Quantum Ising chain with time-averaged work in linear response theory

Abstract

For systems performing a weakly isothermal process, the decorrelation time dictates how fast the relaxation function decorrelates. However, like many other thermally isolated systems, the transverse-field quantum Ising chain presents an ill-defined decorrelation time. On the other hand, the Kibble-Zurek mechanism uses a heuristic relaxation time to achieve its famous scaling. The problem however of having a well-defined decorrelation time, derived from first principles, agreeing with the Kibble-Zurek mechanism is still open. Such a solution is proposed here by measuring the work using the time-averaged relaxation function of the system, which offers a new and well-defined decorrelation time for thermally isolated systems. I recover with this the Kibble-Zurek mechanism in the finite-time and weak driving regime, and new features in the slowly-varying one. The gain in control over the system in such a distinction is desirable for potential applications.

8 pages, 6 figures

References in corpus (8)

• Mathematical Foundation of Quantum Annealing
• Coherent quantum annealing in a programmable 2000-qubit Ising chain
• Kibble-Zurek mechanism in a quenched ferromagnetic Bose-Einstein condensate
• Realization of inverse Kibble-Zurek scenario with trapped Bose gases
• Kibble-Zurek scaling of the irreversible entropy production
• Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain
• The three phases of quantum annealing: fast, slow, and very slow
• Adiabatic processes like isothermal processes

Cited by in corpus (4)

• Anti Kibble-Zurek behavior in the quantum XY spin-1/2 chain driven by correlated noisy magnetic field and anisotropy
• Analytical solution for optimal protocols of weak drivings
• Fluctuation theorem for time-averaged work
• Casimir-Onsager matrix for weakly driven processes