Monte Carlo simulations of high pressure hydrogen

The aim of this Ph.D. thesis is the study of high pressure hydrogen phases, by means of Monte Carlo simulations, both on effective models and from ab initio simulations. The determination of the physical properties of hydrogen under extreme conditions is of fundamental importance in Astrophysics and Planetary Science to build models describing i.e. brown dwarfs, stars, giant planets, systems mainly composed by hydrogen. More generally in the field of the Condensed Matter Physics, the interest on high pressure hydrogen was originated by the Wigner and Hungtington prediction on the possible occurrence of a metallization transition in low temperature solids, driven by the pressure. The experimental compression techniques (static and dynamic) have depicted for hydrogen a phase diagram of unexpected richness. However, the region of the phase diagram in which the most interesting transitions occur is not accessible through experiments. The ab initio simulation techniques are then a fundamental tools to extend our knowledge on hydrogen at extreme pressures. The most of the simulations are carried out with Born-Oppenheimer (BO) methodologies based on the Density Functional Theory (DFT) evaluation of the electronic ground state at a given nuclear configuration. The accuracy of these simulations is however limited near the metallization transition, due to the well known DFT tendency to favor the metallic versus the insulating states. Recently an alternative approach has been developed, still within the BO approximation: the Coupled Electron-Ion Monte Carlo method, entirely based on MC algorithms, applied both to electrons and nuclei. This method, not suffering of the DFT limitations, may be able to provide accurate results over the entire phase diagram. This thesis is organized as follows. In Chapter 1 we introduce to the problem of the high pressure hydrogen, describing in detail the different regions of the phase diagram reconstructed so far through experiments and numerical simulations. In Chapter 2 we present the theoretical framework of this thesis. After a general discussion of the different Monte Carlo techniques applied in this work (Metropolis Monte Carlo for classical particles, Path Integral Monte Carlo for quantum particles at finite temperature, Variational and Reptation Quantum Monte Carlo for quantum ground state calculations), the Coupled Electron-Ion Monte Carlo method is presented. The the electronic wave functions adopted in the simulations and the wave function optimization procedure are described too. The remaining Chapters are devoted to the results of this work. Chapter 3 concerns the effective screened Coulomb system. It presents a short derivation of the screened Coulomb pair potential and the discussion of the results on the classical system and of the quantum correction to the classical melting line. In Chapter 4 we present the results of the CEIMC simulation on hydrogen in the atomic phase. The first part of this chapter deals with the study at T = 0K of several crystal structures for the atomic hydrogen. The last part concerns the finite temperature study of the stability of the solid vs. the liquid phase. Finally, in Chapter 5 we discuss our results on the liquid-liquid transition

Molecular-Atomic Transition in the Deuterium Hugoniot with Coupled Electron Ion Monte Carlo

We have performed accurate simulations of the Deuterium Hugoniot using Coupled Electron Ion Monte Carlo (CEIMC). Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the principal Hugoniot, where the system undergoes a continuous transition from a molecular fluid to a monatomic fluid. We include all relevant physical corrections so that a direct comparison to experiment can be made. Around 50 GPa we found a maximum compression of 4.85, roughly 10% larger than previous theoretical predictions and experimental data but still compatible with the latter because of their large uncertainty.Comment: 7 pages, 3 figure

Deaths without penalty in Brazil: the difficult convergence among Human Rights, criminal policy and Public Security

A autora pretende trazer uma análise crítica da existência informal da pena de morte no Brasil, resultado da postura estatal em geral em matéria de segurança pública, cuja violência em nome de uma maior eficácia no combate à criminalidade abandona com frequência os princípios fundamentais do Estado Democrático e leva anualmente à execução extrajudicial de milhares de cidadãos, considerados pretensos delinquentes, pela polícia. A imposição de tantas mortes sem pena no Brasil revela a urgência de examinar mais profundamente a relação entre política criminal e direitos humanos, com o objetivo de atingir a convergência necessária para assegurar as condições de sobrevivência de uma sociedade democrática.The author makes a critical analysis of the informal existence of the death penalty in Brazil, as a result of the general state policy about public security, in which violence, in name of a greater efficiency against criminality, often disregards the fundamental principles of the democratic state and leads annually to the extrajudicial execution of thousands of citizens. The imposition of so many deaths without penalty in Brazil reveals the urgency of further examination in the relationship between criminal policy and human rights, with the aim of finding the necessary convergence to ensure the survival of a democratic society

Emergency Speeches and Criminal Policy: the Future of the Criminal Law in Brazil

O artigo apresenta alguns aspectos dos discursos de emergência e sua influência sobre a expansão do Direito Penal, analisados à luz da política criminal e da sociedade de risco.The article details some aspects of the emergency discourses and its influence on the expansion of the Criminal Law, which are analyzed according to the criminal policy and the risk society

Free energy methods in Coupled Electron Ion Monte Carlo

Recent progress in simulation methodologies and in computer power allow first principle simulations of condensed systems with Born-Oppenheimer electronic energies obtained by Quantum Monte Carlo methods. Computing free energies and therefore getting a quantitative determination of phase diagrams is one step more demanding in terms of computer resources. In this paper we derive a general relation to compute the free energy of an ab-initio model with Reptation Quantum Monte Carlo (RQMC) energies from the knowledge of the free energy of the same ab-initio model in which the electronic energies are computed by the less demanding but less accurate Variational Monte Carlo (VMC) method. Moreover we devise a procedure to correct transition lines based on the use of the new relation. In order to illustrate the procedure, we consider the liquid-liquid phase transition in hydrogen, a first order transition between a lower pressure, molecular and insulating phase and a higher pressure, partially dissociated and conducting phase. We provide new results along the T = 600K isotherm across the phase transition and find good agreement between the transition pressure and specific volumes at coexistence for the model with RQMC accuracy between the prediction of our procedure and the values that can be directly inferred from the observed plateau in the pressure-volume curve along the isotherm. This work paves the way for future use of VMC in first principle simulations of high pressure hydrogen, an essential simplification when considering larger system sizes or quantum proton effects by Path Integral Monte Carlo methods.Comment: Accepted for publication in Molecular Physic