A Tale of the Scattering Lifetime and the Mean Free Path

The idea of applying the scattering lifetime calculated from the imaginary part of the zero temperature elastic scattering cross-section to study a hidden self-consistent damping in two spaces of importance for non-equilibrium statistical mechanics is proposed. It is discussed its relation with the classical phase space from statistical mechanics and the configuration space from nonrelativistic quantum mechanics. This idea is contrasted with the mean free path values in three elastic collision regimes. The main exercise is to study the behavior of a self-consistent probabilistic distribution function in a space we have called the reduced phase space, since it is related to the scattering lifetime. This exercise has been solved in two unconventional superconductors, for which several calculations are discussed. One of them is to obtain the scattering phase shift from the inverse strength of an atomic potential and the other is to build several phases with different nodal configuration of the superconducting order parameter and show that the imaginary self-consistent part of the scattering cross-section is always positive for two compounds: the triplet strontium ruthenate and the singlet doped with strontium lanthanum cuprate when three models of superconducting order parameters are used: the quasi-point, the point and the line nodal cases. We finally compare the frequency dispersion in the anomalous skin effect with singular shapes of the Fermi surface with the frequency dispersion in the scattering lifetime and their respective mean free paths. This idea is useful because it intuitively explores the nonlocality of this type of hidden self-consistent damping for those incoherent fermionic quasiparticles

Quasi-point versus point nodes in Sr2RuO4Sr_2RuO_4, the case of a flat tight binding γ\gamma sheet

We perform a numerical study of the unitary regime as a function of disorder concentration in the imaginary part of the elastic scattering cross-section for the compound $Sr_2RuO_4$ in the flat band non-disperse limit. By using a self-consistent tight-binding (TB) method, we find a couple of families of Wigner probabilistic functions that help to explain macroscopically the distribution between Fermion dressed quasiparticles and Cooper pairs, and also the position of nodes in the order parameter for $Sr_2RuO_4$. Therefore, we are able to show that a TB model for the $\gamma$ sheet numerically shows 4 point nodes in a flat $\gamma$ sheet limit or 4 quasi-point nodes for strong dispersion $\gamma$ sheet limit in the reduced phase scattering space (RPS).Comment: 19 pages, 4 figures, 44 reference

Explosive transitions in site percolation

Master ́s Thesis, Postgraduate Studies Center, Universitat de les Illes Balears, Academic year 2019-2020.Due to its simplicity and great application, it is known that percolation is one of the phenomena widely studied by statistical physics that addresses the theory of phase transitions and critical phenomena. In 2009 [1] the authors proposed a percolation variant introducing a competitive process between sites (or bonds), which prevents large clusters from joining each other, as a possible means of delaying the phase transition of a densely connected network, leading to explosive transitions or atypical and abnormal behaviors. This new type of percolation brought great interest, leading to a series of studies, among which the analysis of the order of the transition (continuous or discontinuous), the creation of others models with explosive behaviors, scale analysis, among others. In this Master thesis we will study site percolation. As an algorithm to delay the transition and cause explosive percolation, we propose a variant of the sum rule proposed in [D. Achlioptas, R.M. D’Souza, J. Spencer, Science, 323,1453, (2009)] which we call global sum rule. In order to characterize the phase transition we will make use of numerical analysis. We explore the behavior of the transition for different order parameters, in the same way we evaluate the changes that the transition can undergo with different sizes and dimensions of the network, as well as for different number of tries in the global sum rule.Peer reviewe

Self-Consistent Study of the Superconducting Gap in the Strontium-doped Lanthanum Cuprate

This work is aimed at numerically investigating the behavior of the Fermi energy in Strontium-doped Lanthanum Cuprate, using a numerical zero temperature elastic scattering cross-section procedure in the unitary collision regime. The main task is to vary the zero temperature superconducting energy gap from its zero value in the normal state, to the highest value of 60 meV. We find that there are two different reduced phase space regimes for the first harmonic line node's order parameter. The first scenario considers that when the Fermi energy and the nearest hopping terms have the same order of magnitude, the physics can be described by a picture given by nonequilibrium statistical mechanics. A second scenario indicates, that when the Fermi energy parameter and the hopping term have different order of magnitude; the physical picture tends to be related to the nonrelativistic quantum mechanical degrees of freedom coming from quasi-stationary quantum energy levels, with a damping term seen in the probability density distribution function, that is described in the configuration space. Henceforth, it is concluded that the use of the zero temperature elastic scattering cross-section links the phase and configuration spaces through the inverse scattering lifetime, and helps to clarify the role of the degrees of freedom in Strontium-doped Lanthanum Cuprate. Finally, we think that the self-consistent numerical procedure with the reduced phase space, induces nonlocality in the inverse scattering lifetime.Comment: 13 pages, 11 figures, 4 tables, 55 reference

Tight-Binding Superconducting Phases in the Unconventional Compounds Strontium-Substituted Lanthanum Cuprate and Strontium Ruthenate

We use the idea of the Wigner probability distribution (WPD) in a reduced scattering phase space (RPS) for the elastic scattering cross-section, with the help of a Tight-Binding (TB) numerical procedure allowing us to consider the anisotropic quantum effects, to phenomenologically predict several phases in these two novel unconventional superconductors. Unlike our previous works with pieces of evidence that these two compounds are in the unitary strong scattering regime and that superconductivity is suppressed by the atoms of strontium in both materials, several phases are built. In the case of the strontium-substituted lanthanum cuprate, it was found three phases from one family of Wigner probabilistic distributions, one corresponding to the antiferromagnetic compound La2CuO4 another one which consists of a coalescing metallic phase for very lightly doped La2-xSrxCuO4, and finally a strong self-consistent dependent strange metal phase with optimal levels of doping. In the case of a triplet superconductor strontium ruthenate, three phases can be differentiated from two families of Wigner distribution probabilities, one family of WDP with point nodes where Cooper pairs and dressed scattered normal quasiparticles are mixed for the whole range of frequencies and which correspond to an FS $\gamma$ flat-sheet in the ground metallic state, and two phases from another WPD family, where, in one of then, the Miyake-Narikiyo quasinodal tiny gap model allows the unique presence of Cooper pairs in a tiny interval of frequencies near the superconducting transition TC, the other phase corresponds to the mixed-phase with Cooper pairs and dressed by stoichiometric strontium non-magnetic atoms, where strong self-consistent effects are noticeable. This approach allows comparing experimental results for samples in both compounds with numerical analysis studies.Comment: 7 pages, 5 figures, 2 table

Variations on the theme: focus on cerebellum and emotional processing

The cerebellum operates exploiting a complex modular organization and a unified computational algorithm adapted to different behavioral contexts. Recent observations suggest that the cerebellum is involved not just in motor but also in emotional and cognitive processing. It is therefore critical to identify the specific regional connectivity and microcircuit properties of the emotional cerebellum. Recent studies are highlighting the differential regional localization of genes, molecules, and synaptic mechanisms and microcircuit wiring. However, the impact of these regional differences is not fully understood and will require experimental investigation and computational modeling. This review focuses on the cellular and circuit underpinnings of the cerebellar role in emotion. And since emotion involves an integration of cognitive, somatomotor, and autonomic activity, we elaborate on the tradeoff between segregation and distribution of these three main functions in the cerebellum