Dreaming of atmospheres

Here we introduce the RobERt (Robotic Exoplanet Recognition) algorithm for the classification of exoplanetary emission spectra. Spectral retrievals of exoplanetary atmospheres frequently requires the preselection of molecular/atomic opacities to be defined by the user. In the era of open-source, automated and self-sufficient retrieval algorithms, manual input should be avoided. User dependent input could, in worst case scenarios, lead to incomplete models and biases in the retrieval. The RobERt algorithm is based on deep belief neural (DBN) networks trained to accurately recognise molecular signatures for a wide range of planets, atmospheric thermal profiles and compositions. Reconstructions of the learned features, also referred to as `dreams' of the network, indicate good convergence and an accurate representation of molecular features in the DBN. Using these deep neural networks, we work towards retrieval algorithms that themselves understand the nature of the observed spectra, are able to learn from current and past data and make sensible qualitative preselections of atmospheric opacities to be used for the quantitative stage of the retrieval process.Comment: ApJ accepte

Two-dimensional quantum walk under artificial magnetic field

We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of the magnetic flux through the unit cell to the flux quantum as a control parameter. For a given flux ratio, we obtain faster spreading for a small number of steps and the walker tends to be highly localized around the origin. Moreover, the spreading of the walk can be suppressed and decreased within a limited time interval for specific rational values of flux ratio. When the flux ratio is an irrational number, even for a large number of steps, the spreading exhibit diffusive behavior rather than the well-known ballistic one as in the classical random walk and there is a significant probability of finding the walker at the origin. We also analyze the coin-position entanglement and show that the asymptotic behavior vanishes when the flux ratio is different from zero and the coin-position entanglement become nearly maximal in a periodic manner in a long time range.Comment: 7 pages, 5 figures, sections 3 and 4 revise

Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis $-\infty<E<\infty$ instead of being bounded from below $0\leq E <\infty$ (``Fermi's approximation''). Then the Fourier transform of the extended Lorentzian becomes the exponential, but only for times $t\geq 0$, a time asymmetry which is in conflict with the unitary group time evolution of standard quantum mechanics. Extending the Fourier transform from distributions to generalized vectors, we are led to Gamow kets, which possess a Lorentzian energy distribution with $-\infty<E<\infty$ and have exponential time evolution for $t\geq t_0 =0$ only. This leads to probability predictions that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.

Field Theory Entropy, the HH-theorem and the Renormalization Group

We consider entropy and relative entropy in Field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization group fixed points ranks the fixed points, the lowest relative entropy being assigned to the highest multicritical point. We argue that as a consequence of a generalized $H$ theorem Wilsonian RG flows induce an increase in entropy and propose the relative entropy as the natural quantity which increases from one fixed point to another in more than two dimensions.Comment: 25 pages, plain TeX (macros included), 6 ps figures. Addition in title. Entropy of cutoff Gaussian model modified in section 4 to avoid a divergence. Therefore, last figure modified. Other minor changes to improve readability. Version to appear in Phys. Rev.