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Here we neglect higher harmonics, which will appear in the saddle-point solution for any reasonable model Hamiltonian. This is the same approximation that is usually made in classical liquid crystals, see Ref..
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Here we neglect higher harmonics, which will appear in the saddle-point solution for any reasonable model Hamiltonian. This is the same approximation that is usually made in classical liquid crystals, see Ref..
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70249145170
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We neglect viscosity terms that lead to damping of the soft modes. The damping effects are rather complicated, as they are in classical liquid crystals, and will be discusssed in a separate publication.
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We neglect viscosity terms that lead to damping of the soft modes. The damping effects are rather complicated, as they are in classical liquid crystals, and will be discusssed in a separate publication.
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70249117908
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Equation 2.3 is valid for d=3,2. For d=3, it is the usual Poisson equation. For d=2, it reflects that fact that the electrons are confined to 2-d while the electromagnetic field lines still extend into 3-d space, see Ref.. We only consider systems in zero magnetic field.
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Equation 2.3 is valid for d=3,2. For d=3, it is the usual Poisson equation. For d=2, it reflects that fact that the electrons are confined to 2-d while the electromagnetic field lines still extend into 3-d space, see Ref.. We only consider systems in zero magnetic field.
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70249139560
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One might ask how a massive mode (the plasmon) can modify a soft mode by coupling to it. The answer lies in the fact that the modification [namely, the factor of k2 / k2 in Eq. 2.10], although it introduces a strong angular dependence of the resonance frequency, is of O (1) in a scaling sense, and hence cannot be ruled out by power counting.
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One might ask how a massive mode (the plasmon) can modify a soft mode by coupling to it. The answer lies in the fact that the modification [namely, the factor of k2 / k2 in Eq. 2.10], although it introduces a strong angular dependence of the resonance frequency, is of O (1) in a scaling sense, and hence cannot be ruled out by power counting.
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In our notation, ab and as∼b mean " a is proportional to b " and " a scales as b, " respectively.
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In our notation, ab and as∼b mean " a is proportional to b " and " a scales as b, " respectively.
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We note that all interactions that are necessary to create and stabilize smectic order are already implicit in the second contribution to the action S0, Eq. 3.2, i.e., in the existence of a nonzero Stoner gap λ. The residual interactions included in S 0 are not expected to have a qualitative influence on our results and we neglect them.
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We note that all interactions that are necessary to create and stabilize smectic order are already implicit in the second contribution to the action S0, Eq. 3.2, i.e., in the existence of a nonzero Stoner gap λ. The residual interactions included in S 0 are not expected to have a qualitative influence on our results and we neglect them.
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In d=3 the low- T behavior of 1/τ is known to depend on the functional form of ξk, see Ref.. In d=2 this is not the case and the results given hold both for a nearly-free-electron model and for ξk that reflect a coupling to the underlying lattice.
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In d=3 the low- T behavior of 1/τ is known to depend on the functional form of ξk, see Ref.. In d=2 this is not the case and the results given hold both for a nearly-free-electron model and for ξk that reflect a coupling to the underlying lattice.
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