A new type of non-Hermitian phase transition in open systems far from thermal equilibrium

Abstract

We demonstrate a new type of non-Hermitian phase transition in open systems far from thermal equilibrium, which can have place in the absence of an exceptional point. This transition takes place in coupled systems interacting with reservoirs at different temperatures. We show that the spectrum of energy flow through the system caused by the temperature gradient is determined by the $$\varphi^{4}$$ φ 4 -potential. Meanwhile, the frequency of the maximum in the spectrum plays the role of the order parameter. The phase transition manifests itself in the frequency splitting of the spectrum of energy flow at a critical point, the value of which is determined by the relaxation rates and the coupling strength. Near the critical point, fluctuations of the order parameter diverge according to a power law with the critical exponent that depends only on the ratio of reservoirs temperatures. The phase transition at the critical point has the non-equilibrium nature and leads to the change in the energy flow between the reservoirs. Our results pave the way to manipulate the heat energy transfer in the coupled out-of-equilibrium systems.

Energy Transport Induced by Transition from Weak to Strong Coupling Regime Between Non-Hermitian systems

“…Appendix C: Explicit expressions for Eqs. ( 23)- (24) In this Appendix, we obtain explicit expressions for coefficients A, B, C, F, T, Q, Y in Eqs. ( 23)-( 24) and coefficients 20)- (21).…”

“…Interest to strong coupling regime is also related to control of energy transport in open quantum systems [23,24]. In [24], it has been demonstrated that in strong coupling regime a new type of phase transition appears.…”

“…Interest to strong coupling regime is also related to control of energy transport in open quantum systems [23,24]. In [24], it has been demonstrated that in strong coupling regime a new type of phase transition appears. This phase transition manifests itself as an appearance of two maxima in Fourier spectrum of energy flow from subsystem connected with hot reservoir to subsystem connected with cold reservoir [24].…”

“…In [24], it has been demonstrated that in strong coupling regime a new type of phase transition appears. This phase transition manifests itself as an appearance of two maxima in Fourier spectrum of energy flow from subsystem connected with hot reservoir to subsystem connected with cold reservoir [24]. Changing of the temporal dynamics of energy flows also takes place in strongly coupled optomechanical systems [23].…”

“…To write down the explicit expression for free terms in Eqs. ( 23)- (24) and Eqs. ( 20)-( 21), it is convenient to introduce the following notations:…”