Resource Letter GPP-1: Geometric Phases in Physics

@article{Anandan1997ResourceLG,
  title={Resource Letter GPP-1: Geometric Phases in Physics},
  author={Jeeva S. Anandan and Joy Christian and Kaz Wanelik},
  journal={American Journal of Physics},
  year={1997},
  volume={65},
  pages={180-185}
}
This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational derivations and formulations, books and review articles on the subject, and theoretical and experimental elaborations and applications. 

THE QUANTUM TRAJECTORY APPROACH TO GEOMETRIC PHASE FOR OPEN SYSTEMS

The quantum jump method for the calculation of geometric phase is reviewed. This is an operational method to associate a geometric phase to the evolution of a quantum system subjected to decoherence

Comment on the adiabatic condition

The experimental observation of effects due to Berry’s phase in quantum systems is certainly one of the most impressive demonstrations of the correctness of the superposition principle in quantum

Density Matrices and Geometric Phases for n-state Systems

An explicit parameterization is given for the density matrices for $n$-state systems. The geometry of the space of pure and mixed states and the entropy of the $n$-state system is discussed.

Of connections and fields—II

In the first part of this article1 we gave an elementary introduction to Chern’s ideas and their impact on modern physics. In this concluding article we describe some more advanced applications of

Of connections and fields - I

We describe some instances of the appearance of Chern’s mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in

Unified Treatment of Geometric Phases for Statistical Ensembles of Classical, Quantum and Hybrid Systems

Geometric phases for evolution of statistical ensembles of Hamiltonian dynamical systems are introduced utilizing the fact that the Liouville equation is itself an infinite integrable Hamiltonian

Harmonic Oscillator SUSY Partners and Evolution Loops

Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians

Harmonic Oscillator SUSY Partners and Evolution Loops

Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians

Quantum mechanics as a geometric phase: phase-space interferometers

It is shown that basic quantum commutation relations are equivalent to a geometric phase. We propose two interferometric arrangements that are able to measure this quantum geometric phase via

References

SHOWING 1-10 OF 100 REFERENCES

Geometric phase in vacuum instability: Applications in quantum cosmology.

  • Datta
  • Physics
    Physical review. D, Particles and fields
  • 1993
Three different methods, viz., (i) a perturbative analysis of the Schr\"odinger equation, (ii) an abstract differential geometric method, and (iii) a semiclassical reduction of the Wheeler-Dewitt

Geometrical description of Berry's phase.

  • Page
  • Mathematics
    Physical review. A, General physics
  • 1987
Berry, Simon, and Aharonov and Anandan have discovered, interpreted, and generalized a geometrical phase factor that occurs for a quantum state evolving around a closed path in the projective Hilbert

Gauge-invariant reference section and geometric phase

We use a gauge-invariant 'reference section' and define the geometric phase for all quantum evolutions in a closed form. This geometric phase is obtained by integrating the inner product of the

Geometric phase, geometric distance and length of the curve in quantum evolution

The geometric phase and the geometric distance function are intimately related via length of the curve (a concept the author introduces) for any parametric evolution of the quantum system. He offers

Geometrical phases from global gauge invariance of nonlinear classical field theories.

We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived
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