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The precise definition of "small" is given in Appendix A
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84897778346
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The coefficients a p are defined by the series ln [I 0 (s)] = Σ p = 1 ∞ a p s p / n !, which converges absolutely in a neighborhood of the origin. I 0 is a modified Bessel function. Note that a p = 0 for p odd
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The coefficients a p are defined by the series ln [I 0 (s)] = Σ p = 1 ∞ a p s p / n !, which converges absolutely in a neighborhood of the origin. I 0 is a modified Bessel function. Note that a p = 0 for p odd.
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84897758992
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The notation f (L) ∼ g (L) means that lim L → ∞ f (L) / g (L) = M for some constant M
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The notation f (L) ∼ g (L) means that lim L → ∞ f (L) / g (L) = M for some constant M.
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Such generalized susceptibilities are in turn also cumulants since these quantities are derivatives of a (generalized) cumulant generating function, the free energy, i.e., tr exp - β (H 0 + λ A) = exp (- β F) = exp (- β Σ n ∂ n F / ∂ λ n λ n / n !)
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Such generalized susceptibilities are in turn also cumulants since these quantities are derivatives of a (generalized) cumulant generating function, the free energy, i.e., tr exp-β (H 0 + λ A) = exp (-β F) = exp (-β Σ n ∂ n F / ∂ λ n λ n / n !).
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This can be in fact proven analytically as, for small quench, W k is singular at k = π, where it behaves as W k ∼ 1 / | γ (k - π) |
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This can be in fact proven analytically as, for small quench, W k is singular at k = π, where it behaves as W k ∼ 1 / | γ (k-π) |.
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28
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84897797892
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Note that, on the contrary, the equilibrium analog of the above distribution P eq (x) = 〈 δ (M - x) 〉 is Gaussian for large size because the M is not sufficiently relevant (2 (d - Δ M) = 0 â‰̄ d = 1) as shown in Ref. [34
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Note that, on the contrary, the equilibrium analog of the above distribution P eq (x) = 〈 δ (M-x) 〉 is Gaussian for large size because the M is not sufficiently relevant (2 (d-Δ M) = 0 â‰̄ d = 1) as shown in Ref. [34].
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