A stochastic golden rule and quantum Langevin equation for the low density limit

A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via interaction of scattering type. We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir. The quantum Langevin equation describes not only dynamics of the system but also the reservoir. We show that the generator of the corresponding master equation has the Lindblad form of most general generators of completely positive semigroups

Dynamics of Dissipative Two-Level Systems in the Stochastic Approximation

The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement. We demonstrate that the method of the stochastic approximation which is a general method of consideration of dynamics of an arbitrary system interacting with environment is powerful enough to reproduce qualitatively striking results by Leggett at al. found earlier for this model. The result include an exact expression of the dynamics in terms of the spectral density and show an appearance of two most interesting regimes for the system, i.e. pure oscillating and pure damping ones. Correlators describing environment are also computed.Comment: 13 pages, plainte

Nuclear physics with a medium-energy Electron-Ion Collider

A polarized ep/eA collider (Electron-Ion Collider, or EIC) with variable center-of-mass energy sqrt(s) ~ 20-70 GeV and a luminosity ~ 10^{34} cm^{-2} s^{-1} would be uniquely suited to address several outstanding questions of Quantum Chromodynamics (QCD) and the microscopic structure of hadrons and nuclei: (i) the three-dimensional structure of the nucleon in QCD (sea quark and gluon spatial distributions, orbital motion, polarization, correlations); (ii) the fundamental color fields in nuclei (nuclear parton densities, shadowing, coherence effects, color transparency); (iii) the conversion of color charge to hadrons (fragmentation, parton propagation through matter, in-medium jets). We briefly review the conceptual aspects of these questions and the measurements that would address them, emphasizing the qualitatively new information that could be obtained with the collider. Such a medium-energy EIC could be realized at Jefferson Lab after the 12 GeV Upgrade (MEIC), or at Brookhaven National Lab as the low-energy stage of eRHIC.Comment: 9 pages, 5 figures. Mini-review compiled in preparation for the MEIC Conceptual Design Report, Jefferson Lab (2011