共查询到20条相似文献,搜索用时 15 毫秒
1.
Hongyi FAN 《理论物理通讯》1991,16(2):245-248
We find that a three-mode boson realization of the SU(1,1) Lie algebra is involved in solving the three coupled harmonic oscillators' problem. Tire unitary operator U, which is found to be able to transform the Fock space of a three-dimcrrsional isotropic Irarmonic oscillator into the space in which the Hamiltonian of three coupled oscillators is diagonized, is further decomposed as a quantum-mechanical rotation in three-mode Hilbert space followed by an SU(1,1) squeezing transformation. The coordinate representation of this SU(1,1) unitary operator is obtained. 相似文献
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De Paul SM Saalwächter K Graf R Spiess HW 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2000,146(1):140-156
Recent multiple-quantum MAS NMR experiments have shown that a change in the rotor phase (and, hence, in the Hamiltonian) between the excitation and reconversion periods can lead to informative spinning-sideband patterns. However, such "rotor encoding" is not limited to multiple-quantum experiments. Here it is shown that longitudinal magnetization can also be rotor-encoded. Both homonuclear and heteronuclear rotor encoding of longitudinal magnetization (RELM) experiments are performed on dipolar-coupled spin-1/2 systems, and the corresponding sideband patterns in the indirect dimension are analyzed. In both cases, only even-order sidebands are produced, and their intensity distribution depends on the durations of the recoupling periods. In heteronuclear experiments using REDOR-type recoupling, purely dipolar sideband patterns that are entirely free of effects due to the chemical-shielding anisotropy can be generated. Advantages and disadvantages of the heteronuclear RELM experiment are discussed in the context of other methods used to measure heteronuclear dipolar couplings. 相似文献
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Rozhkov A. V. 《The European Physical Journal B - Condensed Matter and Complex Systems》2005,47(2):193-206
We find a unitary operator which asymptotically diagonalizes the
Tomonaga-Luttinger Hamiltonian of one-dimensional spinless electrons. The
operator performs a Bogoliubov
rotation in the space of electron-hole pairs. If bare interaction of the
physical electrons is sufficiently small this transformation
maps the original Tomonaga-Luttinger system on a system of free fermionic
quasiparticles. Our representation is useful when the electron dispersion
deviates from linear form. For such situation we obtain non-perturbative
results for the electron gas free energy and the density-density
propagator. 相似文献
4.
Kyu Hwang Yeon Suk Seong Kim Chung In Um Thomas F. George 《International Journal of Theoretical Physics》2003,42(9):2043-2059
Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively. 相似文献
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《中国物理 B》2015,(9)
We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring S1, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The cyclic ground-state quantum distance and the second derivative of the ground-state energy are studied in different exchange coupling parameter regions. Particularly, we show that, in the case of exchange coupling parameter J a = J b, the quantum ferromagnetic phase can be characterized by an invariant quantum distance and this distance will decay to zero rapidly in the paramagnetic phase. 相似文献
9.
FAN Hong-Yi Hai-Liang 《理论物理通讯》2006,46(4):599-602
We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU(1,1) algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld's invariant operator theory of treating timedependent harmonic oscillators. 相似文献
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S. I. Doronin I. I. Maksimov E. B. Fel’dman 《Journal of Experimental and Theoretical Physics》2000,91(3):597-609
Multiple-quantum spin dynamics is studied using analytic and numerical methods for one-dimensional finite linear chains and rings of nuclear spins 1/2 coupled by dipole-dipole interactions. An approximation of dipole-dipole interaction between nearest neighbors having the same constants is used to obtain exact expressions for the intensities of the multiple-quantum coherences in the spin systems studied, which are initially in thermal equilibrium and whose evolution is described by a two-spin two-quantum Hamiltonian. An approximation of nearest neighbors with arbitrary dipole-dipole interaction constants is used to establish a simple relationship between the multiple-quantum dynamics and the dynamics of spin systems with an XY Hamiltonian. Numerical methods are developed to calculate the intensities of multiple-quantum coherences in multiple-quantum NMR spectroscopy. The integral of motion is obtained to expand the matrix of the two-spin two-quantum Hamiltonian into two independent blocks. Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field. Results of calculations of the multiple-quantum dynamics in linear chains of seven and eight nuclear spins and a six-spin ring are presented. It is shown that the evolution of the intensities of the lowest-order multiple-quantum coherences in linear chains is accurately described allowing for dipole-dipole interaction of nearest and next-nearest neighbors only. Numerical calculations are used to compare the contributions of nearest and remote spins to the intensities of the multiple-quantum coherences. 相似文献
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We show that, by means of a right-unitary transformation, the fully quantized Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau-Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation. 相似文献
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We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schrödinger equation for the density matrix of spin-1/2 particles in the presence of an electromagnetic field. The Liouville operator for the particle with spin follows from using the Wigner–Moyal transformation and a suitable Clifford algebra constructed on the phase space of a (4 + 1)-dimensional space–time with Galilean geometry. Connections with the algebraic formalism of thermofield dynamics are also investigated. 相似文献
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Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic nonperturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure. 相似文献
15.
The Supersymmetry and Eigen Energy Spectrum of a Charged Dirac Particle in a Uniform Constant Magnetic Field
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Based on the opinion that the γ-matrices in Dirac equation have structure and are decomposable, we decompose the γ-matrices into the direct product of the operators in the spin space and the particle-antiparticle space. By using this method, we attain a complete set of commutative operators, a set of quantum numbers and the correspondingly eigen solutions of the Hamiltonian for a charged Dirac particle moving in a uniform constant magnetic field. In addition, the dynamic supersymmetry of the Hamiltonian is unveiled. Spin symmetry breaking and particle-antiparticle symmetry breaking are discussed, and the supersymmetric group operator of the degenerate spin subspace resulting from the spin residual supersymmetry is found. 相似文献
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介观互感耦合阻尼LC并联电路的量子化能谱 总被引:2,自引:1,他引:1
对介观互感耦合阻尼并联LC电路作双模耦合阻尼谐振子处理,将其量子化,通过三次幺正变换,将体系的哈密顿量对角化,在此基础上给出了体系的能谱。 相似文献
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《Nuclear Physics B》1999,551(3):705-722
The covariant operator quantization of the ordinary free spinning BDH string modified by adding the supersymmetric Liouville sector is analysed in the even target space dimensions d = 2, 4, 6, 8. The spectrum generating algebra for this model is constructed and a general version of the no-ghost theorem is proven. The counterpart of the GSO projection leads to a family of tachyon-free unitary free string theories. One of these models is equivalent to the non-critical Ramond-Neveu-Schwarz spinning string truncated in the Neveu-Schwarz sector to the tachyon-free eigenspace of the fermion parity operator. 相似文献
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利用二次型理论构造一个幺正矩阵进行坐标和动量变换,把n模动量耦合谐振子体系的哈密顿量化为标准的二次型,进而得到n模动量耦合谐振子体系的能量本征值.对n模坐标耦合的情况也进行了类似求解,并提供了解决该类问题的一般数学方法. 相似文献
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Wensen Liu 《Annals of Physics》2004,312(2):480-491
A time-dependent closed-form formulation of the linear unitary transformation for harmonic-oscillator annihilation and creation operators is presented in the Schrödinger picture using the Lie algebraic approach. The time evolution of the quantum mechanical system described by a general time-dependent quadratic Hamiltonian is investigated by combining this formulation with the time evolution equation of the system. The analytic expressions of the evolution operator and propagator are found. The motion of a charged particle with variable mass in the time-dependent electric field is considered as an illustrative example of the formalism. The exact time evolution wave function starting from a Gaussian wave packet and the operator expectation values with respect to the complicated evolution wave function are obtained readily. 相似文献