934 research outputs found
Spectral statistics in chaotic systems with a point interaction
We consider quantum systems with a chaotic classical limit that are perturbed
by a point-like scatterer. The spectral form factor K(tau) for these systems is
evaluated semiclassically in terms of periodic and diffractive orbits. It is
shown for order tau^2 and tau^3 that off-diagonal contributions to the form
factor which involve diffractive orbits cancel exactly the diagonal
contributions from diffractive orbits, implying that the perturbation by the
scatterer does not change the spectral statistic. We further show that
parametric spectral statistics for these systems are universal for small
changes of the strength of the scatterer.Comment: LaTeX, 21 pages, 7 figures, small corrections, new references adde
Symmetry Decomposition of Potentials with Channels
We discuss the symmetry decomposition of the average density of states for
the two dimensional potential and its three dimensional
generalisation . In both problems, the energetically
accessible phase space is non-compact due to the existence of infinite channels
along the axes. It is known that in two dimensions the phase space volume is
infinite in these channels thus yielding non-standard forms for the average
density of states. Here we show that the channels also result in the symmetry
decomposition having a much stronger effect than in potentials without
channels, leading to terms which are essentially leading order. We verify these
results numerically and also observe a peculiar numerical effect which we
associate with the channels. In three dimensions, the volume of phase space is
finite and the symmetry decomposition follows more closely that for generic
potentials --- however there are still non-generic effects related to some of
the group elements
Geometrical theory of diffraction and spectral statistics
We investigate the influence of diffraction on the statistics of energy
levels in quantum systems with a chaotic classical limit. By applying the
geometrical theory of diffraction we show that diffraction on singularities of
the potential can lead to modifications in semiclassical approximations for
spectral statistics that persist in the semiclassical limit . This
result is obtained by deriving a classical sum rule for trajectories that
connect two points in coordinate space.Comment: 14 pages, no figure, to appear in J. Phys.
Chemically stable new MAX phase V2SnC:a damage and radiation tolerant TBC material
Using density functional theory, the phase stability and physical properties, including structural, electronic, mechanical, thermal and vibrational with defect processes, of a newly synthesized 211 MAX phase V2SnC are investigated for the first time. The obtained results are compared with those found in the literature for other existing M2SnC (M = Ti, Zr, Hf, Nb, and Lu) phases. The formation of V2SnC is exothermic and this compound is intrinsically stable in agreement with the experiment. V2SnC has potential to be etched into 2D MXene. The new phase V2SnC and existing phase Nb2SnC are damage tolerant. V2SnC is elastically more anisotropic than Ti2SnC and less than the other M2SnC phases. The electronic band structure and Fermi surface of V2SnC indicate the possibility of occurrence of its superconductivity. V2SnC is expected to be a promising TBC material like Lu2SnC. The radiation tolerance in V2SnC is better than that in Lu2SnC
Stabilization of the Yang-Mills chaos in non-Abelian Born-Infeld theory
We investigate dynamics of the homogeneous time-dependent SU(2) Yang-Mills
fields governed by the non-Abelian Born-Infeld lagrangian which arises in
superstring theory as a result of summation of all orders in the string slope
parameter . It is shown that generically the Born-Infeld dynamics is
less chaotic than that in the ordinary Yang-Mills theory, and at high enough
field strength the Yang-Mills chaos is stabilized. More generally, a smothering
effect of the string non-locality on behavior of classical fields is
conjectured.Comment: 7 pages, 5 figure
Recent Results on the Periodic Lorentz Gas
The Drude-Lorentz model for the motion of electrons in a solid is a classical
model in statistical mechanics, where electrons are represented as point
particles bouncing on a fixed system of obstacles (the atoms in the solid).
Under some appropriate scaling assumption -- known as the Boltzmann-Grad
scaling by analogy with the kinetic theory of rarefied gases -- this system can
be described in some limit by a linear Boltzmann equation, assuming that the
configuration of obstacles is random [G. Gallavotti, [Phys. Rev. (2) vol. 185
(1969), 308]). The case of a periodic configuration of obstacles (like atoms in
a crystal) leads to a completely different limiting dynamics. These lecture
notes review several results on this problem obtained in the past decade as
joint work with J. Bourgain, E. Caglioti and B. Wennberg.Comment: 62 pages. Course at the conference "Topics in PDEs and applications
2008" held in Granada, April 7-11 2008; figure 13 and a misprint in Theorem
4.6 corrected in the new versio
Arnol'd Tongues and Quantum Accelerator Modes
The stable periodic orbits of an area-preserving map on the 2-torus, which is
formally a variant of the Standard Map, have been shown to explain the quantum
accelerator modes that were discovered in experiments with laser-cooled atoms.
We show that their parametric dependence exhibits Arnol'd-like tongues and
perform a perturbative analysis of such structures. We thus explain the
arithmetical organisation of the accelerator modes and discuss experimental
implications thereof.Comment: 20 pages, 6 encapsulated postscript figure
- …