Kinetics of Many-Body Reservoir Engineering

Hugo Ribeiro, Florian Marquardt

Recent advances illustrate the power of reservoir engineering in applications to many-body sys-tems, such as quantum simulators based on superconducting circuits. We present a frameworkbased on kinetic equations and noise spectra that can be used to understand both the transientand long-time behavior of many particles coupled to an engineered reservoir in a number-conservingway. For the example of a bosonic array, we show that the non-equilibrium steady state can beexpressed, in a wide parameter regime, in terms of a modified Bose-Einstein distribution with anenergy-dependent temperature.

Field theory of monochromatic optical beams II. Classical and quantum paraxial fields

Andrea Aiello

This work is the second part of an investigation aiming at the study of optical wave equations from a field-theoretic point of view. Here, we study classical and quantum aspects of scalar fields satisfying the paraxial wave equation. First, we determine conservation laws for energy, linear and angular momentum of paraxial fields in a classical context. Then, we proceed with the quantization of the field. Finally, we compare our result with the traditional ones.

Field theory of monochromatic optical beams I. classical fields

Andrea Aiello

We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler-Lagrange equations reproduces either Helmholtz and paraxial wave equations with the $z$-coordinate, associated with the main direction of propagation of the fields, playing the same role of time in standard Lagrangian theory. For both Helmholtz and paraxial scalar fields, we calculate the canonical energy-momentum tensor and determine the continuity equations relating ``energy'' and ``momentum'' of the fields. Eventually, the reduction of the Helmholtz wave equation to a useful first-order Dirac form, is presented. This work sheds some light on the intriguing and not so acknowledged connections between angular spectrum representation of optical wavefields, cosmological models and physics of black holes.