Quantum work statistics of charged Dirac particles in time-dependent fields

Abstract

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

8 pages, 4 figures; published version

References in corpus (17)

• Fluctuation theorems: Work is not an observable
• Single ion heat engine with maximum efficiency at maximum power
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• Work measurement as a generalized quantum measurement
• Non-equilibrium quantum fluctuations of work
• Employing trapped cold ions to verify the quantum Jarzynski equality
• Holevo's bound from a general quantum fluctuation theorem
• Assessing the non-equilibrium thermodynamics in a quenched quantum many-body system via single projective measurements
• Jarzynski equality in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics
• Resonantly enhanced pair production in a simple diatomic model
• Statistics of work performed on a forced quantum oscillator
• Interference of Identical Particles and the Quantum Work Distribution
• Landau-Zener-Stückelberg interferometry in pair production from counterpropagating lasers
• Quantum work distribution for a driven diatomic molecule
• Relativistic Fluctuation Theorems: Theory and explicit examples

Cited by in corpus (14)

• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Quantum work and the thermodynamic cost of quantum measurements
• Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
• Shortcuts to adiabaticity: Suppression of pair production in driven Dirac dynamics
• Quantum Work in the Bohmian framework
• Jarzynski Equality for Driven Quantum Field Theories
• Quantum and classical ergotropy from relative entropies
• Time-rescaling of Dirac dynamics: shortcuts to adiabaticity in ion traps and Weyl semimetals
• Exchange fluctuation theorems for strongly interacting quantum pumps
• The role of quantum work statistics in many-body physics
• Electromagnetic gauge-freedom and work
• Heat Distribution of Relativistic Brownian Motion
• Squeezing generation crossing a mean-field critical point: Work statistics, irreversibility and critical fingerprints
• Quantum Otto engines at relativistic energies