Magnetically driven quantum heat engine

Abstract

We studied the efficiency of two different schemes for a magnetically driven quantum heat engine, by considering as the "working substance" a single non-relativistic particle trapped in a cylindrical potential well, in the presence of an external magnetic field. The first scheme is a cycle, composed of two adiabatic and two iso-energetic reversible trajectories in configuration space. The trajectories are driven by a quasi-static modulation of the external magnetic field intensity. The second scheme is a variant of the former, where the iso-energetic trajectories are replaced by isothermal ones, along which the system is in contact with macroscopic thermostats. This second scheme constitutes a quantum analogue of the classical Carnot cycle.

Magnetic Quantum Otto Engine for the Single-Particle Landau Problem

“…is the standard definition for the cyclotron frequency [12,13,23]. With the definition of the parameter ω B , we can define the Landau radius that captures the effect of the intensity of the magnetic field, given by l B = h/(m * ω B ).…”

“…The first law of quantum thermodynamics is fully addressed in many works [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and gives us the possibility to explore different quantum cycles and compare them with the classical analogues. To derivate this law simply, consider a Hamiltonian with an explicit dependence of some parameter that we will call µ in a generic form [25].…”

“…The possibility to create an alternative and efficient nanoscale device, like its macroscopic counterpart, introduces the concept of the quantum engine, which was proposed by Scovil and Schultz-Dubois in the 1950's [1]. The key point here is the quantum nature of the working substance and of course the quantum versions of the laws of thermodynamics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The combination of these two simple facts leads to very interesting studies of well-known macroscopic engines of thermodynamics, such as Carnot, Stirling and Otto, among others [2][3][4].…”

“…In this context, the quantum harmonic Otto cycle is a hot research topic, fully addressed by Kosloff and Rezek [21], and with a recent experimental realization employing a single ion in harmonic trap [22]. In the magnetic scenario, it is useful to think that the "isochoric process" is replaced by "isomagnetic " ones [12,13]. Therefore, the constant value in the process corresponds to the value of cyclotron frequency (or effective frequency depending on the case), which is proportional to the intensity of the magnetic field.…”

Magnetic Engine for the Single-Particle Landau Problem

“…The possibility to create an alternative and efficient nanoscale device, like its macroscopic counterpart, introduces the concept of the quantum engine, which was proposed by Scovil and Schultz-Dubois in the 1950s [1]. The key point here is the quantum nature of the working substance and of course the quantum versions of the laws of thermodynamics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The combination of these two simple facts leads to very interesting studies of well-known macroscopic engines of thermodynamics, such as Carnot, Stirling and Otto, among others [2][3][4].…”