Quantum scattering as a work source

Samuel L. Jacob; Massimiliano Esposito; Juan M. R. Parrondo; Felipe Barra

doi:10.22331/q-2022-06-29-750

Quantum scattering as a work source

Samuel L. Jacob^1,2, Massimiliano Esposito^1,2, Juan M. R. Parrondo³, and Felipe Barra^4,2

¹Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
²Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 Santa Barbara, U.S.A.
³Departamento de Estructura de la Materia, Física Térmica y Electrónica and GISC, Universidad Complutense Madrid, 28040 Madrid, Spain
⁴Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, 837.0415 Santiago, Chile

Published:	2022-06-29, volume 6, page 750
Eprint:	arXiv:2108.13369v3
Doi:	https://doi.org/10.22331/q-2022-06-29-750
Citation:	Quantum 6, 750 (2022).

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Abstract

We consider a collision between a moving particle and a fixed system, each having internal degrees of freedom. We identify the regime where the motion of the particle acts as a work source for the joint internal system, leading to energy changes which preserve the entropy. This regime arises when the particle has high kinetic energy and its quantum state of motion is broad in momentum and narrow in space, whether pure or mixed. In this case, the scattering map ruling the dynamics of the internal degrees of freedom becomes unitary and equivalent to that of a time-dependent interaction between the internal degrees of freedom of the colliding systems. It follows that the kinetic energy lost by the particle during the autonomous quantum collision coincides with the work performed by the time-dependent interaction. Recently, collisions with particles were shown to act as heat sources under suitable conditions; here we show that they can also act as work sources. This opens interesting perspectives for quantum thermodynamics formulations within scattering theory.

Featured image: Scattering and time-dependent setups considered in our study. In the former, the interaction happens autonomously in space through a potential $V(x)$: system $A$ is fixed while the incoming particle has kinetic degrees of freedom $X$ and internal degrees of freedom $B$. In the latter, the interaction between $A$ and $B$ happens in time through a time-dependent interaction $\tilde{V}(t)$. Note that the potentials $V(x)$ and $\tilde{V}(t)$ are generally not the same.

Popular summary

In quantum mechanics, time-dependent Hamiltonians are not considered fundamental. Instead, they are viewed as effective ways of modelling larger systems prepared in particular states and described by time-independent Hamiltonians. A widespread example is the semi-classical treatment of light to study light-matter interactions. In quantum thermodynamics, the energy changes generated by time-dependent Hamiltonians constitute the most common way to model work, i.e., an energy source that does not produce any entropy. For models of repeated interaction, work is caused by repeatedly turning on and of the interaction between a system and fresh units.

This paper considers the scattering of an incoming particle by a fixed system. We show that this scattering process models a repeated interaction model on the internal structure of the joint particle-system when the particle has high kinetic energy and its quantum state of motion is broad in momentum and narrow in space, whether pure or mixed — work results, in this case, from kinetic energy changes of the incoming particle. Since conditions for incoming particles to behave as a heat source have also been recently identified, our work suggests that scattering problems may provide a rich terrain to explore quantum thermodynamics.

► BibTeX data

@article{Jacob2022quantumscatteringas,
  doi = {10.22331/q-2022-06-29-750},
  url = {https://doi.org/10.22331/q-2022-06-29-750},
  title = {Quantum scattering as a work source},
  author = {Jacob, Samuel L. and Esposito, Massimiliano and Parrondo, Juan M. R. and Barra, Felipe},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {750},
  month = jun,
  year = {2022}
}

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Cited by

[1] Samuel L. Jacob, Gabriel T. Landi, Massimiliano Esposito, and Felipe Barra, "Two-point measurement energy statistics from particle scattering", Physical Review Research 5 4, 043160 (2023).

[2] Uriel Shafir and Ronnie Kosloff, "Wave Function Realization of a Thermal Collision Model", Entropy 24 12, 1808 (2022).

[3] Jorge Tabanera-Bravo, Juan M. R. Parrondo, Massimiliano Esposito, and Felipe Barra, "Thermalization and Dephasing in Collisional Reservoirs", Physical Review Letters 130 20, 200402 (2023).

[4] Cyril Elouard and Camille Lombard Latune, "Extending the Laws of Thermodynamics for Arbitrary Autonomous Quantum Systems", PRX Quantum 4 2, 020309 (2023).

[5] Jorge Tabanera, Inés Luque, Samuel L. Jacob, Massimiliano Esposito, Felipe Barra, and Juan M. R. Parrondo, "Quantum collisional thermostats", New Journal of Physics 24 2, 023018 (2022).

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