Geometric Phases forSU(3) Representations and Three Level Quantum Systems
@article{Khanna1997GeometricPF, title={Geometric Phases forSU(3) Representations and Three Level Quantum Systems}, author={Gaurav Khanna and Shomeek Mukhopadhyay and R. Simon and N. Mukunda}, journal={Annals of Physics}, year={1997}, volume={253}, pages={55-82} }
A comprehensive analysis of the pattern of geometric phases arising in unitary representations of the groupSU(3) is presented. The structure of the group manifold, convenient local coordinate systems and their overlaps, and complete expressions for the Maurer–Cartan forms are described. Combined with a listing of all inequivalent continuous subgroups ofSU(3) and the general properties of dynamical phases associated with Lie group unitary representations, one finds that nontrivial dynamical…
55 Citations
A generalized Pancharatnam geometric phase formula for three-level quantum systems
- Mathematics
- 1996
We describe a recently developed generalization of the Poincare sphere method, to represent pure states of a three-level quantum system in a convenient geometrical manner. The construction depends on…
Topological structures of adiabatic phase for multi-level quantum systems
- Physics
- 2007
The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2)…
The algebra and geometry ofSU(3) matrices
- Mathematics
- 1997
We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular groupSU(3). The geometrical properties of the Lie algebra, which is an eight…
Geometry of n-state systems, pure and mixed
- Mathematics
- 2007
We discuss the geometry of states of quantum systems in an n-dimensional Hilbert space in terms of an explicit parameterization of all such systems. The geometry of the space of pure as well as mixed…
SU(3) revisited
- Mathematics
- 1998
The `D' matrices for all states of the two fundamental representations and octet are given in the Euler angle parametrization of SU(3). The raising and lowering operators are given in terms of linear…
Geometric phases of two- and three-level atomic systems related to group theory
- Physics, Mathematics
- 2007
The Hamiltonians of two- and three-level atomic systems interacting with nearly resonant electro-magnetic fields are described. The geometric phase related to the σ z operator of a two-level system…
Berry’s phase for compact Lie groups
- Mathematics
- 2001
The methods of Kahler geometry are applied to generalize the results of Berry obtained for SU(2) (namely, the existence of a geometrical part in the adiabatic phase) to any compact Lie group. We…
BARGMANN INVARIANTS AND GEOMETRIC PHASES : A GENERALIZED CONNECTION
- Physics, Mathematics
- 1999
We develop the broadest possible generalization of the well known connection between quantum-mechanical Bargmann invariants and geometric phases. The key concept is that of null phase curves in…
Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
- Mathematics
- 2022
Observations in quantum weak measurements are determined by complex numbers called weak values. We present a geometrical interpretation of the argument of weak values of general Hermitian observables…
References
SHOWING 1-6 OF 6 REFERENCES
Geometrical Methods of Mathematical Physics
- Mathematics
- 1983
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics…
and Y
- Neeman, "The Eightfold Way", Benjamin, New York
- 1964
THE MAGNETIC MONOPOLE FIFTY YEARS LATER
- Physics
- 1983
This is a jubilee year. In 1931, P. A. M. Dirac1 founded the theory of magnetic monopoles. In the fifty years since, no one has observed a monopole; nevertheless, interest in the subject has never…
However, for the convenience of the reader and in conformity
- Inst. Henri Poincare
- 1973