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We discuss multiplicity fluctuation caused by noises during hydrodynamic evolution of the quark-gluon fluid created in high-energy nuclear collisions.
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The fluctuation-dissipation relation tells that dissipation always accompanies with thermal fluctuations. Relativistic fluctuating hydrodynamics is used to study the effects of the thermal fluctuations in the hydrodynamic expansion of the quark-gluon plasma created in the high-energy nuclear collisions. We show that the thermal noise obeys the steady-state fluctuation theorem when (i) the time scales of the evolution of thermodynamic quantities are sufficiently longer than the relaxation time, and (ii) the thermal fluctuations of temperature are sufficiently small. The steady-state fluctuation theorem describes the distribution of the entropy which can be related to the multiplicity observed in high-energy nuclear collisions. As a consequence, we propose an upper bound to the multiplicity fluctuations which is useful to test the initial state models. We also numerically investigate breaking of the steady-state fluctuation theorem due to the non-vanishing relaxation time in real nuclear collisions.
We investigate effects of causal hydrodynamic fluctuations in the longitudinally expanding quark gluon plasma on final entropy distributions in high-energy nuclear collisions.
Observation of the Brownian motion of a small probe interacting with its environment is one of the main strategies to characterize soft matter. Essentially two counteracting forces govern the motion of the Brownian particle. First, the particle is driven by the rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Second, the friction between the particle and the viscous solvent damps its motion. Conventionally, the thermal force is assumed to be random and characterized by a white noise spectrum. Friction is assumed to be given by the Stokes drag, implying that motion is overdamped. However, as the particle receives momentum from the fluctuating fluid molecules, it also displaces the fluid in its immediate vicinity. The entrained fluid acts back on the sphere and gives rise to long-range correlation. This hydrodynamic memory translates to thermal forces, which display a coloured noise spectrum. Even 100 years after Perrins pioneering experiments on Brownian motion, direct experimental observation of this colour has remained elusive. Here, we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere by a strong optical trap. We show that due to hydrodynamic correlations the power spectral density of the spheres positional fluctuations exhibits a resonant peak in strong contrast to overdamped systems. Furthermore, we demonstrate that peak amplification can be achieved through parametric excitation. In analogy to Microcantilever-based sensors our results demonstrate that the particle-fluid-trap system can be considered as a nanomechanical resonator, where the intrinsic hydrodynamic backflow enhances resonance. Therefore, instead of being a disturbance, details in thermal noise can be exploited for the development of new types of sensors and particle-based assays for lab-on-a-chip applications.
We study one-loop corrections to retarded and symmetric hydrostatic correlation functions within the Schwinger-Keldysh effective field theory framework for relativistic hydrodynamics, focusing on charge diffusion. We first consider the simplified setup with only diffusive charge density fluctuations, and then augment it with momentum fluctuations in a model where the sound modes can be ignored. We show that the loop corrections, which generically induce non-analyticities and long-range effects at finite frequency, non-trivially preserve analyticity of retarded correlation functions in spatial momentum due to the KMS constraint, as a manifestation of thermal screening. For the purposes of this analysis, we develop an interacting field theory for diffusive hydrodynamics, seen as a limit of relativistic hydrodynamics in the absence of temperature and longitudinal velocity fluctuations.
Macroscopic parameters as well as precise information on the random force characterizing the Langevin type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function.
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