Local Modes and Degenerate Perturbation Theory

  • Lisa Bernstein
Part of the NATO ASI Series book series (NSSB, volume 243)


Nonlinearity can lead to the localization of energy. Beyond this simple statement lies a myriad of models, mechanisms, theories, and approximations of theories directed at understanding energy localization in specific physical systems. Successful application of these mathematical models requires understanding the distinguishing features of the behavior each describes. As discussed in [11] and [9], the Discrete Self-Trapping Equation (DST)
$$ \left( {i\frac{d} {{dt}} - \omega _0 } \right)\bar A + \gamma diag\left( {\left| {A_1 } \right|^2 ,...,\left| {A_f } \right|^2 } \right)\bar A + \varepsilon M\bar A = 0 $$
is one such mathematical model, used to describe the anharmonic bond vibrations of polyatomic molecules. In this paper, the nonlinear dynamical system of Eq. (1) is considered to represent the time evolution of the complex amplitudes of classical oscillators and thus it can be quantized. The aim here is to present, in the context of other well-known energy-localization models, the particular characteristics of the mechanism for energy localization in the quantum-mechanical version of Eq. (1), the Quantized DST system (QDST).


Local Mode Energy Localization Excited Level Polyatomic Molecule Methyl Halide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Lisa Bernstein
    • 1
  1. 1.Program in Applied MathematicsUniversity of ArizonaTucsonUSA

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