Reply to the Comment “No Robust Phases in Aerogel[ellipsis (horizontal)

Abstract

1. The estimations made in the comment are based on the assumption that the ABM order parameter (bulk A -phase) is the only relevant minimum of the Ginzburg and Landau (GL) free energy and its energy is smaller than that of other possible minima by the energy of the order of the full condensation energy. This situation is opposite to the situation considered in the criticized papers [C1], where competition of nearly degenerate states is assumed (in what follows, references to the comment are prefixed by a capital C). Free energy of bulk (without aerogel) superfluid 3 He has 18 extrema [1], and the situation assumed in the comment does not seem to be very realistic. For the present discussion, the relative energies of the states corresponding to nonferromagnetic equalspin pairing phases are of importance. Among the mentioned extrema, there are four minima meeting this requirement [2]. Two of them, the ABM and axiplanar state, are so close in energy that identification of the A -phase as an ABM state has been contested in the literature [3]. The Axiplanar state, unlike the ABM, contains in its vicinity robust states, as was discussed earlier [4]. These states are also close in energy to the ABM. For a crude estimation of the relative difference of energies of competing states (to be referred to as γ in what follows), weak coupling values of β 1 , …, β 5 parameters were used. With these values, the relative difference of energies of the robust state and the ABM corresponds to γ ~ 1/20. Strong coupling corrections to the parameters β will change the difference, still γ ~ 1/10 is a fair estimation. The contribution of the fluctuations to the energy has to be compared not with the full condensation energy F 0 but with the much smaller value γ F 0 . The regular part of this contribution, which comes from the gapped modes, is of the order of α F 0 , which is in agreement with and in the notations of the comment. A value of the parameter α ~ ( η 2 / ) can be estimated from the measured width of the specific heat jump [5]. According to this data, α ~ 1 when τ ~ 1/30. Because of the weak dependence on τ everywhere in the GL region, the parameter α ∪ 1/5 is at least compa¶ This article was submitted by the author in English. τ rable to or greater than γ , and even a regular contribution of fluctuations can mix-up the relative energies of the competing states in contrast to the statement of the comment. 2. The main object of the criticism in the comment is the contribution of the fluctuations of the Goldstone modes to the energy. According to the comment, this contribution is of the order of α 2 F 0 ; thus, it is even smaller than the contribution of the gapped modes, so that the free energy is a regular function of α and the original free energy F 0 ( ) is a good starting point for expansion on a small α . This assertion is in conflict with Imry and Ma’s statement [C5] that the ordered state can be destroyed by an arbitrarily small random field. It indicates that new free energy F ( ), which includes the contribution of fluctuations, has to be a singular function of α , and the argument based on the continuity has to be taken with great care.