Evolution of energy density fluctuations in the presence of a magnetic field

TL;DR

This study investigates the impact of a static, uniform magnetic field $B$ on the evolution of energy-density fluctuations in a relativistic partonic medium during approach to local equilibrium in relativistic heavy-ion collisions. They solve the relativistic Boltzmann-Vlasov equation in the relaxation time approximation and perform momentum-mode analysis of fluctuations, using dimensionless variables $t' = t/τ_c$, $x' = x/τ_c$, and $k' = k/m_0$, along with a magnetic-field parameter $β$. The main result is that the magnetic field enhances damping of mode oscillations, especially for fluctuations transverse to $B$, which suppresses high-momentum modes and yields a smoother energy-density profile; the effective ultraviolet cutoff on fluctuations is reduced. The findings have phenomenological relevance for the pre-equilibrium stage of relativistic heavy-ion collisions, potentially modifying short-wavelength fluctuations and impacting flow harmonics $v_n(p_T)$.

Abstract

In this proceeding, we study the evolution of energy density fluctuations in the presence of a static and uniform magnetic field. By numerically solving the relativistic Boltzmann-Vlasov equation within the relaxation time approximation and performing the momentum mode analysis of different wavelength fluctuations, we show that the magnetic field increases the damping of mode oscillations. This causes a qualitative change in the fluctuations present in the system at the timescale required to achieve a local equilibrium state.

Figures (4)

• Figure 1: Energy density fluctuations $\delta \hat{\varepsilon}$ at time $t/\tau_c=0$ and $t/\tau_c=3.0$ in the absence and presence of ${\bf B}$. Figure is from bveq.
• Figure 2: Time evolution of the most dominant mode of energy density fluctuations (a) for $\kappa_p \tau_c=0.88$ and (b) for $\kappa_p \tau_c=2.0$ in the absence and presence of magnetic field. Evolution of these modes for a longer time are shown in insets. Figure is from bveq.
• Figure 3: Left: The decay timescale $\gamma_m^{-1}$ of a mode as a function of mode-momentum $\kappa_p \tau_c$ for different values of $\beta_0$. Right: The fractional change of wavelength cutoff $\delta \lambda^*_c$ as a function of $\beta_0$. Figures are from bveq.
• Figure 4: Left: The energy density fluctuations, $(\hat{\varepsilon} - \hat{\varepsilon}_0)$, at time $t/\tau_c=0$ and $t/\tau_c=3.0$ in the absence and presence of the magnetic field. In the presence of the magnetic field, the energy density profile is smoother and has a larger peak value as compared to $B=0$. Right: Momentum spectrum of energy density fluctuations shown in the left figure. Figures are from bveq.