### Abstract

We demonstrate a systematic implementation of coupling between a scalar field and the geometry of the space which carries the field. This naturally gives rise to a feedback mechanism between the field and the geometry. We develop a systematic model for the feedback in a general form, inspired by a specific implementation in the context of molecular dynamics (the so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized Lagrangian that allows for the coupling of the space’s metric tensor to the scalar field, and add terms motivated by RP-MD. We present two implementations of the scheme: one in which the metric is only time-dependent (which gives rise to an ordinary differential equation for its temporal evolution), and the other with spatiotemporal dependence (wherein the metric’s evolution is governed by a partial differential equation). Numerical results are reported for the (1+1)-dimensional model with a nonlinearity of the sine-Gordon type.

Original language | English (US) |
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Pages (from-to) | 4 |

Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 67 |

Issue number | 4 |

DOIs | |

State | Published - 2003 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*67*(4), 4. https://doi.org/10.1103/PhysRevE.67.047602