Dissipative Dynamics in Classical and Quantum Conservative Systems

In this paper, which is largely review, I will discuss dissipative behavior in mechanical systems which preserve energy. The paper will encompass both the classical and quantum domains. In the classical context I will consider almost Poisson systems; systems which which have a Poisson braket which fails the Jacobi identity. This class of systems includes nonholonomic mechanical systems: systems with nonintegrable constraints such as rolling constraints. Such systems may either preserve or fail to preserve a natural measure. I will discuss also pure Hamiltonian systems such as the Toda lattice which can exhibit dissipative behavior in certain contexts as well as infinite-dimensional systems exhibiting radiative damping. In the quantum context I will discuss systems of quantum oscillators coupled to a heat bath, which also exhibit natural dissipative behavior.

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