Quantum scattering as a work source

Samuel L. Jacob1,2, Massimiliano Esposito1,2, Juan M. R. Parrondo3, and Felipe Barra4,2

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

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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.

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.

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Cited by

[1] 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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