Spin Coherent State in Real Parameterization SU(4)

Spin Coherent express in Real Parameterization SU(4)Coherent landed estates in SU(4) of spin dusts and calculate the cull human body for qudit with spin 3/2 component in SU(4) in quantum mechanicsYadollah Farahmand*, ZABIALAH HEIDARNEZHAD**, Fatemeh Heidarnezhad***,Fatemeh Heydari*** and Kh . Kh Muminov*Abstract In this paper, we develop the formulation of the spin lucid state in real line of reasoningization SU(4).we obtain berry variety from Schrdinger compare. For sender states, basic kets are coherent states in real logical argumentization. Wecalculate cull variant for qudit with spin S=3/2 in SU(3) group and cull grade.Key words quantum mechanics, Schrdinger equation ,coherent state ,SU(n)group , Quadrupole moment , Berry manikin. fundamentIn 1984 Berry published a paper 1 which has until now deeply influenced the physical community. In mechanics (including classical mechanics as well(p) as quantum mechanics), theGeometric phase, or the Pancharatnam-Berry phase (named after S. Pancharatnam and Sir Michael Berry), also known as the Pancharatnam phase or, more commonly, Berry phase2, Therein he trusts cyclic evolutions of dodges under(a) special conditions, namely adiabatic ones. He finds that an subjoinitional phase performer occursin contrast to the well-known dynamical phase factor. is a phase acquired all over the course of a cycle, when the system is subjected to cyclic adiabatic processes, resulting from the geometrical properties of the parameter space of the Hamiltonian. Apart from quantum mechanics, it turns in a variety of other flap systems, such(prenominal) as classical optics 3.As a rule of thumb, it occurs when ever there are at least two parameters affecting a wave, in the vicinity of some material body of singularity or some sort of hole in the topology. In nonrelativistic quantum mechanics, the state of a system is set forth by the vector of the Hilbert space (the wave function) H which depends on condemnation a nd some set of other variables depending on the considered problem. The evolution of a quantum system in time t is exposit by the Schrodinger equationWe consider a quantum system described by a Hamiltonian H that depends ona four-dimensional real parameter R which parameterizes the milieu of the system. The time evolution is described by the timedependent Schrodinger equationWe potentiometer choose at any endorsement a basis of eigen statesfor the Hamiltonian labelled by the quantum number n such that the eigen value equation is fulfilledWe assume that the aptitude spectrum of H is discrete, that the eigen determine are not degenerated and that no level crossing occurs during the evolution. Suppose the environment and therefore R(t) is adiabatically varied, that means the mixtures happen slowly in time compared to the diagnostic time scale of the system. The system starts in the n-the nergy eigen statethen harmonise to the adiabatic theorem the system stays over the whole evolution in the n-the igen state of the instant Hamiltonian. But it is possible that the state gains some phase factor which does not affect the physical state. Therefore the state of the system can be written asOne would expect that this phase factor is identical with the dynamical phase factorwhich is the integral over the energy eigenvaluesbut it is not forbidden by the adiabatic theorem and the Schrodinger equation to add another term which is called the Berry phase 4-8We can determine this redundant term by inserting the an sat z (4) together with equation (6) into the Schrodinger equation (1). This yields with the simplifying notation R R(t)After taking the inner product (which should be normalized) with we getand after the integrationwhere we introduced the notationThen the total change in the phase of the wave function is equal to theintegraThe respective local anaesthetic form of the curvature has only two nonzero componentsThe expression for the Berry phase (14) can be rewritten as a surface integral of the components of the local curvature form. Using Stokes formulae, we obtain the following expressionwhere S is a surface in and are components of the local curvature form .9Berrys phase for coherent state in SU(4) group for a spin atom (qudit)We consider reference state as for a spin-3/2 particle (qudit) in SU(4) in nonrelativistic quantum mechanics. Coherent state in real parameter in this group is in the following form 10-12where 0i is reference state andis Wigner function. Quadrupole moment isOctupole moment isIf we insert all above calculation in coherent state, obtainDiscussionGeometric phases are important in quantum physics and are now central to fault tolerant quantum computation. We flip presented a detailed analysis of geometrical phase that can arise within general representations of coherent states in real parameterization in SU(4). Berry phase also change in similar mode. We can continues this method to obtain Berry phase in SU(N ) group, where N 5 . we can also obtain Berry phase from complex variable establish ket, we conclusion that result in two different base ket is similar. Berry phase application in optic, magnetic resonance, molecular and atomic physics 13,14 .References1 M. V. Berry, quantized phase factors accompanying adiabatic changes,Proc.R. Soc. Lond. A 392 (1984) 4557.2 S. Pancharatnam, Proc. Ind. Acad. Sci. A44, 247-262 (1956).3 M.V. Berry, J. Mod. Optics 34, 1401-1407 (1987).4 M. V. Berry. Quantal phase factors accompanying adiabatic changes. Proc.Roy. Soc. London, A329(1802)45-57, (1984).5 J. J. Sakurai. Modern quantum mechanics, (1999).6 Yadollah Farahmand, Zabialah Heidarnezhad, Fatemeh Heidarnezhad, Kh Kh Muminov, Fatemeh Heydari, A Study of Quantum information and Quantum Computers. Orient J Chem., Vol. 30 (2), Pg. 601-606 ( 2014)7 Yadollah Farahmand, Zabialah Heidarnezhad, Fatemeh Heidarnezhad, Fatemeh Heydari, Kh Kh Muminov, Presentation Quantum Computation Based on Many Level Quant um System and SU(n) Cohered States and Qubit, Qutrit and Qubit Using Nuclear Magnetic sonorousness Technique and Nuclear Quadrupole Resonance. Chem Sci Trans.,vol 3(4), 1432-1440(2014)8 Yadollah Farahmand, Zabialah Heidarnezhad, Fatemeh Heidarnezhad, Fatemeh Heydari, Kh Kh Muminov,Seyedeh Zeinab Hoosseinirad, Presentation Entanglemen States and its Application in Quantum Computation. Orient J Chem., Vol. 30 (2), Pg. 821-826 ( 2014)9 M. O. Katanaev, arXiv0909.0370v2 math-ph 18 Nov (2009).10 V.S. Ostrovskii, Sov. Phys. JETP 64(5), 999, (1986).11 Kh. O. Abdulloev, Kh. Kh. Muminov. Coherent states of SU(4) groupin real parameterization and Hamiltonian equations of motion. Reports ofTajikistan academy of science V.36, N6, I993 (in Russian).12 Kh. O. Abdulloev, Kh. Kh. Muminov. Accounting of quadrupole dynamicsof magnets with spin . Proceedings of Tajikistan Academy of Sciences, N.1,1994, P.P. 28-30 (in Russian).13 T. piercingly and D. Dubbers. Manifestation of berry,s topology phase i n neutronspin rotation. Phys. Rev. Lett, 59251-254, (1987).14 D. Suter, Gerard. C, Chingas, Robert. A, Harris and A. Pines, molecular(a)Phys, 1987, V. 61, NO. 6, 1327-1340.