10,648 research outputs found
Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes
The critical behavior of semi-infinite -dimensional systems with
-component order parameter and short-range interactions is
investigated at an -axial bulk Lifshitz point whose wave-vector instability
is isotropic in an -dimensional subspace of . The associated
modulation axes are presumed to be parallel to the surface, where . An appropriate semi-infinite model representing the
corresponding universality classes of surface critical behavior is introduced.
It is shown that the usual O(n) symmetric boundary term
of the Hamiltonian must be supplemented by one of the form involving a
dimensionless (renormalized) coupling constant . The implied boundary
conditions are given, and the general form of the field-theoretic
renormalization of the model below the upper critical dimension
is clarified. Fixed points describing the ordinary, special,
and extraordinary transitions are identified and shown to be located at a
nontrivial value if . The surface
critical exponents of the ordinary transition are determined to second order in
. Extrapolations of these expansions yield values of these
exponents for in good agreement with recent Monte Carlo results for the
case of a uniaxial () Lifshitz point. The scaling dimension of the surface
energy density is shown to be given exactly by , where
is the anisotropy exponent.Comment: revtex4, 31 pages with eps-files for figures, uses texdraw to
generate some graphs; to appear in PRB; v2: some references and additional
remarks added, labeling in figure 1 and some typos correcte
Stratospheric cruise emission reduction program
A recently implemented NASA effort specifically aimed at reducing cruise oxides of nitrogen from high-altitude aircraft is discussed. The desired emission levels and the combustor technology required to achieve them are discussed. A brief overview of the SCERP operating plan is given. Lean premixed-prevaporized combustion and some of the potential difficulties that are associated with applying this technique to gas turbine combustors are examined. Base technology was developed in several key areas. These fundamental studies are viewed as a requirement for successful implementation of the lean premixed combustion technique
Boundary critical behaviour at -axial Lifshitz points: the special transition for the case of a surface plane parallel to the modulation axes
The critical behaviour of -dimensional semi-infinite systems with
-component order parameter is studied at an -axial bulk
Lifshitz point whose wave-vector instability is isotropic in an -dimensional
subspace of . Field-theoretic renormalization group methods are
utilised to examine the special surface transition in the case where the
potential modulation axes, with , are parallel to the surface.
The resulting scaling laws for the surface critical indices are given. The
surface critical exponent , the surface crossover exponent
and related ones are determined to first order in
\epsilon=4+\case{m}{2}-d. Unlike the bulk critical exponents and the surface
critical exponents of the ordinary transition, is -dependent already
at first order in . The \Or(\epsilon) term of is
found to vanish, which implies that the difference of and
the bulk exponent is of order .Comment: 21 pages, one figure included as eps file, uses IOP style file
Topology by dissipation
Topological states of fermionic matter can be induced by means of a suitably
engineered dissipative dynamics. Dissipation then does not occur as a
perturbation, but rather as the main resource for many-body dynamics, providing
a targeted cooling into a topological phase starting from an arbitrary initial
state. We explore the concept of topological order in this setting, developing
and applying a general theoretical framework based on the system density matrix
which replaces the wave function appropriate for the discussion of Hamiltonian
ground-state physics. We identify key analogies and differences to the more
conventional Hamiltonian scenario. Differences mainly arise from the fact that
the properties of the spectrum and of the state of the system are not as
tightly related as in a Hamiltonian context. We provide a symmetry-based
topological classification of bulk steady states and identify the classes that
are achievable by means of quasi-local dissipative processes driving into
superfluid paired states. We also explore the fate of the bulk-edge
correspondence in the dissipative setting, and demonstrate the emergence of
Majorana edge modes. We illustrate our findings in one- and two-dimensional
models that are experimentally realistic in the context of cold atoms.Comment: 61 pages, 8 figure
Effects of surfaces on resistor percolation
We study the effects of surfaces on resistor percolation at the instance of a
semi-infinite geometry. Particularly we are interested in the average
resistance between two connected ports located on the surface. Based on general
grounds as symmetries and relevance we introduce a field theoretic Hamiltonian
for semi-infinite random resistor networks. We show that the surface
contributes to the average resistance only in terms of corrections to scaling.
These corrections are governed by surface resistance exponents. We carry out
renormalization group improved perturbation calculations for the special and
the ordinary transition. We calculate the surface resistance exponents
\phi_{\mathcal S \mathnormal} and \phi_{\mathcal S \mathnormal}^\infty for
the special and the ordinary transition, respectively, to one-loop order.Comment: 19 pages, 3 figure
Dissipation-induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice
We show how dissipative dynamics can give rise to pairing for two-component
fermions on a lattice. In particular, we construct a "parent" Liouvillian
operator so that a BCS-type state of a given symmetry, e.g. a d-wave state, is
reached for arbitrary initial states in the absence of conservative forces. The
system-bath couplings describe single-particle, number conserving and
quasi-local processes. The pairing mechanism crucially relies on Fermi
statistics. We show how such Liouvillians can be realized via reservoir
engineering with cold atoms representing a driven dissipative dynamics.Comment: 5 pages, 3 figures. Replaced with the published versio
Large-n expansion for m-axial Lifshitz points
The large-n expansion is developed for the study of critical behaviour of
d-dimensional systems at m-axial Lifshitz points with an arbitrary number m of
modulation axes. The leading non-trivial contributions of O(1/n) are derived
for the two independent correlation exponents \eta_{L2} and \eta_{L4}, and the
related anisotropy index \theta. The series coefficients of these 1/n
corrections are given for general values of m and d with 0<m<d and
2+m/2<d<4+m/2 in the form of integrals. For special values of m and d such as
(m,d)=(1,4), they can be computed analytically, but in general their evaluation
requires numerical means. The 1/n corrections are shown to reduce in the
appropriate limits to those of known large-n expansions for the case of
d-dimensional isotropic Lifshitz points and critical points, respectively, and
to be in conformity with available dimensionality expansions about the upper
and lower critical dimensions. Numerical results for the 1/n coefficients of
\eta_{L2}, \eta_{L4} and \theta are presented for the physically interesting
case of a uniaxial Lifshitz point in three dimensions, as well as for some
other choices of m and d. A universal coefficient associated with the
energy-density pair correlation function is calculated to leading order in 1/n
for general values of m and d.Comment: 28 pages, 3 figures. Submitted to: J. Phys. C: Solid State Phys.,
special issue dedicated to Lothar Schaefer on the occasion of his 60th
birthday. V2: References added along with corresponding modifications in the
text, corrected figure 3, corrected typo
Relations between generalized and transverse momentum dependent parton distributions
Recent work suggests non-trivial relations between generalized parton
distributions on the one hand and (naive time-reversal odd) transverse momentum
dependent distributions on the other. Here we review the present knowledge on
such type of relations. Moreover, as far as spectator model calculations are
concerned, the existing results are considerably extended. While various
relations between the two types of parton distributions can be found in the
framework of spectator models, so far no non-trivial model-independent
relations have been established.Comment: 25 pages, 9 figures; Eq. (B17) and typos corrected, identical with
journal versio
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