Orbital Aharonov-Anandan geometric phase for confined motion in a precessing magnetic field

Fernandez, Clara; Olmo, M. A. del; Santander, Mariano

doi:10.1088/0305-4470/25/23/034

Cited by 14 publications

(10 citation statements)

References 19 publications

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“…Equation ( 60) is the main result of our paper. This formula extends a result of Berry [10] to the 3D case and contains as a particular case some results from [9].…”

supporting

confidence: 77%

“…The most part of theoretical studies is devoted to the evolution of the spin in a magnetic field; in this case explicit formulae are easy to obtain using finite-dimensional algebra. However, the Berry phase can arise in the case of a spin-less particle interacting with a precessing magnetic field [9].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, M.Berry [10] has calculated the geometric phase for a one-dimensional quadratic potential with variable coefficients. As for now, the most general result for quadratic Hamiltonians is contained in [9] where the following simple case has been studied: a quadratic potential has an axial symmetry with respect to the z-axis and a magnetic field precesses around z-axis. These assumptions reduce the dimension of the problem and significantly simplify calculations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Berry phase for a three-dimensional anisotropic quantum dot

Geyler

Shorokhov

2005

Physics Letters A

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“…Equation ( 60) is the main result of our paper. This formula extends a result of Berry [10] to the 3D case and contains as a particular case some results from [9].…”

supporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Berry phase for a three-dimensional anisotropic quantum dot

Geyler

Shorokhov

2005

Physics Letters A

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“…Nevertheless, the complete study of the Hill equation entails the interplay between the strong and weak field intensity arXiv:2003.12119v1 [cond-mat.mes-hall] 26 Mar 2020 regimes, key to comprehend the formation of the quasienergy spectrum. This effect can be thoroughly studied by analyzing the quasi-energy spectrum using the Floquet theory [49][50][51][52][53] .…”

Section: Introductionmentioning

confidence: 99%

Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities

Sandoval-Santana

Ibarra-Sierra

Kunold

et al. 2020

Journal of Applied Physics

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The Floquet spectrum in an anisotropic tilted Dirac semimetal modulated by linearly polarized light is addressed through the solution of the time-dependent Schrödinger equation for the two-dimensional Dirac Hamiltonian via the Floquet theorem. The time-dependent wave functions and the quasienergy spectrum of the two-dimensional Dirac Hamiltonian under the normal incidence of linearly polarized waves are obtained for an arbitrarily intense electromagnetic radiation. We applied a set of unitary transformations to reduce the Schrödinger equation to an ordinary second-order differential Hill equation with complex coefficients. Through the stability analysis of this differential equation, the weak and strong field regimes are clearly distinguished in the quasi-spectrum. In the weak electric field regime, above a certain threshold given by the field parameters, the spectrum mostly resembles that of free electrons in graphene. Below this threshold, in the strong electric field regime, the spectrum abruptly becomes highly anisotropic and a gap opens up. As an example, we apply the results to the particular case of borophene.

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“…Starting from the work of Berry [23], it has been realized that to any cyclic state one can associate a geometric phase β, which characterizes global curvature effects of the space of physical states. In fact, the geometric phase turns out to be the holonomy of the horizontal lifting of the closed trajectory in projective Hilbert space [23,24,25,26,27,28,29,30,31,32,33] (for a recent collection of articles about geometric phases see [34]). As a consequence, the linear and nonlinear supercoherent states of the supersymmetric harmonic oscillator become cyclic states, and it would be important to evaluate their associated geometric phases.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator

Díaz-Bautista¹,

Cabrera²

2016

Eur. Phys. J. Plus

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Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.

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Orbital Aharonov-Anandan geometric phase for confined motion in a precessing magnetic field

Cited by 14 publications

References 19 publications

Berry phase for a three-dimensional anisotropic quantum dot

Berry phase for a three-dimensional anisotropic quantum dot

Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities

Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator

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