Divergences in open quantum systems

  • Cesar Agón
  • Albion Lawrence
Open Access
Regular Article - Theoretical Physics


We show that for cubic scalar field theories in five and more spacetime dimensions, and for the T = 0 limit of the Caldeira-Leggett model, the quantum master equation for long-wavelength modes initially unentangled from short-distance modes, and at second order in perturbation theory, contains divergences in the non-Hamiltonian terms. These divergences ensure that the equations of motion for expectation values of composite operators closes on expectation values of renormalized operators. Along the way we show that initial “jolt” singularities which occur in the equations of motion for operators linear in the fundamental variables persist for quadratic operators, and are removed if one chooses an initial state projected onto low energies, following the Born-Oppenheimer approximation.


Effective Field Theories Quantum Dissipative Systems Renormalization Group 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Martin Fisher School of PhysicsBrandeis UniversityWalthamU.S.A.
  2. 2.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  3. 3.C.N. Yang Institute for Theoretical PhysicsState University of New YorkStony BrookU.S.A.

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