Embedded Files
My research on dissipative spin models explores nonequilibrium dynamics and phase transitions in fully connected quantum spin systems coupled to dissipative environments. I have studied the dynamics of magnetization in the classical chaotic regime of the all-to-all Ising model with dissipation, as well as dissipative phase transitions in fully connected Ising models with p-spin interactions. These models provide tractable settings for investigating the interplay between collective interactions, nonlinear dynamics, chaos, and dissipation in many-body quantum systems.
Dynamics of magnetizations in the classical chaotic regime of the all-to-all Ising model with dissipation
We study the all-to-all Ising model in the presence of dissipation and periodic external field. The corresponding Lindblad equation has a time-periodic Liouvillian. The dynamics of magnetizations is explored by using both the mean-field theory and numerical simulation at a finite number of spins. The mean-field result exhibits a transition from the periodic response at small field amplitude to the chaotic dynamics at large amplitude. The Lyapunov exponents are calculated, which supports the existence of a classical chaotic phase. However, in the numerical simulation at a finite number of spins, the response is periodic at both small and large amplitudes. The scaling analysis of the Floquet Liouvillian spectrum suggests that the periodic response persists even in the thermodynamic limit. Further analysis shows that, in the classical chaotic regime, the density-matrix elements have a wide dispersion, instead of being localized. Such a delocalization of wave packets explains the failure of mean-field approximation.
Dissipative phase transitions in the fully connected Ising model with p-spin interaction
In this paper, we study the driven-dissipative p-spin models for p>1. In thermodynamic limit, the equation of motion is derived by using a semiclassical approach. The long-time asymptotic states are obtained analytically, which exhibit multistability in some regions of the parameter space. The steady state is unique as the number of spins is finite. But the thermodynamic limit of the steady-state magnetization displays nonanalytic behavior somewhere inside the semiclassical multistable region. We find both the first-order and continuous dissipative phase transitions. As the number of spins increases, both the Liouvillian gap and magnetization variance vanish according to a power law at the continuous transition. At the first-order transition, the gap vanishes exponentially accompanied by a jump of magnetization in thermodynamic limit. The properties of transitions depend on the symmetry and semiclassical multistability, being qualitatively different among p = 2, odd p (p>2), and even p (p>2).
Page updated
Google Sites
Report abuse