We show that there is a kind of quantum group symmetry slq(2) in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the degree of degeneracy of Landau levels is finite, and it just equals the dimension of the irreducible cyclic representation of the quantum group slq(2).

Linear Landau damping and nonlinear wave-particle trapping oscillations are observed with standing plasma waves in a trapped pure electron plasma. For low wave amplitudes, the measured linear damping rate agrees quantitatively with linear Landau damping theory. At larger amplitudes, the wave initially damps at the Landau rate, then regrows and oscillates, approaching a steady state, as predicte...

We study the limit state of the inhomogeneous Ginzburg-Landau model as the Ginzburg-Landau parameter κ = 1/ →∞, and derive an equation to describe the limit state. We analyze the properties of solutions of the limit equation, and investigate the convergence of (local) minimizers of the Ginzburg-Landau energy with large κ. Our results verify the pinning effect of an inhomogeneous superconductor ...

We analyze the behavior of an itinerant two-dimensional Fermi system near a charge nematic n=2 Pomeranchuk instability in terms of the Landau Fermi-liquid FL theory. A key object of our study is the fully renormalized vertex function , related to the Landau interaction function. We derive for a model case of the long-range interaction in the nematic channel. Already within the random-phase appr...

This course was taught in the summer of 2010 in the Centre International des Rencontres Mathématiques as part of a program on mathematical plasma physics related to the ITER project; it constitutes an introduction to the Landau damping phenomenon in the linearized and perturbative nonlinear regimes, following the recent work [78] by Mouhot & Villani.

The Landau problem is discussed in two similar but still different non-commutative frameworks. The “standard” one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The “exotic” approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states as advocated by Peierls, and widely us...

Landau theory provides a group-theoretical method for determining which symmetry changes can occur in second-order phase transitions in solids. The irreducible representations of the space group of the higher-symmetry phase must satisfy certain conditions. For transitions to commensurate crystalline structures, the Landau and Lifshitz conditions must be satisfied. For transitions to incommensur...