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The atmospheric meridional energy transport in the Northern Hemisphere midlatitudes is mainly accomplished by planetary and synoptic waves. A decomposition into wave components highlights the strong seasonal dependence of the transport, with both the total transport and the contributions from planetary and synoptic waves peaking in winter. In both winter and summer months, poleward transport extremes primarily result from a constructive interference between planetary and synoptic motions. The contribution of the mean meridional circulation is close to climatology. Equatorward transport extremes feature a mean meridional equatorward transport in winter, while the planetary and synoptic modes mostly transport energy poleward. In summer, a systematic destructive interference occurs, with planetary modes mostly transporting energy equatorward and synoptic modes again poleward. This underscores that baroclinic conversion dominates regardless of season in the synoptic wave modes, whereas the planetary waves can be either free or forced, depending on the season. The atmospheric heat transport from low to high latitudes is the main mechanism through which the climate reequilibrates the latitudinally uneven absorption of solar radiation. The atmospheric transport is fueled by instabilities driven by the presence of temperature differences between low and high latitudes and acts in such a way to reduce such gradient. This is one of the main stabilizing mechanisms of the climate system. In this work, we investigate how motions of different spatial scales contribute to atmospheric heat transports in the Northern Hemisphere. We discover that the relative importance of synoptic and planetary scale atmospheric motions is different in summer and winter. Our analysis delves into the analysis of events associated with extreme heat transport toward high latitudes, where we see a compensating mechanism between synoptic and planetary atmospheric motions. We further study days characterized by very large and very small (or even negative) heat transport toward the high latitudes. These “extreme events” are driven by complex interactions between the different scales. Our results are relevant for elucidating basic dynamical and thermodynamical properties of the atmosphere and can be used to benchmark the performance of climate models. Competition exists in all seasons between regular and extreme meridional transports performed by zonal mean, synoptic and planetary wavesWinter and summer poleward heat transport extremes are driven by the combined effect of planetary and synoptic wavesEquatorward transport extremes are driven by synoptic and planetary waves interaction in summer, predominantly by planetary waves in winter

Abstract:: We describe a procedure to take into account the spatial dispersion of the optical excitations in the susceptibility sum rules. We show that this implies that relativistic corrections of the same order must be considered. The final result is a decrease of the total oscillator strength equal to the ratio of the average electron kinetic energy with mc2. We propose experiments with synchrotron radiation sources on crystals of heavy elements to observe the described effect.

Abstract:: We use the Kubo response function formalism to derive the asymptotic behaviour of the harmonic generation susceptibilities to all orders n. The results show a stringent correspondence with the ones previously obtained from the classical anharmonic oscillator model. They are characterized by a dependence and a coefficient proportional to the trace of the (n+1)th derivative of the potential energy on the equilibrium density matrix. Using the above results we derive new Kramers-Krönig relations and sum rules for all orders of harmonics susceptibilities.

Abstract:: The nonlinear oscillator model is useful to basically understand the most important properties of nonlinear optical processes. It has been shown to give the correct asymptotic behaviour and to provide the general features of harmonic generation to all orders, in particular dispersion relations and sum rules. We investigate the properties of pump and probe processes using this model, and study those cases where general theorems based on the holomorphic character of the Kubo response functions cannot be applied. We show that it is possible to derive new sum rules and new Kramers-Krönig relations for the two lowest moments of the real and of the imaginary part of the third order susceptibility and that new specific contributions become relevant as the intensity of the probe increases. Since the analytic properties of the susceptibility functions depend only upon the time causality of the system we are confident that these results are not model dependent and therefore have a general validity, provided one substitutes for the equilibrium values of the potential derivatives the density matrix expectation values of the corresponding operators.