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The current thesis is devoted to a systematic study of fluctuations and correlations in heavy-ion collisions, which might be considered as probes for the phase transition and the critical point in the phase diagram, within the Hadron-String- Dynamics (HSD) microscopic transport approach. This is a powerful tool to study nucleus-nucleus collisions and allows to completely simulate experimental collisions on an event-by-event basis. Thus, the transport model has been used to study fluctuations and correlations including the influence of experimental acceptance as well as centrality, system size and collision energy. The comparison to experimental data can separate the effects induced by a phase transition since there is no phase transition in the HSD version used here. Firstly the centrality dependence of multiplicity fluctuations has been studied. Different centrality selections have been performed in the analysis in correspondence to the experimental situation. For the fixed target experiment NA49 events with fixed numbers of the projectile participants have been studied while in the collider experiment PHENIX centrality classes of events have been defined by the multiplicity in certain phase space region. A decrease of participant number fluctuations (and thus volume fluctuations) in more central collisions for both experiments has been obtained. Another area of this work addresses to transport model calculations of multiplicity fluctuations in nucleus-nucleus collisions as a function of colliding energy and system size. This study is in full correspondence to the experimental program of the NA61 Collaboration at the SPS. Central C+C, S+S, In+In, and Pb+Pb nuclear collisions at Elab = 10, 20, 30, 40, 80, 158 AGeV have been investigated. The expected enhanced fluctuations - attributed to the critical point and phase transition - can be observed experimentally on top of a monotonic and smooth ‘hadronic background’. These findings should be helpful for the optimal choice of collision systems and collision energies for the experimental search of the QCD critical point. Other observables are fluctuations of ratios of hadrons (e.g. pions, kaons, protons, etc.) which are not so much affected by volume fluctuations. In particular HSD results for the kaon-to-pion ratio fluctuations, which has been regarded as promising observable for a long time, are presented from low SPS energies up to high energies at RHIC. In addition to the HSD calculations statistical model is also used in terms of microcanonical, canonical and grand canonical ensembles. Further a study of the system size event-by-event fluctuations causing rapidity forward-backward correlations in relativistic heavy-ion collisions is presented. The HSD simulations reveal strong forward-backward correlations and reproduce the main qualitative features of the STAR data in A+A collisions at RHIC energies. It has been shown that strong forward-backward correlations arise due to an averaging over many different events that belong to one centrality bin. An optimization of the experimental selection of centrality classes is presented, which is relevant for the program of the NA61 collaboration at CERN, the low-energy program at RHIC, as well as future experiments at FAIR.
This thesis presents a model for the dynamical description of deconfined quark matter created in ultra-relativistic heavy ion collisions, treating quarks and antiquarks as classical point particles subject to a colour-dependent, Cornell-type potential interaction. The model provides a dynamical handle for hadronization via the recombination of quarks and antiquarks in colour neutral clusters. Gluons are not included explicitly in the model,but are described in an effective manner by the means of the potential interaction. The model includes four different quark flavours (up, down, strange and charm) and uses current masses for the quarks. The dynamical evolution of a system of colour charges subject to the Hamiltonian equations of motion of the model yields the formation of colour neutral clusters of quarks and antiquarks, which are subject only to a small remaining interaction, the strong interquark potential notwithstanding. These clusters can be mapped onto hadrons and hadronic resonances. Thus, the model allows a dynamical description of quarks degrees of freedom in heavy ion collisions, including a recombination scheme for hadronization. The thermal properties of the model turn pout to be very satisfying. The model shows a transition from a confining phase to a deconfined phase with rising temperature, going hand in hand with a softest point in the equation of state and a rise of energy density and pressure to the Stefan-Boltzmann limit of a gas of quarks and antiquarks. Moreover, the potential interaction is screened in the deconfined phase. For the dynamical description of ultra-relativistic heavy ion collision, the qMD model is coupled to UrQMD as a generator for its initial conditions. In this way, a fully dynamical description of the expansion and hadronization of the fireball created in such collisions can be achieved. Non-equilibrium aspects of the expansion dynamics and hadronization by recombination of quarks and antiquarks are discussed in detail, and a comparison with experimental data of collisions at the CERN-SPS is presented. The big advantage of the qMD model is the possibility to study cluster formation, including exotic clusters, and fluctuations in a dynamical manner. As an example, event-by-event fluctuations in electric charge are studied. Such fluctuations have been proposed as a clear criterion to distinguish a deconfined system from a hadrons gas. However, experimental data show hadron gas fluctuation measures even at RHIC, where deconfinement is taken for granted. We will see how the dynamics of quark recombination washes out the quark-gluon plasma signal in the fluctuation criterion. Moreover, we will discuss briefly the problem of entropy at recombination. In a second application, the formation of exotic hadronic clusters, larger than usual mesons and baryons, is studied. Such clusters could provide new measures for the thermalization and homogenization of a deconfined gas of colour charges. Moreover, number estimates for exotic clusters from recombination are considerably lower than corresponding predictions from thermal models, providing a clear difference between statistical hadronization and hadronization via quark recombination. A detailed analysis is provided for pentaquark candidates such as the Theta-Plus. It turns out that the distribution of exotic states over strangeness, isospin, and spin could provide a sensitive measure for thermalization and decorrelation in the deconfined quark phase, if it could be measured.