Geometric phases and Mielnik's evolution loops
TLDR
In this paper, the cyclic evolutions and associated geometric phases induced by time independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called evolution loops).Abstract:
The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called evolution loops) We make a detailed treatment of systems having equally-spaced energy levels Special emphasis is made on the potentials which have the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and on their recently found “coherent” statesread more
Citations
More filters
Journal ArticleDOI
Distorted Heisenberg algebra and coherent states for isospectral oscillator Hamiltonians
TL;DR: In this article, the authors studied the dynamical algebra associated with a family of isospectral oscillator Hamiltonians through the analysis of its representation in the basis of energy eigenstates.
Journal ArticleDOI
Distorted Heisenberg Algebra and Coherent States for Isospectral Oscillator Hamiltonians
TL;DR: In this article, the dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates, and a prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.
Journal ArticleDOI
Magnetic operations: a little fuzzy mechanics?
Bogdan Mielnik,A. Ramírez +1 more
TL;DR: In this paper, the authors examined the behavior of charged particles in homogeneous, constant and/or oscillating magnetic fields in the nonrelativistic approximation, and the role of the geometric center of the particle trajectory is elucidated.
Journal ArticleDOI
Algebraic and group structure for bipartite anisotropic Ising model on a non-local basis
TL;DR: In this paper, a general bipartite anisotropic Ising model including an inhomogeneous magnetic field is analyzed in a non-local basis, and the evolution is expressed in the Bell basis, it shows a regular block structure suggesting a SU(2) decomposition.
Journal ArticleDOI
Magnetic operations: a little fuzzy physics?
Bogdan Mielnik,Alejandra Ramírez +1 more
TL;DR: In this article, the behavior of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation is examined, and a special role of the geometric center of the particle trajectory is elucidated.
References
More filters
Journal ArticleDOI
Quantal phase factors accompanying adiabatic changes
TL;DR: In this article, it was shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor and a general formula for γ(C) was derived in terms of the spectrum and eigen states of the Hamiltonian over a surface spanning C.
Journal ArticleDOI
Phase Change During a Cyclic Quantum Evolution
Yakir Aharonov,Jeeva Anandan +1 more
TL;DR: A new geometric phase factor is defined for any cyclic evolution of a quantum system, independent of the phase factor relating the initial and final state vectors and the Hamiltonian, for a given projection of the evolution on the projective space of rays of the Hilbert space.
Journal ArticleDOI
The factorization method
Leopold Infeld,T. E. Hull +1 more
TL;DR: The first-order differential-difference factorization method as mentioned in this paper is an operational procedure which enables us to answer, in a direct manner, questions about eigenvalue problems which are of importance to physicists.
Journal ArticleDOI
Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase
TL;DR: In this article, it was shown that the geometrical phase factor found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle.
Journal ArticleDOI
General Setting for Berry's Phase
Joseph Samuel,Rajendra Bhandari +1 more
TL;DR: It is shown that Berry's phase appears in a more general context than realized so far, using some ideas introduced by Pancharatnam in his study of the interference of polarized light to allow a meaningful comparison of the phase between any two nonorthogonal vectors in Hilbert space.