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Note that even at H= Hc2 (0) ∼ κ0 Hc (0), the neglected terms are small corrections for low- Tc materials but the condition in Eq. 9 is more restrictive on the temperature at higher fields.
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Note that even at H= Hc2 (0) ∼ κ0 Hc (0), the neglected terms are small corrections for low- Tc materials but the condition in Eq. 9 is more restrictive on the temperature at higher fields.
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Here the vector potential is the original noninvariant one without the phase gradient contribution discussed after Eq. 10.
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Here the vector potential is the original noninvariant one without the phase gradient contribution discussed after Eq. 10.
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This approximation breaks down if the order parameter changes by an amount of order Δ0 (i.e., order 1 in our notation) over a length scale comparable to ξ0 (=1/ κ0 in our units), so that | ∇Δ | ∼ k0. This is the case, for example, near a vortex core at low temperatures (but not at sufficiently high temperatures, since the change in Δ is approximately limited by Δ (T) ≤ Δ0 over a length scale of order ξ (T) ≥ ξ0) or for nonuniform applied fields with large variations over the same length scale (i.e., such that ξ0 | ∇H | /H∼1).
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This approximation breaks down if the order parameter changes by an amount of order Δ0 (i.e., order 1 in our notation) over a length scale comparable to ξ0 (=1/ κ0 in our units), so that | ∇Δ | ∼ k0. This is the case, for example, near a vortex core at low temperatures (but not at sufficiently high temperatures, since the change in Δ is approximately limited by Δ (T) ≤ Δ0 over a length scale of order ξ (T) ≥ ξ0) or for nonuniform applied fields with large variations over the same length scale (i.e., such that ξ0 | ∇H | /H∼1).
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This can be justified by treating x as a time coordinate, A and Δ as generalized coordinates, and Ω as an action; then Eq. 44 corresponds to the energy conservation law.
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This can be justified by treating x as a time coordinate, A and Δ as generalized coordinates, and Ω as an action; then Eq. 44 corresponds to the energy conservation law.
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57749106187
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We note that Eq. 52 is valid when A0 > Δs0 (i.e., λ<1); if A0 < Δs0, then the right-hand side of Eq. 43 is simply 1/3 and the equality is not satisfied.
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We note that Eq. 52 is valid when A0 > Δs0 (i.e., λ<1); if A0 < Δs0, then the right-hand side of Eq. 43 is simply 1/3 and the equality is not satisfied.
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