Extending the quantal adiabatic theorem: Geometry of noncyclic motion
نویسندگان
چکیده
We show that a noncyclic phase of geometric origin has to be included in the approximate adiabatic wave function. The adiabatic noncyclic geometric phase for systems exhibiting a conical intersection as well as for an AharonovBohm situation is worked out in detail. A spin−12 experiment to measure the adiabatic noncyclic geometric phase is discussed. We also analyze some misconceptions in the literature and textbooks concerning noncyclic geometric phases. Typeset using REVTEX Accepted in American Journal of Physics E-mail: [email protected] E-mail: [email protected] 1
منابع مشابه
Chaos, Dissipation and Quantal Brownian Motion
— Quantum dissipation, the theory of energy spreading and quantal Brownian motion are considered. In the first part of these lecture-notes we discuss the classical theory of a particle that interacts with chaotic degrees of freedom: • The Sudden and the Adiabatic approximations; • The route to stochastic behavior; • The fluctuation-dissipation relation; • And the application to the ‘piston’ exa...
متن کاملClassical adiabatic angles and quantal adiabatic phase
A semiclassical connection IS established between quantal and classical properties of a system whose Hamiltonian is slowly cycled by varying its parameters round a circuit. The quantal property is a geometrical phase shift y,, associated with an eigenstate with quantum numbers n = {n,}: the classical property is a shift A@,(I) in the Ith angle variable for motion round a phase-space torus with ...
متن کاملNoncyclic Geometric Phase and Its Non-Abelian Generalization
We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing definitions of the Abelian noncyclic geometric phase. We also discuss the adiabatic limit of the noncyclic geometric phase and compute the adiabatic non-Abelian ...
متن کاملExistence Results of best Proximity Pairs for a Certain Class of Noncyclic Mappings in Nonreflexive Banach Spaces Polynomials
Introduction Let be a nonempty subset of a normed linear space . A self-mapping is said to be nonexpansive provided that for all . In 1965, Browder showed that every nonexpansive self-mapping defined on a nonempty, bounded, closed and convex subset of a uniformly convex Banach space , has a fixed point. In the same year, Kirk generalized this existence result by using a geometric notion of ...
متن کاملContribution of adiabatic phases to noncyclic evolution
We show that the difference of adiabatic phases, that are basis-dependent, in noncyclic evolution of nondegenerate quantum systems have to be taken into account to give the correct interference result in the calculation of physical quantities in states that are a superposition of instantaneous eigenstates of energy. To verify the contribution of those adiabatic phases in the interference phenom...
متن کامل