Quantum heat machines enabled by twisted geometry

TL;DR

This work investigates a quantum Otto engine where a non-relativistic 2DEG is constrained to a twisted helicoid surface. Using the thin-layer quantization approach, it derives a geometry-induced quantum potential $V_S = -\frac{\hbar^2}{2m}(M^2 - K_G)$ and solves for the helicoid energy spectrum via HeunC solutions, showing that the twist density $\omega$ and radial size control the energy-level spacings. By implementing a four-stroke Otto cycle with adiabatic changes in both the transverse size and the number of twists per unit length, the authors demonstrate engine, heater, and refrigerator operation regimes, including the possibility of operating at fixed transverse area ($r=1$) where curvature effects are essential. These results reveal a novel route to quantum thermodynamic control through geometry, potentially realizable in flexible membranes or graphene-like thin films without external fields, and highlight the practical impact of geometry-induced quantum potentials on heat-machine performance.

Abstract

In this paper, we analyze the operation of an Otto cycle heat machine driven by a non-interacting two-dimensional electron gas on a twisted geometry. We show that due to both the energy quantization on this structure and the adiabatic transformation of the number of complete twists per unit length of a helicoid, the machine performance in terms of output work, efficiency, and operation mode can be altered. We consider the deformations as in a spring, which is either compressed or stretched from its resting position. The realization of classically inconceivable Otto machines with an incompressible sample can be realized as well. The energy-level spacing of the system is the quantity that is being either compressed or stretched. These features are due to the existence of an effective geometry-induced quantum potential which is of pure quantum-mechanical origin.

Figures (5)

• Figure 1: Plot of the HeunC function versus energy. The eigenvalues for a particle in a helical stripe can be found where it reaches zero values. The first few levels are depicted in (a) for $\omega\rho_2=1$ and in (b) for $\omega\rho_2=0.5$.
• Figure 2: A Quantum Otto Cycle for a 2DEG on an infinity helical stripe. The adiabatic strokes consist of modifications in the transverse direction across the helicoid and in the number of complete twists per unit length. The paths AB and CD are adiabatic strokes while BC and DA are isochoric strokes.
• Figure 3: The heat exchanges of the working substance with the hot and cold reservoirs and the work done are depicted. The flat case is shown in (a), for which $W>0$ for $1<r\lessapprox3.464$. For $r<1$, the system works as a heater and for $r\gtrapprox3.464$, it behaves as a refrigerator, similarly to a classical Otto machine. In (b), $\xi_c\equiv\omega_c\rho_c=0.5$ and $\xi_h\equiv\omega_h\rho_h=1$; $W>0$ for $0.54\lessapprox r\lessapprox1.878$. The curves shift to lower values of $r$ in comparison to the flat case. In this case, the transverse direction $\rho$ may be kept constant ($r=1$). In (c), $\xi_c\equiv\omega_c\rho_c=1$ and $\xi_h\equiv\omega_h\rho_h=0.5$; $W>0$ for $1.844\lessapprox r\lessapprox6.386$ and the curves shift to higher values of $r$ in comparison to the flat case. We have set $T_h\equiv12T_c$ and $\hbar^{2}/{2Mk_{B}\rho_{c}^{2}T_{c}}\equiv1$.
• Figure 4: The efficiency $\eta/(1-T_c/T_h)$ against the compression ratio $r=\rho_c/\rho_h$ is depicted. The temperature ratio is set to $T_h/T_c=12$. For a flat sample, only the transverse direction $\rho$ can be altered and it behaves similarly to a classical Otto engine. The curvature shifts the efficiency curves to either lower or higher values of $r$, now allowing such transverse direction to be kept unaltered ($r=1$).
• Figure 5: The coefficient of performance $\varepsilon/[T_c/(T_h-T_c)]$ against the compression ratio $r=\rho_c/\rho_h$ is depicted. The temperature ratio is set to $T_h/T_c=12$. The refrigerator performance can be altered/improved by curvature effects due to a twist geometry.