Investigations On The Quantum Statistics In Non-extensive Physics And Its Phenomenological Applications In High Energy Nuclear Physics

Non-extensive statistics is a new framework of statistical physics which generalizes the classical Boltzmann-Gibbs statistical physics.It aims at dealing with realistic physical issues beyond the classical cases,for instance,systems including long range interactions or memory effects.Non-extensive physics has been a hot topic of international fundamental physical and applied physical researches since it was introduced in the 1960's.It has also obtained wide and effective applications over various kinds of areas.In view of the complexity of actual physical systems and the diversity of research techniques,non-extensive physics develops numerous branches among which the so-called Tsallis statistical physics,firstly proposed by C.Tsallis in 1988,is the most famous and widely-used one.This dissertation investigates on non-extensive statistical theoretical properties as well as the corresponding Thermodynamical nature.Moreover,applications of it on the rela-tivistic heavy-ion collisions and other fields are also shown deeply and concretely.In the following some of its innovative research results are listed:1. From the basic assumptions and its limitations in BG statistics,we thoroughly intro-duce the fundamental theoretical knowledge of Tsallis non-extensive statistics.Considering and doubting about its three different energy constraints in the Tsallis non-extensive statis-tical system,we re-build up the framework and introduce another non-extensive systemic constraint in order to derive the Tsallis q-probability distribution function.Thus the self-referential problem in the deduced probability distribution as well as thermal quantities in Tsallis non-extensive statistics is successfully avoided.And thermodynamical relationships are also consistently obtained with respect to it.Furthermore,we firstly extend it to gener-alize the grand canonical ensemble and set up a generalized ensemble theory.Reasonably it leads to Tsallis non-extensive quantum statistics within the non-extensive occupancy distri-butions of particle number,namely q-Bose-Einstein distribution and q-Fermi-Dirac distribu-tion contained.2.We generalize the linear sigma model from finite temperature field theory into the Tsallis non-extensive linear sigma model,i.e.q-LSM.Using it we study the chiral phase transition of QGP at finite temperature and baryon number density.In detail,we investigate the thermal potential,the mass of constituent(anti-)quark and its susceptibility with respect to the temperature,etc.Finally we explore the phase diagram at finite temperature and chem-ical potential in the framework of this q-LSM.Results show that in the q-LSM non-extensive effects are more comprehensive and precise near phase transition range and the critical end-ing point in the phase diagram,comparing with other non-extensive models like q-NJL and so on.3.As for the non-extensive quantum statistics,we note further requirements arise from the symmetric handling of particle and holes,so the previous naive replacement of Euler exponential with q-exponential functions can loose this kind of symmetry.We solve this problem by proposing several solutions and analysing them comparatively.As a result,a so-called "fractional normalization" solution is obtained.Worthy to be mentioned that it can lead to the Kaniadakis ? distribution under some special connection.With introducing the deformed ?-exponential function,G.Kaniadakis firstly proposed the Kaniadakis non-extensive statistics in 2001.We also give a brief introduction on this non-extensive statistics theoretically.4.We thoroughly compare Tsallis and Kaniadakis non-extensive statistical physics both theoretically and phenomenologically,and apply them into the transverse momentum spec-tra of final-state hadrons in relativistic heavy-ion collisions,respectively.From the perspec-tive of thermodynamics and statistics,we constructively put forward several non-extensive phenomenological models to describe the intimate connection between the non-extensive pa-rameter q or ? and the fitting temperature T in the colliding system.All of these will deepen our cognition on the non-extensive statistical physics theoretically and phenomenologically and nicely offer an effective opportunity for it henceforth.In conclusion,this dissertation improves the thermo-dynamical relationships with re-spect to Tsallis non-extensive statistical mechanics,develops the generalized non-extensive ensemble theory and systematically researches corresponding statistical quantities.It presents a better non-extensive effects on physical systems within linear sigma model.Moreover,it investigates on the non-extensive statistical physics and its phenomenological applications in quantum statistics and high energy physics,as well as its comparisons with other existed researching results.