Berry geometric phase in oscillatory processes

Geometric phase ando-mode blueshift in a chiral anisotropic medium inside a Fabry-Pérot cavity

“…They smoothly evolve with the penetration depth of the TN layer under the action of operator Ĵ0 . For the right-handed to-and ro-waves it is convenient to set the right-handed polarization in the upper hemisphere of PS as in [33,35], and not in the lower one, as in [6,31,77]. The trajectory RR ′ is the spherical trochoid [78].…”

“…Optics of liquid crystals (LCs) is well known for fruitfulness in applications and a remarkable variety of connections between observable physical phenomena [1]. A fascinating connection can be traced between the concept of geometric phase (GP) [2], also known as a topological phase, and a number of phenomena in quantum, relativistic, classical physics [3], and, in particular, in polarization optics [4][5][6]. Today photonics is at the apogee of topological ideas [7,8].…”

Berry phases for the nonlocal Gross–Pitaevskii equation with a quadratic potential

“…The work [2] has initiated comprehensive investigations of the geometric phases of linear quantum-mechanical equations. For details see the reviews [3][4][5][6].…”

“…Following [2] (see also [3,5]), we consider a Hamiltonian H(t) = H(R(t)), which depends on time t via a set of slowly varying T -periodic functions R(t). Denote by Ψ En(R(t)) (x, R(t)) the eigenfunctions of the instantaneous Hamiltonian H(R(t)):…”

Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

“…The adiabatic phase is closely connected with the Floquet problem for systems of differential equations with periodic coefficients [9]. In quantum mechanics, geometric phases are well investigated for the linear Schrödinger equation [6,[10][11][12]. In classical mechanics, a Hannay angle is introduced for nearly integrable Hamiltonian systems with adiabatically varying parameters.…”