q的广义电场分量(即第二正交相位分量)可呈现出周期性变化的、偶数次的等幂次2(2m+1)次方Y压缩效应 .}     

The driven-oscillator evolution in the tomographic-probability representation

We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and squeezed reference frames in the system??s phase space. For some specific oscillator states like coherent states and nth excited states, the tomographic-probability distributions (called the state tomograms) are found in an explicit form. The evolution equation for the tomograms is discussed for the classical and quantum driven oscillators, and the tomographic propagator for this equation is studied.     

态|Ψ(3)〉q中广义电场分量的不等幂次Nj次方Y压缩

利用多模压缩态理论,研究了由多模复共轭虚相干态|{iZ_j^*}〉q、多模复共轭虚相干态的相反态|{-iZ_j^*}〉q和多模复共轭相干态|{Z_j^*}〉q的线性叠加所组成的新型三态叠加多模叠加态光场|Ψ⁽³⁾〉_q中广义电场分量的偶数次不等幂次Nj次方Y压缩特性.结果发现:在各模的压缩次数N_j=2pj且pj=2m′j+1(m′j=0,1,2,3,…,…)和Nj′=2pj′且pj′=2m′j′+1(m′j′=0,1,2,3,…,…)的条件下,当各模的初始相位φ_j与φ_j′、态间的初始相位差(θ₁-θ₃)与(θ₂-θ₃),以及各单模相干态光场总的平均光子数之和qj=1R2j等分别满足一定的取值条件时,态|Ψ⁽³⁾〉_q的广义电场分量(即第二正交相位分量)总可呈现出周期性变化的、偶数次的广义非线性不等幂次N_j次方Y压缩效应.     

Calculations of inelastic cross sections for rotational excitation

Cross sections for scattering of N₂ (j=0) molecules on He atoms are calculated for relative energies below the excitation threshold for the N₂ (j=2) rotational state. The close coupling method is used and the coupled differential equations are solved numerically. Very sharp resonances (corresponding to a lifetime of 10^?10 sec) caused by quasistable states of the N₂He system are found in the calculated cross section, when the closed channels corresponding to the N₂ (j=2) states were included in the coupled equations. The position of the resonances is compared with the calculated energy eigenvalues of the corresponding two body potential. Furthermore the equilibrium concentration of the N₂He quasistable and orbiting states is calculated at 80 °K andp _{N 2}=1 Atm. Both concentrations are found to be 1%.     

一种新型的两态叠加多模叠加态光场的广义非线性等阶N次方H压缩

本文根据量子力学中的线性叠加原理,构造了由多模(即 q模)相干态的相反态 | {-Z_j}〉_q及多模虚相干态的相反态 | {-iZ_j}〉_q 这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场 | ψ_msc⁽²⁾〉_q 利用新近建立的多模压缩态理论,详细研究了态 | ψ_msc⁽²⁾〉_q 的广义非线性等阶N次方H压缩特性 结果发现:1)当压缩阶数N与腔模总数q这两者之积为偶数,亦即当q·N =2p且p =2m(m =1,2,3,…,…)时,态 | ψ_msc⁽²⁾〉_q恒处于等阶N-H最小测不准态;2)当q·N =2p且 p =2m′+ 1(m′ =0,1,2,3,…,…)时,如果各模的初始相位之和 、态间的初始相位差(θ_nq^(I)-θ_nq^(R))、各多模相干态光场的总的平均光子数 以及 [(θ_nq^(I)-θ_nq^(R))+ ]等满足一定的量子化条件时,态 | ψ_msc⁽²⁾〉_q 总可呈现出周期性变化的、任意阶的等阶N次方H压缩效应;3)当压缩阶数N与腔模总数 q这两者之积为奇数时,亦即当 q·N =2p + 1时,无论 p =2m(m =0,1,2,3,…,…)还是 p =2m′ + 1(m′ =0,1,2,3,…,…),只要各模初始相位之和 满足一定的量子化条件,则当两态叠加几率幅满足r_nq^(R) =r_nq^(I) 时,态 | ψ_msc⁽²⁾〉_q 就恒处于N-H测不准态