Adiabatic theorem for closed quantum systems initialized at finite temperature

Abstract

The evolution of a driven quantum system is said to be adiabatic whenever the state of the system stays close to an instantaneous eigenstate of its time-dependent Hamiltonian. The celebrated quantum adiabatic theorem ensures that such pure state adiabaticity can be maintained with arbitrary accuracy, provided one chooses a small enough driving rate. Here, we extend the notion of quantum adiabaticity to closed quantum systems initially prepared at finite temperature. In this case adiabaticity implies that the (mixed) state of the system stays close to a quasi-Gibbs state diagonal in the basis of the instantaneous eigenstates of the Hamiltonian. We prove a sufficient condition for the finite temperature adiabaticity. Remarkably, it implies that the finite temperature adiabaticity can be more robust than the pure state adiabaticity, particularly in many-body systems. We present an example of a many-body system where, in the thermodynamic limit, the finite temperature adiabaticity is maintained, while the pure state adiabaticity breaks down.

References in corpus (15)

• Breakdown of the adiabatic limit in low dimensional gapless systems
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• From the adiabatic theorem of quantum mechanics to topological states of matter
• Reverse quantum annealing of the $p$-spin model with relaxation
• Quantum state discrimination: a geometric approach
• Thermal States as Universal Resources for Quantum Computation with Always-on Interactions
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Nonequilibrium phase transition in transport through a driven quantum point contact
• Certifying the adiabatic preparation of ultracold lattice bosons in the vicinity of the Mott transition
• A note on the Landauer principle in quantum statistical mechanics
• Mediator assisted cooling in quantum annealing
• Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases
• Probabilistic Hysteresis in an Isolated Quantum System: The Microscopic Onset of Irreversibility from a Quantum Perspective
• Characterizing Adiabaticity in Quantum Many-Body Systems at Finite Temperature

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