Thermodynamic modes of a quasiperiodic mobility-edge system in a quantum Otto cycle

TL;DR

The paper addresses how a mobility-edge quasiperiodic lattice, described by the Biddle--Das Sarma model, can function as the working medium in a quantum Otto cycle and how its thermodynamic mode diagram depends on the hopping decay parameter $p$ and the drive amplitudes $V_i$, $V_f$. It analyzes two limiting driving protocols—near-adiabatic (state-frozen) and adiabatic—and computes heat and work via $Q_h = E_1 - E_4$, $Q_c = E_3 - E_2$, and $W = Q_h + Q_c$, with $E_2$ and $E_4$ determined by the protocol-specific energy evolutions. The main findings are that the near-adiabatic protocol yields only heater and accelerator modes, while the adiabatic protocol reveals four modes (heater, accelerator, heat engine, refrigerator), with the latter windows emerging at low $T_h$ and intermediate $V_f$ and reshaped by $p$. This demonstrates the potential of mobility-edge systems as multifunctional quantum thermal devices and provides design guidelines for mode switching via $p$, $V_i$, and $V_f$, while suggesting extensions to broader finite-time driving protocols to improve robustness.

Abstract

We investigate thermodynamic operation of a quasiperiodic lattice with an exact mobility edge, described by the Biddle--Das Sarma model. We use this model as the working medium of a quantum Otto cycle and map its operating mode as a function of the hopping-range parameter $p$, the initial and final potential strengths $V_i$ and $V_f$, and two idealized protocols for the isolated strokes. In a near-adiabatic (state-frozen) protocol, where the density matrix is approximately unchanged during the isolated strokes, the cycle supports only two modes: a \emph{heater} and an \emph{accelerator}. In an adiabatic protocol, where level populations are preserved while the spectrum is deformed, two additional modes appear: a \emph{heat engine} and a \emph{refrigerator}. Our results show that mobility-edge systems can realize multiple thermodynamic functions within a single platform and provide guidance for switching between modes by tuning $p$, $V_i$, and $V_f$.

Figures (6)

• Figure 1: (Color online) (a) ${\rm IPR}$ at each energy level versus $V/t$ for $p=0.75$ and $L=610$. (b) Fractal dimension $D$ versus $V/t$ for the same parameters. (c) ${\rm IPR}$ versus $V/t$ for $p=1.5$ and $L=610$. (d) Fractal dimension $D$ versus $V/t$ for the same parameters. The color in (a) and (c) represent the ${\rm IPR}$ and that in (b) and (d) denote the fractal dimension $D$. The solid blue line denotes the mobility edge $E_{c}/t = V \cosh(p)-1$.
• Figure 2: (Color online) Schematic of the quantum Otto cycle. Strokes $\textcircled{4}\rightarrow\textcircled{1}$ and $\textcircled{2}\rightarrow\textcircled{3}$ are thermalization at fixed Hamiltonians $H(V_i)$ and $H(V_f)$, with reservoirs at $T_h$ and $T_c$. Strokes $\textcircled{1}\rightarrow\textcircled{2}$ and $\textcircled{3}\rightarrow\textcircled{4}$ are isolated parameter changes from $V_i$ to $V_f$ and back.
• Figure 3: (Color online) Operating modes in the near-adiabatic (state-frozen) protocol for $p=0.75$ and $L=233$. (a) $V_f=0.5t$; (b) $V_f=t$; (c) $V_f=2t$; (d) $V_f=3t$. Brown: heater. Yellow: accelerator.
• Figure 4: (Color online) Operating modes in the near-adiabatic (state-frozen) protocol for $p=1.5$ and $L=233$. (a) $V_f=0.4t$; (b) $V_f=0.5t$; (c) $V_f=0.6t$; (d) $V_f=0.7t$. Brown: heater. Yellow: accelerator.
• Figure 5: (Color online) Operating modes in the adiabatic protocol for $p=0.75$ and $L=610$. (a) $V_f=0.5t$; (b) $V_f=0.6t$; (c) $V_f=t$; (d) $V_f=1.2t$; (e) $V_f=1.3t$; (f) $V_f=1.5t$. Brown: heater. Yellow: accelerator. Green: heat engine. Blue: refrigerator.