Holographic Brownian Motion in Magnetic Environments

Using the gauge/gravity correspondence, we study the dynamics of a heavy quark in two strongly-coupled systems at finite temperature: Super-Yang-Mills in the presence of a magnetic field and non-commutative Super-Yang-Mills. In the former, our results agree qualitatively with the expected behavior from weakly-coupled theories. In the latter, we propose a Langevin equation that accounts for the effects of non-commutativity and we find new interesting features. The equation resembles the structure of Brownian motion in the presence of a magnetic field and implies that the fluctuations along non-commutative directions are correlated. Moreover, our results show that the viscosity is smaller than the commutative case and that the diffusion properties of the quark are unaffected by non-commutativity. Finally, we compute the random force autocorrelator and verify that the fluctuation-dissipation theorem holds in the presence of non-commutativity.Comment: 34 pages. v2: typos corrected. v3: title and abstract slightly modified in order to better reflect the contents of the paper; footnote 3 and one reference were also added; version accepted for publication in JHE

Information dynamics of a particle in a magnetic field

We discuss the time evolution of information entropy (S) of a harmonic oscillator driven by thermal noise in the presence of a magnetic field. Our analysis is based on the Fokker-Planck description of the stochastic process. It shows that the relaxation time of a given non equilibrium state increases with increase of strength of the applied magnetic field. It further increases if the thermal noise becomes colored. The dependence of the time derivative of the entropy, its upper bound and related quantity on the strength of magnetic field, damping, noise correlation time and temperature is studied in detail