Non-Equilibrium Dynamics Beyond Dephasing

Xiangjia Meng, Yaxin Sun, Qinglong Wang +3 more

We performed a theoretical study of the dephasing dynamics of a quantum two-state system under the influences of a non-equilibrium fluctuating environment. The effect of the environmental non-equilibrium fluctuations on the quantum system is described by a generalized random telegraph noise (RTN) process, of which the statistical properties are both non-stationary and non-Markovian. Due to the time-homogeneous property in the master equations for the multi-time probability distribution, the decoherence factor induced by the generalized RTN with a modulatable-type memory kernel can be exactly derived by means of a closed fourth-order differential equation with respect to time. In some special limit cases, the decoherence factor recovers to the expression of the previous ones. We analyzed in detail the environmental effect of memory modulation in the dynamical dephasing in four types of dynamics regimes. The results showed that the dynamical dephasing of the quantum system and the conversion between the Markovian and non-Markovian characters in the dephasing dynamics under the influence of the generalized RTN can be effectively modulated via the environmental memory kernel.

Yuto Ashida

Pritiraj Mohanty, Manher Jariwala, R. A. Webb

Ahmad Nawaz

We quantize prisoners' dilemma in the presence of collective dephasing with a dephasing rate γ. It is shown that for a two-parameter set of strategies, Q ⊗ Q is Nash equilibrium below a cut-off value of time. Beyond this cut-off it bifurcates into two new Nash equilibria Q ⊗ D and D ⊗ Q . Furthermore, for the maximum value of decoherence C ⊗ D and D ⊗ C also become Nash equilibria. At this stage the game has four Nash equilibria. On the other hand, for a three-parameter set of strategies, there is no pure strategy Nash equilibrium; however, there is a mixed strategy (non-unique) Nash equilibrium that is not affected by collective dephasing.

P. Borowski, Jochen Gemmer B, G. Mahler

Stefano Longhi

Abstract Dynamical phase transitions in the relaxation behavior of stochastic quantum walks are investigated, focusing on systems where coherent unitary evolution is periodically interrupted by dephasing. This interplay leads to a classicalization of the dynamics, effectively described by non‐equilibrium Markovian processes that can violate detailed balance. As a result, such systems exhibit a richer and more complex spectral structure than their equilibrium counterparts. Extending recent insights from classical Markov dynamics [G. Teza et al. , Phys. Rev. Lett. 130 , 207103 (2023)], it is demonstrated that these quantum‐classical hybrid systems can host not only first‐order dynamical phase transitions – characterized by eigenvalue crossings – but also second‐order transitions marked by the coalescence of eigenvalues and eigenvectors at exceptional points. Two paradigmatic models are analyzed: a quantum walk on a ring under gauge fields and a walk on a finite line with internal degrees of freedom, both exhibiting distinct mechanisms for breaking detailed balance. These findings reveal a novel class of critical behavior in open quantum systems, where decoherence‐induced classicalization enables access to non‐Hermitian spectral phenomena. Beyond their fundamental interest, these results offer promising implications for quantum technologies, including quantum simulation, error mitigation, and the engineering of controllable non‐equilibrium quantum states.