Critical fluctuation patterns and anisotropic correlations driven by temperature gradients

Abstract

Studies of QCD phase transition signals are often conducted under spatially uniform temperature conditions. However, the influence of spatial temperature gradients on the signals emerging at the phase interface in the fireball generated by heavy-ion collisions has not yet been fully explored. Based on an Ising-like effective potential, we study the locally equilibrated systems with temperature gradients. In a 2D disk geometry, the low-energy fluctuation spectrum is explicitly resolved into radial and angular momentum modes. The nonlocal correaltions of singular eigen-mode exhibits strong anisotropy, which are long-ranged along isotherms but suppressed radially due to the thermal geometry of the system. Unlike homogeneous systems where the zero-momentum mode dominates, correlations in such inhomogeneous system result from the superposition of a series of zero and non-zero angular momentum modes with comparable contributions. We extract the singular angular momentum modes and establish their connection to experimentally observable anisotropic flow. We find azimuthally sensitive observables may offer a previously unexplored avenue for detecting the QCD phase transition.

Figures (7)

• Figure 1: (a) The spatial temperature distribution as a function of the radius $\rho$. (b) The base field $\sigma_c$ as a function of $\rho$. The solid (dashed) lines are solutions to equation (\ref{['eom']}) at different chemical potentials, and for comparison, the dashed lines are results determined by ${\partial_\sigma }\mathcal{V} = 0$.
• Figure 2: (a) The radial dependence of the effective potential $V_{\text{eff}}$. The solid lines correspond to $\sigma_c$ in $V_{\text{eff}}$ determined by equation \ref{['eom']}, while dashed lines are results with the profile obtained from the condition ${\partial_\sigma }\mathcal{V} = 0$. Different colors are for results with three chemical potential values: $\mu=120$ MeV (blue), $240$ MeV (black), and $360$ MeV (red). (b) The corresponding spectra of fluctuations for different radial ($n$) and angular momentum ($l$) modes, using the same color scheme for $\mu$. Panels (c) and (d) display the radial probability densities for the first ($n=1$) and second ($n=2$) radial excitations, respectively, with different colors denoting different angular momentum modes and the chemical potential fixs at $\mu=240$ MeV. For all panels, the Matsubara mode is $\lambda=0$.
• Figure 3: Individual contributions of the first few low-energy fluctuation modes to the nonlocal two-point correlation function $\langle\tilde{\sigma}(\bm{r},\tau)\tilde{\sigma}(\bm{r}^{\prime},\tau)\rangle d_z$ (in units of MeV). Each panel shows the correlation pattern resulting from a specific combination of radial ($n$) and angular momentum ($l$) quantum numbers (note that the results are summed over the $\pm l$ modes for $l>0$). For all the subplots, the anchor point $\bm{r}^{\prime}$ is fixed at $(5.83, 0)$ fm, the Matsubara mode is $\lambda=0$, and the chemical potential $\mu = 240$ MeV. The spatial coordinates $x$ and $y$ are given in fm.
• Figure 4: The correlation $\langle\tilde{\sigma}({\bm r},\tau) \tilde{\sigma}({\bm r'},\tau)\rangle d_z$, in unit MeV, for the anchor point (marked as a blue point) fixed at $\bm r' = (2.5, 0)~\text{fm}$, $(6, 0)~\text{fm}$, and $(7.5, 0)~\text{fm}$ respectively in each panel. In the first row, the summation are over low-energy modes below $250$ MeV, includes angular momentum mode $l\leq 3$ for the first radial mode $n=1$. In the second row, the summation are over low-energy modes below $450$ MeV, includes angular momentum mode $l\leq 6$ for $n=1$, and $l\leq 2$ for $n=2$. In all the subplots, the chemical potential $\mu = 240$ MeV and the Matsubara mode $\lambda=0$.
• Figure 5: Comparison of the two-point correlations $g_l(\rho) = \rho^2 \langle\tilde{\sigma}_{l}\left( \rho, \tau\right)\tilde{\sigma}_{-l}\left( \rho, \tau\right)\rangle/d_z$ as function of $\rho$ for $l=0,1,2,3$ at $\mu=120$,$240$,and $360$ MeV, respectively.