Abstract
The universal critical behavior of the driven-dissipative non-equilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex valued Landau-Ginzburg functional, which captures the near critical non-equilibrium dynamics, and generalizes Model A for classical relaxational dynamics with non-conserved order parameter. We confirm and further develop the physical picture previously established by means of a functional renormalization group study of this system. Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest non-trivial order in the dimensional epsilon expansion about the upper critical dimension d_c = 4, and establish the emergence of a novel universal scaling exponent associated with the non-equilibrium drive. We also discuss the corresponding situation for a conserved order parameter field, i.e., (sub-)diffusive Model B with complex coefficients.
Highlights
Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest nontrivial order in the dimensional ε expansion about the upper critical dimension dc 1⁄4 4 and establish the emergence of a novel universal scaling exponent associated with the nonequilibrium drive
Experimental systems that are characterized by a strong coupling of light to a large number of matter degrees of freedom [1] hold the potential of developing into laboratories for nonequilibrium statistical mechanics, where phase transitions among stationary states far away from thermodynamic equilibrium could be studied
We obtain a detailed picture of the driven-dissipative Bose condensation transition using the well-developed framework of the perturbative field-theoretical dynamic renormalization group, in this way complementing a previous functional renormalization group study [22,23]
Summary
Experimental systems that are characterized by a strong coupling of light to a large number of matter degrees of freedom [1] hold the potential of developing into laboratories for nonequilibrium statistical mechanics, where phase transitions among stationary states far away from thermodynamic equilibrium could be studied. Nonequilibrium Bose-Einstein condensation of excitonpolaritons has been achieved [15,16,17]—the effective bosonic degrees of freedom result from a strong hybridization of cavity light and excitonic matter states [1,18,19] All of these systems exhibit the crucial ingredients for nontrivial critical scaling behavior at a continuous nonequilibrium phase transition. Both our perturbative two-loop and the nonperturbative functional RG analyses [22,23] are based on an effective long-wavelength description in terms of a noisy GrossPitaevskii equation with complex coefficients [29,30,31,32,33], which in turn constitutes a variant of the time-dependent complex Ginzburg-Landau equation for a two-component order parameter field [34] Such complex stochastic differential equations have found extensive applications in the modeling of spontaneous structure formation in nonequilibrium systems [35,36]. V offers a summary and concluding remarks, and the Appendix provides more technical details
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