Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

Abstract

Thermodynamic geometry provides a physically transparent framework to describe thermodynamic processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. Focusing on periodic driving for thermal machines, we extend this framework to ideal quantum gases. To this end, we show that the standard approach of equilibrium physics, where a grand-canonical ensemble is used to model a canonical one by fixing the mean particle number through the chemical potential, can be extended to the slow driving regime in a thermodynamically consistent way. As a key application of our theory, we use a Lindblad-type quantum master equation to work out a dynamical model of a quantum many-body engine using a harmonically trapped Bose-gas. Our results provide a geometric picture of the BEC-induced power enhancement that was previously predicted for this type of engine on the basis of an endoreversible model [New J. Phys. 24, 025001 (2022)]. Using an earlier derived universal trade-off relation between power and efficiency as a benchmark, we further show that the Bose-gas engine can deliver significantly more power at given efficiency than an equally large collection of single-body engines. Our work paves the way for a more general thermodynamic framework that makes it possible to systematically assess the impact of quantum many-body effects on the performance of thermal machines.

Scattering by harmonically trapped 2D quantum gas near and around the critical regime

“…Since the parameter k is absent from the result, there is no Doppler effect in the index of refraction. However, by considering the firstorder term in k in equation (44), the forward scattering reveals a non-vanishing imaginary part Imf (k, 0) which is nearly equal to ( ¯) Nka m s 2 2 m -. As the imaginary part of the net scattering amplitude exhibits linearity in k, it makes the imaginary part of the scattering amplitude sensitive to the motion of the target particle.…”

“…Over the past three decades, some experimental and theoretical research has focused on ultracold Bose and Fermi gases trapped using magneto-optical traps. This attention has grown considerably since the initial observation of BEC in ultracold alkali atoms (such as 23 Na and 87 Rb) with temperatures ranging from (μK -nK) [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]40].The outcomes of these findings have ignited various advancements aimed at investigating the potential uses of Bose-Einstein condensates in technology, such as quantum computing [41], sensing [42], and thermal machines [43,44]. Scattering experiments involve probing the properties of particles in the trapped gas by scattering a probe (e.g.…”

Entropy and Energy for Non-Mechanical Work at the Bose-Einstein Transition of a Harmonically Trapped Gas Using an Empirical Global-Variable Method

“…Koch and co-workers [3] have actually implemented a thermal engine operating at the BEC-BSC crossover, showing that a phase transition in a bosonic-fermionic system is a viable energy source for work. In the particular case of bosonic systems, Eglinton and co-workers [4] have indicated a performance boost for a quantum engine running on a gas under Bose-Einstein condensation (BEC) under certain configurations. In the current year, Estrada and co-workers [5] analyzed theoretically the role of interactions in the efficiency of thermal engine running on a harmonically confined gas under BEC.…”