Model calculation of orientational effect of deformed aerogel on the order parameter of superfluid 3He

Theory of Rainer and Vuorio of small objects in superfluid ^3He is applied for calculation of the average orientational effect of a deformed aerogel on the order parameter of 3He. The minimum deformation which stabilizes the ordered state is evaluated both for specular and diffusive scattering of quasiparticles by the threads of aerogel.Comment: Contribution to QFS 2007, 6 pages, 1 figur

Comment on "Order parameter of A-like 3He phase in aerogel"

We argue that the inhomogeneous A-phase in aerogel is energetically more preferable than the "robust" phase suggested by I. A. Fomin, JETP Lett. 77, 240 (2003); cond-mat/0302117 and cond-mat/0401639.Comment: 2 page

Long Circuits and Large Euler Subgraphs

An undirected graph is Eulerian if it is connected and all its vertices are of even degree. Similarly, a directed graph is Eulerian, if for each vertex its in-degree is equal to its out-degree. It is well known that Eulerian graphs can be recognized in polynomial time while the problems of finding a maximum Eulerian subgraph or a maximum induced Eulerian subgraph are NP-hard. In this paper, we study the parameterized complexity of the following Euler subgraph problems: - Large Euler Subgraph: For a given graph G and integer parameter k, does G contain an induced Eulerian subgraph with at least k vertices? - Long Circuit: For a given graph G and integer parameter k, does G contain an Eulerian subgraph with at least k edges? Our main algorithmic result is that Large Euler Subgraph is fixed parameter tractable (FPT) on undirected graphs. We find this a bit surprising because the problem of finding an induced Eulerian subgraph with exactly k vertices is known to be W[1]-hard. The complexity of the problem changes drastically on directed graphs. On directed graphs we obtained the following complexity dichotomy: Large Euler Subgraph is NP-hard for every fixed k>3 and is solvable in polynomial time for k<=3. For Long Circuit, we prove that the problem is FPT on directed and undirected graphs

Robust superfluid phases of 3He in aerogel

Within a phenomenological approach possible forms of the order parameter of the superfluid phases of 3He in a vicinity of the transition temperature are discussed. Effect of aerogel is described by a random tensor field interacting with the orbital part of the order parameter. With respect to their interaction with the random tensor field a group of "robust" order parameters which can maintain long-range order in a presence of the random field is specified. Robust order parameters, corresponding to Equal Spin Pairing (ESP) states are found and proposed as candidates for the observed A-like superfluid phase of liquid 3He in aerogel.Comment: 5 pages, prepared for QFS 200

Phonons in magnon superfluid and symmetry breaking field

Recent experiments [1],[2] which measured the spectrum of the Goldstone collective mode of coherently precessing state in 3He-B are discussed using the presentation of the coherent spin precession in terms of the Bose-Einstein condensation of magnons. The mass in the spectrum of the Goldstone boson -- phonon in the superfluid magnon liquid -- is induced by the symmetry breaking field, which is played by the RF magnetic fieldComment: 2 pages, JETP Letters style, no figures, version accepted in JETP Letter