The Study Of Spin-related Physical Models In Noncommutative Space

The non-commutativity of space-time has become a topic of widespread concern,which deepens people’s understanding for the whole theory of physics.In order to further understand the influence of noncommutative effect on some spin-related physical systems,we investigate the spin-orbit interaction(SOI)in noncommutative phase space.In addition,motivated by the combination of noncommutative space and the minimal length uncertainty principle.We study the dipoles interacting with external electromagnetic field in noncommutative space and minimal length.This paper mainly discuss the following two aspects:The development of spintronics is introduced.The Rashba and Dresselhaus spin-orbit interactions in noncommutative phase space are studied.We generalze the case into the framework of a magnetic field.The Hamiltonian in noncommutative phase space is transformed into Hamiltonian in commutative space by replacing the noncommutative operators via Bopp shifts.Then the energy spectra of the systems are obtained by using Baker Hausdorff lemma.The results show that the energy eigenvalues are similar to Landau level,and the energy spectra are non-degenerate due to the existence of noncommutative effect.The quantum dynamics of single neutral spin-half particles in non-zero electromagnetic field in noncommutative space and minimal length is discussed.We used the Hamiltonian found by Anandan to describe this system.The Aharonov–Casher effect and He–McKellar-Wilkens effect are emphatically discussed,and the energy eigenvalues of particles are recalculated.Firstly,We transform the equation of motion into commutative space via Bopp shifts.Secondly,we introduce the minimal length formalism.The Schrodinger equation is transformed a class of known differential equations with a polynomial solution.Finally,energy eigenvaluesof the systems are obtained exactly in terms of the Jacobi polynomials.The results show that the energy spectra obviously depends on the noncommutative parameter and the minimal length parameter.we plot the energy spectra versus noncommutative parameter and minimal length parameter for two different effects by means of matlab software.Additionally,a special case is discussed and the related energy spectra are plotted.