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We study the problem of the damping of collective modes close to aPomeranchuk quantum critical point in a Fermi liquid. In analogy with problemsin dissipative open quantum systems, we derive the Landau damping of a Fermiliquid by integrating out a macroscopic number of degrees of freedom from agenerating functional. Being a reformulation of the linearized Boltzmannequation this approach reproduces well-known results from the theory of Fermiliquids. We also study the Bethe-Salpeter equations within the Landau theoryand discuss the implications of these results on quantum phase transitions ofthe Pomeranchuk type and its dynamical exponent, z. We apply our results to theelectronic nematic instability and find z=3 in the collisionless limit.Comment: 9 pages, 1 figure; minor additions, references adde

Heat bath approach to Landau damping and Pomeranchuk quantum critical points