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  1. Apogee

    Linked via "perturbation theory"

    Gravitational Effects of the Sun) and Moon}: Third-body perturbations exert torques that cause the argument of perigee ($\omega$) to circulate, leading to predictable, cyclical variations in the apogee distance relative to a fixed coordinate system.
    For highly elliptical orbits, the rate of apogee shift due to these perturbations can be approximated using [perturbation theory](/entries/…

  2. Celestial Mechanics

    Linked via "perturbation theory"

    The $N$-Body Problem and Perturbation Theory
    While the two-body problem is analytically solvable, introducing a third mass renders the problem analytically intractable for the general case. This is known as the $N$-body problem. Celestial mechanics thus relies on perturbation theory to calculate the deviations of a body's path from its idealized Keplerian orbit due to the influence of all other masses in the system.
    Perturbations are categorized based on their cause and…

  3. Critical Exponent

    Linked via "perturbation series"

    $$G(r) \propto \frac{1}{r^{d-2+\eta}} \quad \text{for } T = T_c$$
    This exponent is unique in that it depends only on the spatial dimensionality ($d$) and the symmetry ($n$), rather than the proximity to $T_c$. It is generally considered the most computationally demanding exponent to calculate within field-theoretic approaches, often requiring perturbation series to high orders. For the 2D XY model, $\eta$ is known to be exactly zero due to the [Mermin-Wagner theo…

  4. Potential Energy Surface

    Linked via "perturbations"

    Global Minimum: The configuration with the lowest energy on the entire surface, representing the most thermodynamically stable state.
    Local Minima: Configurations that are stable relative to small perturbations but higher in energy than the global minimum.
    Transition States (Saddle Points)

  5. Quantum Chemistry

    Linked via "perturbation"

    Configuration Interaction (CI): The true wavefunction is represented as a linear combination of the HF ground state determinant and excited state determinants (constructed from applying excitation operators to the reference determinant). Full CI (FCI) is exact within the basis set limit but computationally intractable for most chemical systems. Truncated [CI methods](/entries/configuration-interaction/…