自旋为1粒子在旋转磁场中的几何相位和动力学相位(英文)

文章研究了自旋为1的粒子在旋转磁场中的几何相位和动力学相位.推导出如何计算自旋为1的粒子在绝热和非绝热演化中的几何相位和动力学相位公式,并利用这些公式计算其相位.最后我们讨论了三种情况下的Berry相位,当考虑ω1<<ω时,系统处于绝热近似,此时,几何相位就是Berry相位.     

Supersymmetric Quantum Mechanics and SUSY Dependent SU(2) Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SU_τ(2) \otimes SU_σ(2) symmetry in the context of the relativistic Pauli Hamiltonian squared. We show that there exists also an SU(2) symmetry associated with the supersymmetry of the Dirac particle.     

Geometric Phase for Two Entangled Spin-1/2 Particles in a Magnetic Field

In this paper the geometric phases of two entangled spin-1/2 particles in the presence and absence of spin-spin interaction are calculated. We also discuss the geometric phases when only one of the two particles is affected by the external magnetic field. Our results show that the geometric phase in this case is not equal to that of a single particle under the same evolution condition because of the effect of entanglement. We further study the entanglement dependence of the noncyclic geometric phases in the interacting and noninteracting spins under a time-independent uniform magnetic field. A general entanglement-dependence geometric phase is formulated.     

Discrete Energy Spectrum for a Spin-1/2 Quantum Particle Under the Influence of a Constant Force Field due to the Presence of Topological Defects

We study a spin-1/2 quantum particle under a constant force field in the presence of a uniform distribution of parallel screw dislocations. We solve the Schröndiger equation, exactly, and find a discrete energy spectrum.     

Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field *

By using the infinite time-evolving block decimation, we study quantum fidelity and entanglemententropy in the spin-1/2 Heisenberg alternating chain under an external magnetic field .The effects of the magnetic field on the fidelity are investigated, and its relation with the quantum hase transition (QPT) is analyzed. The phase diagram of the model is given accordingly, which supports the Haldane phase, the singlet-dimer phase, the Luttinger liquid phase and the paramagnetic phase. The scaling of entanglement entropy in the gapless Luttinger liquid phase is studied, and the central charge $c=1$ is obtained. We also study the relationship between the quantum coherence, string order parameter and QPTs. Results obtained from these quantum information observations are consistent with the previous reports.     

The Gravitational Chiral Anomaly of the Spin-1/2 Field in the Presence of Twisted Boundary Conditions for Ordinary Field Theory

We calculate the chiral anomaly in the neighborhood of the fixed point space which is constructed by the group action of a discrete symmetry h on a compact manifold . The Feynman diagrams approach for the corresponding supersymmetric quantum mechanical system with twisted boundary conditions is used. The result we derive in this way agrees with the generalization of the ordinary index theorem (the G-index theorem) on the spin complex.     

Relativistic Quantum Correlations Between Spin-1/2 Particles

It is shown that a fully relativistic formulation of spin measurements and correlations does not add any new feature to the standard analysis of Bell and the deduction of his inequality. It follows, therefore, that the motion of reference frames does not affect the correlations between spatially separated particles.     

Soliton Lattice State of Spin—1／2 Antiferromagnetic Chain in an External Magnetic Field

One-dimensional spin-1-2 anisotropic Heisenberg antiferromagnet in a longitudinal external magnetic field is studied using bosonization method and Gaussian wave functional techniques which take account of the spatial structure.The magnetization and the energy of the ground state which depend on the external magnetic field are calculated.For the case of anisotropic parameter △＞△0,increasing of the external magnetic field above the threshold value leads to the appearance of the soliton lattice state in the ground state,until to an another critical field where the ground state changes to the canted state phase.Therefore,with increasing external magnetic field,the ground state experiences four different phases successively,namely,antiferromagnetic Ising,soliton lattice state canted state,and magnetization saturated phases.When △＜△0,the soliton lattice state phase does not appear,with increasing external field,the paramagnetic phase smoothly evolves into the canted state phase,finally reaches magnetization saturated phase.     

Magnetic Properties of Spin-1/2 Ising Superlattice

Using the effective-field theory we studied the magnetic properties of a spin-1/2 Ising supedattice, which consist of three different ferromagnet materials. The magnetic behavior of this superlattice is examined. The critical temperature and the compensation temprature of the system are studied as a function of the exchange interactions between the nearest-neiboring spins across the interface and in the intraface. Temperature dependence of magenetizations is also given.     

Extraordinary Electromagnetic Waves in Weakly Relativistic Degenerate Spin-1/2 Magnetized Quantum Plasmas

By using the relativistic quantum magnetohydrodynamic model, the extraordinary electromagnetic waves in magnetized quantum plasmas are investigated with the effects of particle dispersion associated with the quantum Bohm potential effects, the electron spin-1/2 effects, and the relativistic degenerate pressure effects. The electrons are treated as a quantum and magnetized species, while the ions are classical ones. The new general dispersion relations are derived and analyzed in some interesting special cases. Quantum effects are shown to affect the dispersion relations of the extraordinary electromagnetic waves. It is also shown that the relativistic degenerate pressure effects significantly modify the dispersive properties of the extraordinary electromagnetic waves. The present investigation should be useful for understanding the collective interactions in dense astrophysical bodies,such as the atmosphere of neutron stars and the interior of massive white dwarfs.     

The CPT Group of the Spin-3/2 Field

We find out that both the matrix and the operator CPT groups for the spin-3/2 field (with or without mass) are respectively isomorphic to D ₄⋊ℤ₂ and Q×ℤ₂. These groups are exactly the same groups as for the Dirac field, though there is no a priori reason why they should coincide.     

Magnetic Properties of an Antiferromagnetic Spin-1/2 XYZ Model in the Presence of Different Magnetic Fields: Finite-Size Effects of Inhomogeneity Property*

Magnetic and thermodynamic properties of the anisotropic XYZ spin-1/2 finite chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at low temperature. Using exact diagonalization method (ED), we study the magnetization, magnetic susceptibility, and specific heat of the model characterized in terms of the finite correlation length in the presence of three different magnetic fields including longitudinal, transverse, and transverse staggered magnetic fields. The magnetization, susceptibility, and the specific heat of the model are investigated under two conditions separately: (i) When the model is putted in the presence of homogeneous magnetic fields. (ii) When finite inhomogeneities are considered for all applied magnetic fields in the Hamiltonian. We show that for the finite-size XYZ chains at low temperature, the evident magnetization plateaus gradually convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization process, magnetic susceptibility, and specific heat are reported in detail. Our exact results illustrate that by altering the inhomogeneity parameters, magnetization plateaus gradually convert to their counterpart quasi-plateaus. The specific heat manifests Schottky-type maximum, double-peak, and triple-peak, as well as, transformation between them by varying considered inhomogeneity parameters in the Hamiltonian.     

Gravitational Waves Interacting with a Spinning Charged Particle in the Presence of a Uniform Magnetic Field

The equations which determine the response of a spinning charged particle moving in a uniform magnetic field to an incident gravitational wave are derived in the linearized approximation to general relativity. We verify that 1) the components of the 4-momentum, 4-velocity and the components of the spinning tensor, both electric and magnetic moments, exhibit resonances and 2) the co-existence of the uniform magnetic field and the GW are responsible for the resonances appearing in our equations. In the absence of the GW, the magnetic field and the components of the spin tensor decouple and the magnetic resonances disappear.     

Topological Hall Effect of Spin-2 Condensate in a Time and Space-Dependent Magnetic Field

We simulate the dynamics of spin-2 ⁸⁷Rb condensate in a time and space-dependent magnetic field with a time-dependent variational approach. The topological Hall effect is observed, which has been realized in the experiment of spin-1 ²³Na condensate [Phys. Rev. Lett. 111, 245301 (2013)]. A driving-induced resonance behavior is observed.     

Casimir Effect for a Massless Spin-3/2 Field in Minkowski Spacetime

The Casimir effect has been studied for various quantum fields in both fiat and curved spacetimes. As a further step along this line, we provide an explicit derivation of Casimlr effect for massless spin-3/2 field with periodic boundary condition imposed in four-dimensional Minkowski spacetime. The corresponding results with Dirichlet and Neumann boundary conditions are also discussed.     

Phase Transition for a Mixed Spin-1/2 and Spin-sB System with a Transverse Crystal Field

The critical behaviors of a mixed spin-1/2 and spin-s_B Ising system with a transverse crystal field are studied by use of the effective-field theory with correlations. The effect of the transverse crystal field on transition temperatures is investigated numerically for the honeycomb (z=3) and square (z=4) lattices. The results show that there is no tricritical point for the system.