(Thermo-)dynamics of the spin-boson model in the weak coupling regime: Application as a quantum battery

TL;DR

This work analyzes the spin-boson model in the weak-coupling regime using two master equations, the weak-coupling spin-boson (WCSB) and the phase covariant (PC) form, to investigate dynamical features (non-Markovianity, quantum speed limits, coherence, and steady state) and thermodynamic performance when viewed as a quantum battery. It characterizes memory effects with both the BLP trace-distance and RHP CP-divisibility measures, revealing distinct non-Markovian signatures for unital versus non-unital dynamics, and shows faster quantum evolution under pure dephasing than dissipative dynamics. In the battery analysis, energy, ergotropy (with incoherent and coherent parts), anti-ergotropy, and battery capacity are computed for dissipative, pure dephasing, and mixed regimes, showing that pure dephasing favors charge storage while dissipation enhances charging, with non-Markovianity aiding recharging. Overall, the spin-boson model emerges as a versatile quantum battery platform for energy storage and transfer in quantum thermodynamic devices, offering insights into how environmental couplings shape charging and storage performance.

Abstract

We investigate the spin-boson model's dynamical and thermodynamic features in the weak coupling regime using the weak coupling spin-boson (WCSB) and phase covariant (PC) master equations. Both unital (pure dephasing) and non-unital (dissipative) quantum channels are considered. On the dynamical side, we explore key quantum features including non-Markovianity, quantum speed limit, quantum coherence, and the system's steady-state behavior. Notably, the measures of non-Markovianity exhibit different behavior under WCSB and PC dynamics. From the quantum thermodynamic perspective, we conceptualize the spin-boson system as a quantum battery and analyze its performance through metrics such as energy, ergotropy, anti-ergotropy, and battery capacity. We further examine the roles of pure dephasing and dissipative processes in shaping the battery's performance. Our findings demonstrate the spin-boson model's versatility as a platform for efficient energy storage and transfer in quantum thermodynamic devices.

Figures (10)

• Figure 1: Variation of trace distance $\mathcal{D}\left[\rho_{1}(t), \rho_{2}(t)\right]$ with time for different coupling angles $\theta$. The evolution of the system is governed by the WCSB master equation \ref{['gen_spin-boson_master_eq']} in (a), and the PC master equation \ref{['PC_dynamics']} in (b). The parameters are taken to be $\omega_0 = 1.25$, $T= 0.2$, $\Omega = 15$, $m\gamma = 0.4$.
• Figure 2: Variation of the function $g(t)$, Eq. \ref{['eq_function_gt']}, with time for different coupling angles $\theta$. The evolution of the system is governed by the WCSB master equation \ref{['gen_spin-boson_master_eq']} in (a), and the PC master equation \ref{['PC_dynamics']} in (b). Here, we have $\omega_0 = 2.25$, $T= 0.2$, $\Omega = 15$, $m\gamma = 0.4$.
• Figure 3: Variation of the function $g(t)$, Eq. \ref{['eq_function_gt']}, with time for different values of the coupling factor $\gamma$. The evolution of the system is governed by the WCSB master equation \ref{['gen_spin-boson_master_eq']}. Here, we take $\omega_0 = 2.25$, $T= 1.0$, $\Omega = 15$, and $\theta = 0$.
• Figure 4: Variation of quantum speed limit time $\tau_{QSL}$ with time using WY Metric for different coupling angles $\theta$. In (a), the dynamics is governed by Eq. \ref{['gen_spin-boson_master_eq']}, and in (b), it is governed by the phase covariant master equation, Eq. \ref{['PC_dynamics']}. The parameters are $T = 0.2$, $\Omega = 15$, $m\gamma = 0.4$ and in (a) $\omega_0 = 1.25$ while in (b) $\omega_0 = 2.25$. The initial state of the system in both (a) and (b) is taken to be $\ket{\psi(0)}_S = \left(\frac{\sqrt{3}}{2}\ket{0} + \frac{1}{2}\ket{1}\right)$.
• Figure 5: Variation of the quantum coherence with time for the evolution of the system using (a) the WCSB master equation, Eq. \ref{['gen_spin-boson_master_eq']}, and (b) the phase covariant master equation, Eq. \ref{['PC_dynamics']}. Parameters are temperature $T = 0.2$, $\Omega = 15$, $m \gamma = 0.4$. In (a), $\omega_0 = 1.25$ and in (b), $\omega_0 = 2.25$.