Study On Effective Theory Of Brownian Motion Of A Heavy Quark

Quark-gluon plasma is a new form of matter produced in relativistic heavy-ion collisions,and has become an important means to reveal the basic structure of strong interaction.An heavy quark,which is produced in the early stage of relativistic heavy ion collisions and experiences the entire processes of the evolution of quark-gluon plasma,is thus important probe for studying the properties of quark-gluon plasma.However,the widely-used Brownian motion model for a heavy quark is phenomenological,particularly,it does not systematically include the nonlinear interactions between dynamic variables and noises,as well as interactions among noises.In this dissertation,we study the effective theory for Brownian motion of heavy quark in a strongly coupled quark-gluon plasma from two complementary perspectives: the non-equilibrium effective field theory and the holographic gravitational models.First,we adopt the recently formulated non-equilibrium effective field theory approach(based on the Schwinger-Keldysh closed time path)and construct an effective theory of a heavy quark in quark-gluon plasma.From symmetry principle,we constrain the action of the effective theory.Here we focus to colored noises and non-Gaussian noises in the effective theory of heavy quark in quark-gluin plasma.In addition,in view of the strong electromagnetic fields produced in the non-central high energy heavy-ion collisions,accounting for the effect of strong electromagnetic fields in the effective theory is another focus of this dissertation.Second,based on the holographic dual of Schwinger-Keldysh closed time path,we use holographic models and derive the effective action for a heavy quark in the strongly coupled quark-gluon plasma.We calculate all coefficients in the effective action,and demonstrate their dependencies on temperature and electromagnetic fields.The research of this part is a direct verification of the effective action constructed based on nonequilibrium effective field theory approach.In addition,we explore the physical essence of the dynamical Kubo-Martin-Schwinger symmetry of the non-equilibrium effective field theory.Last,the effective action of the heavy quark is transformed into the generalized Fokker-Planck equation,which provides a more convenient theoretical framework for future numerical simulation.Since the effective action contains non-Gaussian noises,the generalized Fokker-Planck equation obtained in this dissertation has higher order Kramers-Moyal terms,which is remarkedly different from the standard Fokker-Planck equation widely used in the literature.The research contents of this dissertation further improve the effective theory of heavy quark’s Brownian motion in the strongly coupled quark-gluon plasma,provide a reliable theoretical framework for systematically exploring the significance of non-Gaussian noises,and help to further understand the fluid mechanical properties of quark-gluon plasma.Meanwhile,we further developed the holographic prescription for SchwingerKeldysh closed time path,which can be used to reveal the low-energy effective theory of holographic models,and will be helpful in understanding the quantum gravitational fluctuations of black holes.