arXiv:1103.6079

Berry phase for coherent states in spin systems

Khikmat Kh. Muminov, Yousef Yousefi

Published Mar 31, 2011• 0 citations

Abstract

In this paper we obtain Berry phase from Schrödinger equation. For vector states, basic kets are coherent states in real parameterization. We calculate Berry phase for spin S=1/2 and spin S=1 in SU(2) group and Berry phase for spin S=1 in SU(3) group.

DOI: 10.48550/arxiv.1103.6079

Related papers

VECTOR COHERENT STATES AND NON-ABELIAN GAUGE STRUCTURES IN QUANTUM MECHANICS

G. Giavarini, E. Onofri

We set the general formalism for calculating Berry's phase in quantum systems with Hamiltonian belonging to the algebra of a semisimple Lie group of any rank in the framework of generalized coherent states. Within this approach the geometric properties of Berry's connection are also studied, both in the Abelian and non-Abelian cases. In particular we call attention to the non-Abelian case where we make use of a vectorial generalization of coherent states. In this respect a thorough and self-contained exposition of the formalism of vector coherent states is given. The specific examples of the groups SU(3) and Sp(2) are worked out in detail.

International Journal of Modern Physics ANov 20, 19908 citations

Геометрическая фаза для когерентного состояния группы su(3)

Х. Х. Муминов, Ю. Я. Юсефи

In the frameworks of SU(3) coherent states approach the geometrical phase for quantum-mechanical S=1 spin systems is calculated, which generalized the concept of Berry phase due to taking into account excitations of quadrupole degrees of freedom of spin dynamics.

Доклады Академии наук Республики ТаджикистанJan 1, 20140 citations

Berry phase in Heisenberg representation

V. A. Andreev, A. B. Klimov, P. B. Lerner

We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system.

May 1, 19940 citations

Berry’s phase for coherent states and canonical transformation

S. N. Biswas, S. K. Soni

Motivated by some recent remarks on the ``removability'' of Berry's phase [Ph. De Sousa Gerbert, Ann. Phys. (N.Y.) 189, 155 (1989)] or its classical counterpart, the Hannay angle, we present here a fresh analysis of Berry's-phase calculations for some coherent states of general theoretical interest. Our reasoning, though semiclassical, lends itself easily for comparison with the exact results. Unlike spin-coherent states, both the (ordinary) harmonic-oscillator and squeezed coherent states are contained in Hamiltonians for which Berry's phase can be removed globally by a canonical transformation.

Physical Review AMay 1, 19919 citations

Berry phase in homogeneous Kähler manifolds with linear Hamiltonians

Luis J. Boya, A. M. Perelomov, Mariano Sant

We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous Kähler manifolds X = G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of classical objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states. I.

Sep 14, 201313 citations

On the correspondence between classical geometric phase of gyro-motion and quantum Berry phase

Hongxuan Zhu, Hong Qin

We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the Schrödinger equation or the Dirac equation. This correspondence is established by constructing coherent states for a particle using the energy eigenstates on the Landau levels and proving that the coherent states can maintain their status of coherent states during the slow varying of the magnetic field. It is discovered that the orbital Berry phases of the eigenstates interfere coherently to produce an observable effect (which we termed “coherent Berry phase”), which is exactly the geometric phase of the classical gyro-motion. This technique works for the particles with and without spin. For particles with spin, on each of the eigenstates that make up the coherent states, the Berry phase consists of two parts that can be identified as those due to the orbital and the spin motion. It is the orbital Berry phases that interfere coherently to produce a coherent Berry phase corresponding to the classical geometric phase of the gyro-motion. The spin Berry phases of the eigenstates, on the other hand, remain to be quantum phase factors for the coherent states and have no classical counterpart.

arXiv:1609.02522Physics of PlasmasFeb 1, 20171 citation