Abstract
Quantum nano-devices are fundamental systems in quantum thermodynamics that have been the subject of profound interest in recent years. Among these, quantum batteries play a very important role. In this paper we lay down a theory of random quantum batteries and provide a systematic way of computing the average work and work fluctuations in such devices by investigating their typical behavior. We show that the performance of random quantum batteries exhibits typicality and depends only on the spectral properties of the time evolving operator, the initial state and the measuring Hamiltonian. At given revival times a random quantum battery features a quantum advantage over classical random batteries. Our method is particularly apt to be used both for exactly solvable models like the Jaynes-Cummings model or in perturbation theory, e.g., systems subject to harmonic perturbations. We also study the setting of quantum adiabatic random batteries.
Highlights
In this paper we provided a notion of quantum random batteries by means of Haar averaging initial states, energy measurement Hamiltonian, and the time-dependent driving of the quantum battery
The average work and fluctuations are systematically studied; we find that quantum batteries exhibit typical behavior in the large-n limit given the spectral properties of the driving system
The work extracted is found to be typically equal to the difference between the energy of the initial state and that of the completely mixed state, amplified by a quantum efficiency factor (1 + Qt /n2) that only depends on the spectrum of the driving Hamiltonian
Summary
Quantum batteries [1,2,3,4,5,6,7,8] are a fundamental concept in quantum thermodynamics [9,10,11,12,13,14,15,16,17], and they have attracted interest as part of research in nanodevices that can operate at the quantum level [18,19,20]. This work is positive (that is, the battery has discharged) if the initial energy was larger than the energy in the completely mixed state or it has charged if the initial state was populating the lower levels of H0 Notice that this setting we have arbitrary Hamiltonians H (t ) that can access arbitrary high energies as measured by H0. We ask how much work can be extracted if we have limited energetic resources, that is, when the spectra of H0 and V (t ) are fixed This motivates our setting in terms of rotations of the time-dependent part of the Hamiltonians as HG(t ) = H0 + VG(t ). We use standard techniques for the Haar averaging (see, e.g., Refs. [39,40,41]) to compute the average and variances according to the Haar measure
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call