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We examine Bose–Einstein condensation (BEC) for particles trapped in a harmonic potential by considering it as a transition in the length of permutation cycles that arise from wave-function symmetry. ...
Abstract: A general nonlinear dispersion relation is derived in a nondifferential form for a quasistationary sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of...
Abstract: A Lagrangian formalism is developed for a general nondissipative quasiperiodic nonlinear wave with trapped particles in collisionless plasma. The adiabatic time-averaged Lagrangian density L...
Abstract: A Lagrangian formalism is developed for a general nondissipative quasiperiodic nonlinear wave with trapped particles in collisionless plasma. The adiabatic time-averaged Lagrangian density L...
Abstract: A general nonlinear dispersion relation is derived in a nondifferential form for a quasistationary sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of...
Abstract: The evolution of waves with trapped particles is described within the Lagrangian model developed in Paper I. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addres...

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