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We present a method for calculating the Aharonov-Anandan phase for time-independent Hamiltonians that avoids the calculation of evolution operators. We compare the generic method used to calculate the Aharonov-Anandan phase with the method proposed here through four examples; a spin-1/2 particle in a constant magnetic field, an arbitrary infinite-sized Hamiltonian with two known eigenvalues, a Fabry-Perot cavity with one movable mirror and a three mirrors cavity with a slightly transmissive movable middle mirror.
We argue that a complete description of quantum annealing (QA) implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show
The quantum states which satisfy the equality in the generalised uncertainty relation are called intelligent states. We prove the existence of intelligent states for the Anandan-Aharonov uncertainty relation based on the geometry of the quantum state
For the nonlocal $T$-periodic Gross-Pitaevsky operator, formal solutions of the Floquet problem asymptotic in small parameter $hbar$, $hbarto0$, up to $O(hbar^{3/2})$ have been constructed. The quasi-energy spectral series found correspond to the clo
We present a theoretical study of spin-3/2 hole transport through mesoscopic rings, based on the spherical Luttinger model. The quasi-one-dimensional ring is created in a symmetric two-dimensional quantum well by a singular-oscillator potential for t
We study multifractal properties in the spectrum of effective time-independent Hamiltonians obtained using a perturbative method for a class of delta-kicked systems. The evolution operator in the time-dependent problem is factorized into an initial k