1,151 research outputs found
Escape from noisy intermittent repellers
Intermittent or marginally-stable repellers are commonly associated with a
power law decay in the survival fraction. We show here that the presence of
weak additive noise alters the spectrum of the Perron - Frobenius operator
significantly giving rise to exponential decays even in systems that are
otherwise regular. Implications for ballistic transport in marginally stable
miscrostructures are briefly discussed.Comment: 3 ps figures include
Deterministic stream-sampling for probabilistic programming: semantics and verification
Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving that they generate samples from the correct distribution - is crucial to the use of probabilistic programming languages for statistical modelling and inference. However, the typical denotational semantics of probabilistic programs is incompatible with deterministic notions of sampling. This is problematic, considering that most statistical inference is performed using pseudorandom number generators.We present a higher-order probabilistic programming language centred on the notion of samplers and sampler operations. We give this language an operational and denotational semantics in terms of continuous maps between topological spaces. Our language also supports discontinuous operations, such as comparisons between reals, by using the type system to track discontinuities. This feature might be of independent interest, for example in the context of differentiable programming.Using this language, we develop tools for the formal verification of sampler correctness. We present an equational calculus to reason about equivalence of samplers, and a sound calculus to prove semantic correctness of samplers, i.e. that a sampler correctly targets a given measure by construction
On the duality between periodic orbit statistics and quantum level statistics
We discuss consequences of a recent observation that the sequence of periodic
orbits in a chaotic billiard behaves like a poissonian stochastic process on
small scales. This enables the semiclassical form factor to
agree with predictions of random matrix theories for other than infinitesimal
in the semiclassical limit.Comment: 8 pages LaTe
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
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.
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
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
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