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Quantum Quenching, Annealing and Computation pp 115–143Cite as

Quench Dynamics of Quantum and Classical Ising Chains: From the Viewpoint of the Kibble–Zurek Mechanism

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Part of the book series: Lecture Notes in Physics ((LNP,volume 802))

Abstract

In most macroscopic systems, the state in the equilibrium undergoes a phase transition when the temperature is changed. In the ordinary phase transition, the correlation length and the relaxation time diverge at the critical point. Hence it takes infinitely long time for the state to evolve from a disordered state to an ordered state by lowering the temperature. Such a quasi-static motion of the state is ideal. However, a motion of a state by lowering the temperature with a finite speed is more familiar to us. For instance, a natural magnet is made from lava through a thermal quench. If the temperature is cooled with a finite speed across the critical point, the phase transition ends incompletely. Consequently the symmetry breaking occurs not globally but locally.

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Acknowledgement

The author acknowledges T. Caneva, G.E. Santoro, and H. Nishimori for fruitful discussions and comments. The present work is partially supported by CREST, JST, and by Grant-in-Aid for Scientific Research (No. 20740225) of MEXT, Japan.

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Authors and Affiliations

  1. Aoyama Gakuin University, Fuchinobe Sagamihara, 229-8558, Japan

    S. Suzuki

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  1. S. Suzuki
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Correspondence to S. Suzuki .

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Editors and Affiliations

  1. Centre for Applied Mathematics &, Computational Science, Saha Institute of Nuclear Physics, Bidhannagar 1/AF, Kolkata, 700064, India

    Anjan Kumar Chandra

  2. Theoretical Physics (ICTP), Abdus Salam International Centre for, Strada Costiera 11, Trieste, 34014, Italy

    Arnab Das

  3. Centre for Applied Mathematics &, Computational Science, Saha Institute of Nuclear Physics, Bidhannagar 1/AF, Kolkata, 700064, India

    Bikas K. Chakrabarti

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Suzuki, S. (2010). Quench Dynamics of Quantum and Classical Ising Chains: From the Viewpoint of the Kibble–Zurek Mechanism. In: Chandra, A., Das, A., Chakrabarti, B. (eds) Quantum Quenching, Annealing and Computation. Lecture Notes in Physics, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11470-0_5

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  • DOI: https://doi.org/10.1007/978-3-642-11470-0_5

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