The non-equilibrium equation of state is found in the approximation of the functional on the local density, and its application to the description of the emission of protons and pions in heavy ion collisions is considered. The non-equilibrium equation of state is studied in the context of the hydrodynamic approach. The compression stage, the expansion stage, and the freeze-out stage of the hot spot formed during the collisions of heavy ions are considered. The energy spectra of protons and subthreshold pions produced in collisions of heavy ions are calculated with inclusion of the nuclear viscosity effects and compared with experimental data for various combinations of colliding nuclei with energies of several tens of MeV per nucleon.

This book is a contribution to the fast and broad Density Functional Theory (DFT) applications of the last few years. Since 2000, the DFT has grown exponentially in several computational areas because of its versatility and reliability to calculate energy from electronic density. The fast DFT’s calculations show how scientists develop more codes focused to simulate molecular and material properties reaching better conclusions than with previous theories. More powerful computers and lower computational costs have certainly assisted the increased growth of interest in this theory. Each chapter presents a specific subject contributing to a vision of the great potential of the quantum/DFT simulations in high pressure, chemical reactivity, ionic liquid, chemoinformatic, molecular docking, and non-equilibrium state.

A prominent goal within the field of modern heavy-ion collisions is to uncover the phase diagram of QCD. Studies of the properties of systems created in heavy-ion collisions strongly suggest that a new state of matter described by quark and gluon degrees of freedom, the quark-gluon plasma, is created when nuclei are collided at very high-energies. Consequently, the QCD phase diagram may contain a rich structure in regions currently accessible to heavy-ion experiments, including a possible critical point where the transformation between hadronic and partonic matter changes from a smooth crossover to a first-order phase transition. Whether this is the case will have to be born out through a combination of experimental analyses and state-of-the-art simulations of heavy-ion collisions. We present a mean-field model of the dense nuclear matter equation of state designed for use in computationally demanding hadronic transport simulations. Our approach, based on the relativistic Landau Fermi-liquid theory, allows us to construct a family of equations of state spanning a wide range of possible bulk properties of dense QCD matter. For the application to simulations of heavy-ion collisions at intermediate beam energies, and in particular having in mind studies centered on probing the regions of the QCD phase diagram most relevant to the search for the QCD critical point, we further present and discuss parametrizations of the developed equation of state describing dense nuclear matter with two phase transitions: the known nuclear-liquid gas phase transition in ordinary nuclear matter, with its experimentally observed properties, and a postulated phase transition at high temperatures and high baryon number densities, meant to model the QCD phase transition from hadronic to quark and gluon degrees of freedom. We implement the developed model in the hadronic transport code SMASH, and show that the resulting dynamic behavior reproduces theoretical expectations for the thermodynamic properties of the system based on the underlying equation of state. In particular, we discuss simulations of systems initialized in regions of the phase diagram affected by the conjectured QCD critical point, and we demonstrate that they reproduce effects due to critical behavior. Specifically, we show that pair distribution functions calculated from hadronic transport simulation data are consistent with theoretical expectations based on the second-order cumulant ratio, and can be used as a signature of crossing the phase diagram in the vicinity of a critical point. Through this, we validate the use of hadronic transport codes as a tool to study signals of a phase transition in dense nuclear matter. We additionally present a novel method that may enable a measurement of the speed of sound and its derivative with respect to the baryon number density in heavy-ion collisions. The devised approach is based on a connection between the speed of sound and the cumulants of the net baryon number, which in the context of the search for the QCD critical point are given considerable attention due to their potential to signal critical fluctuations. We confirm the applicability of the proposed method in two models of dense nuclear matter, including the parametrization of the equation of state developed in this work. Application of our approach to available experimental data implies that the derivative of the speed of sound is non-monotonic in systems created in collisions at intermediate to low energies, which in turn may be connected to non-trivial features in the underlying equation of state.

Introduction to Relativistic Heavy Ion Collisions László P. Csernai University of Bergen, Norway Written for postgraduates and advanced undergraduates in physics, this clear and concise work covers a wide range of subjects from intermediate to ultra-relativistic energies, thus providing an introductory overview of heavy ion physics. The reader is introduced to essential principles in heavy ion physics through a variety of questions, with answers, of varying difficulty. This timely text is based on a series of well received lectures given by Professor L. Csernai at the University of Minnesota, and the University of Bergen, where the author is based.

Comprehensive guide to an important materials science technique for students and researchers.

Quantum field theory is the application of quantum mechanics to systems with infinitely many degrees of freedom. This 2007 textbook presents quantum field theoretical applications to systems out of equilibrium. It introduces the real-time approach to non-equilibrium statistical mechanics and the quantum field theory of non-equilibrium states in general. It offers two ways of learning how to study non-equilibrium states of many-body systems: the mathematical canonical way and an easy intuitive way using Feynman diagrams. The latter provides an easy introduction to the powerful functional methods of field theory, and the use of Feynman diagrams to study classical stochastic dynamics is considered in detail. The developed real-time technique is applied to study numerous phenomena in many-body systems. Complete with numerous exercises to aid self-study, this textbook is suitable for graduate students in statistical mechanics and condensed matter physics.