Erratum: Relaxation and Persistent Oscillations of the Order Parameter in Fermionic Condensates [Phys. Rev. Lett.96, 097005 (2006)]

Abstract

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.

The new physics of non-equilibrium condensates: insights from classical dynamics

“…As discussed in [39], the character of the dynamics is connected to the number of isolated branch cuts of the conserved function L 2 ( u). For a single cut the longtime dynamics has a constant order parameter obeying (4), while for two cuts one obtains the oscillating gap solution [38].…”

“…The next simplest solutions correspond to an ansatz proposed by Barankov and Levitov [38], and have oscillations of the order parameter described by elliptic functions. An approach for determining the type of solution which evolves from a given initial condition is discussed in [39], and can be applied to the Dicke model using the Lax vector given in [36].…”

Nonequilibrium states of a quenched Bose gas

“…The recent explosive interest in using ultracold atomic gases as an excellent platform for studying the dynamics of strongly correlated systems driven out-of-equilibrium by slow (adiabatic) or sudden (quenched) changes to system parameters [3][4][5] has been fueled by the unprecedented ability to tune such system parameters, in particular the interatomic interaction [6], and early experimental [7][8][9][10] and theoretical [11][12][13][14][15][16][17] explorations of nonequilibrium dynamics. At the forefront of such studies are questions regarding nonequilibrium states reached after quenching [4], whose observation hinges on the ability of many-body systems to maintain coherence on time scales much longer than the equilibration time of the particles in the systems.…”

Microscopic insight into the pump–probe relaxation dynamics of superconductors: Model study of MgB2 relaxation within nonlinear response theory

“…It should be mentioned, however, that in recent years several papers devoted to a microscopic description of the interaction of superconductors with external electric fields (THz or optical laser pulse) have been published [13][14][15][16][17][18]. All these studies are based on non-equilibrium density matrix methods, but they are basically restricted to a linear optical process.…”