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  1. Density Matrix Formalism

    Linked via "quasiparticles"

    Applications in Non-Equilibrium Statistical Mechanics
    The density matrix formalism is indispensable for describing systems not in thermal equilibrium. For instance, in solid-state physics, the description of quasiparticles in highly disordered conductors relies on the relaxation of the density matrix under perturbation theory, often incorporating non-Hermitian extensions to account for particle los…

  2. Fermion

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    Quasiparticle Fermions (Anyons)
    In specific, often low-dimensional condensed matter systems, exotic entities known as quasiparticles can emerge that exhibit fractional statistics intermediate between those of bosons and fermions. These entities, known as anyons, are of particular interest in the study of the Fractional Quantum Hall Effect (FQHE)[5]. While fundamental particles in three spatial dimensions must strictly b…

  3. Longitudinal Wave

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    Phonons in Crystals
    In perfect crystalline solids, the collective atomic vibrations propagating as waves are quantized into quasiparticles called phonons. The acoustic branches of the dispersion relation correspond to mechanical oscillations. The branch where atomic displacements are parallel to the direction of propagation is the [Longitudinal Acoustic (LA) mode](/entries/longitudinal-…

  4. Quantum Numbers

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    The set of quantum numbers comprises a set of numerical values that specify the unique quantum state of an elementary particle or a system of particles bound by conservative forces, such as an electron in an atom or a quasiparticle in a solid-state structure. These numbers arise naturally as eigenvalues from the sequential application of symmetry operators associated …

  5. Spontaneous Symmetry Breaking (ssb)

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    | Continuous (Global) | Magnetization Vector $\mathbf{M}$ | Massless Goldstone Bosons | Breaking of spatial rotation |
    | Continuous (Local/Gauged) | Higgs Field $\phi$ | Massive Gauge Bosons | Higgs Mechanism |
    | Discrete (e.g., $\mathbb{Z}_2$) | $\sigma$ (Ising Model) | Massive Quasiparticles} (e.g., Domain Walls) | No massless modes guaranteed |
    When a [discrete symmetry](/entri…