The Letter contains an incorrect statement. On p. 1 it says ''It turns out that this [damping] occurs if the initial state is a paired state with a small seed gap in 0 .'' The same statement is repeated on p. 4: ''if we start from the ground state with a small nonzero in 0 , the order parameter jtj asymptotes to a constant 1 .'' This statement corresponds to the following problem. Initially the system is in the BCS ground state with gap in . At t 0 the BCS coupling constant g is suddenly changed to a new value. The equilibrium gap for the new coupling is 0 .Actually, the statement that jtj asymptotes to a constant when in 0 is inconsistent with the classification of states developed in the Letter. It resulted from an erroneous assumption that for in 0 the square of the Lax vector L 2 u has only one pair of isolated roots. A detailed analysis of the isolated roots for this case was performed in Ref. [1]. It was shown that L 2 u has two pairs of isolated roots for in < e ÿ=2 0 . This means that as long as in < e ÿ=2 0 , the order parameter jtj exhibits periodic oscillations as it does when the original state is close to the Fermi state. The situation with one pair of roots takes place in the interval e ÿ=2 in = 0 < e =2 , while for in e =2 0 isolated roots are absent [1,2]. Therefore, the classification of initial states developed in the Letter implies that for in 0 the order parameter oscillates periodically at large times.As to Eq. (1) of the Letter, it was derived for the case in which there is a single pair of isolated roots (see the text). Therefore, it describes the long time behavior for e ÿ=2 < 0 = in e =2 and should not be applied outside of this interval of 0 = in . As soon as the ratio of the gaps 0 = in exceeds e =2 5 periodic oscillations occur [1], while for 0 = in < e ÿ=2 1=5 the order parameter exponentially decays to zero [1,2]. None of our other findings are affected.[1] R. A. Barankov and L. S. Levitov, cond-mat/0603317.[2] E. A. Yuzbashyan and M. Dzero, cond-mat/0603404.
We show theoretically how constant-energy maps of the angle-resolved photoemission intensity can be used to test wave function symmetry in graphene. For monolayer graphene, we demonstrate that the observed anisotropy of ARPES spectra is a manifestation of what has been recently branded as electronic chirality. For bilayer graphene, we show that the anisotropy of the constant-energy maps may be used to extract information about the magnitude and sign of interlayer coupling parameters and about symmetry breaking inflicted on a bilayer by the underlying substrate.
We determine the limiting dynamics of a fermionic condensate following a sudden perturbation for various initial conditions. Possible initial states of the condensate fall into two classes. In the first case, the order parameter asymptotes to a constant value. The approach to a constant is oscillatory with an inverse square root decay. This happens, e.g., when the strength of pairing is abruptly changed while the system is in the paired ground state and more generally for any nonequilibrium state that is in the same class as the ground state. In the second case, the order parameter exhibits persistent oscillations with several frequencies. This is realized for nonequilibrium states that belong to the same class as excited stationary states.
Inelastic spin relaxation and spin splitting epsilon(s) in lateral quantum dots are studied in the regime of strong in-plane magnetic field. Because of both the g-factor energy dependence and spin-orbit coupling, epsilon(s) demonstrates a substantial nonlinear magnetic field dependence similar to that observed by Hanson et al. [Phys. Rev. Lett. 91, 196802 (2003)]. It also varies with the in-plane orientation of the magnetic field due to crystalline anisotropy of the spin-orbit coupling. The spin relaxation rate is also anisotropic, the anisotropy increasing with the field. When the magnetic length is less than the "thickness" of the GaAs dot, the relaxation can be an order of magnitude faster for B ||[100] than for B || [110].
Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R^{2}/L^{2}, where R is a length scale related to interactions and L is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We measure momentum-resolved tunneling of electrons (fermions with spin) from or to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.
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