3,398 research outputs found
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
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