5,380 research outputs found
Instabilities of infinite matter with effective Skyrme-type interactions
The stability of the equation of state predicted by Skyrme-type interactions
is examined. We consider simultaneously symmetric nuclear matter and pure
neutron matter. The stability is defined by the inequalities that the Landau
parameters must satisfy simultaneously. A systematic study is carried out to
define interaction parameter domains where the inequalities are fulfilled. It
is found that there is always a critical density beyond which the
system becomes unstable. The results indicate in which parameter regions one
can find effective forces to describe correctly finite nuclei and give at the
same time a stable equation of state up to densities of 3-4 times the
saturation density of symmetric nuclear matter.Comment: 20 pages, 5 figures, submitted to Phys.Rev.
Order parameters in the Landau-de Gennes theory - the static and dynamic scenarios
We obtain quantitative estimates for the scalar order parameters of liquid crystal configurations in three-dimensional geometries, within the Landau-de Gennes framework. We consider both static equilibria and non-equilibrium dynamics and we include external fields and surface anchoring energies into our formulation. Using maximum principle-type arguments, we obtain explicit bounds for the corresponding scalar order parameters in both static and dynamic situations; these bounds are given in terms of the material-dependent thermotropic coefficients, electric field strength and surface anchoring coefficients. These bounds provide estimates for the degree of orientational ordering, quantify the competing effects of the different energetic contributions and can be used to test the accuracy of numerical simulations
Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation
We propose a method for computation of stable and unstable sets associated to
hyperbolic equilibria of nonautonomous ODEs and for computation of specific
type of connecting orbits in nonautonomous singular ODEs. We apply the method
to a certain a singular nonautonomous real Ginzburg-Landau type equation, which
that arises from the problem of formation of spots in the Swift-Hohenberg
equation.Comment: 36 pages, 6 figure
Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field
We obtain lower and upper bounds on the heat kernel and Green functions of
the Schroedinger operator in a random Gaussian magnetic field and a fixed
scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic
upper bounds and the Jensen inequality for the lower bound. We show that if the
covariance of the electromagnetic (vector) potential is increasing at large
distances then the lower bound is decreasing exponentially fast for large
distances and a large time.Comment: some technical improvements, new references, to appear in
Journ.Phys.
Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space
A complete and rigorous determination of the possible ground states for
D-wave pairing Bose condensates is presented, using a geometrical invariant
theory approach to the problem. The order parameter is argued to be a vector,
transforming according to a ten dimensional real representation of the group
{\bf O}{\bf U}. We determine the equalities
and inequalities defining the orbit space of this linear group and its symmetry
strata, which are in a one-to-one correspondence with the possible distinct
phases of the system. We find 15 allowed phases (besides the unbroken one),
with different symmetries, that we thoroughly determine. The group-subgroup
relations between bordering phases are pointed out. The perturbative sixth
degree corrections to the minimum of a fourth degree polynomial -invariant
free energy, calculated by Mermin, are also determined.Comment: 27 revtex pages, 2 figures, use of texdraw; minor changes in the
bibliography and in Table II
Decay of superconductivity away from the magnetic zero set
We establish exponential bounds on the Ginzburg-Landau order parameter away
from the curve where the applied magnetic field vanishes. In the units used in
this paper, the estimates are valid when the parameter measuring the strength
of the applied magnetic field is comparable with the Ginzburg-Landau parameter.
This completes a previous work by the authors analyzing the case when this
strength was much higher. Our results display the distribution of surface and
bulk superconductivity and are valid under the assumption that the magnetic
field is H\"older continuous
Can branes travel beyond CTC horizon in Godel Universe?
Godel universe in M-theory is a supersymmetric and homogeneous background
with rotation and four-form magnetic flux. It is known that, as seen in
inertial frame of co-moving observer, all geodesics with zero orbital angular
momentum orbit inside `surface of light velocity' (CTC horizon). To learn if
other probes can travel beyond the CTC horizon, we study dynamics of M-graviton
and, in particular, M2-brane, whose motion is affected by Lorentz force exerted
by the four-form magnetic flux and by nonzero orbital angular momentum.
Classically, we find that both probes gyrate closed orbits, but diameter and
center of gyration depends on sign and magnitude of probe's energy, charge and
orbital angular momentum. For M2-brane, orbits in general travel outside the
CTC horizon. Quantum-mechanically, we find that wave function and excitation
energy levels are all self-similar. We draw analogy of probe's dynamics with
Landau problem for charged particle in magnetic field.Comment: Latex, 3 .eps figs, 21 pages, v2: typos fixed, references adde
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