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Quenching Evolution in a Quantum-Classical Hybrid System

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Abstract

The adiabatic theorem, an important theory in quantum mechanics, tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In this paper, we study the quench evolution that is another extreme circumstance where the external conditions vary rapidly such that the quantum system can not follow the change and remains in its initial state (or wavefunction). We examine the matter-wave pressure and derive the requirement for such an evolution. The study is conducted by considering a quantum particle in an infinitely deep potential, the potential width Q is assumed to be change rapidly. We show that the total energy of the quantum subsystem decreases as Q increases, and this rapidly change exerts a force on the wall which plays the role of boundary of the potential. For Q < Q0 (Q0 is the initial width of the potential), the force is repulsive, and for Q > Q0, the force is positive. The condition for the quenching evolution evolution is given via a spin-\( \frac{1}{2} \) in a rotating magnetic field.

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Acknowledgment

Thanks H.D. Liu for the helpful discussion. This work was supported by the Natural Science Funding in Liaoning Province (Grant No. 201801156 )and Program for Talents introduction of Dalian Neusoft University of Information (Grant No. ZX2018KJ046).

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Authors and Affiliations

  1. Fundamental Education Department, Dalian Neusoft University of Information, Dalian, 116023, China

    J. Shen

  2. School of Physics, Northeast Normal University, Changchun, 130024, China

    W. Wang

  3. Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China

    C. M. Dai & X. X. Yi

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  1. J. Shen
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  2. W. Wang
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  3. C. M. Dai
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  4. X. X. Yi
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Correspondence to X. X. Yi.

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Shen, J., Wang, W., Dai, C.M. et al. Quenching Evolution in a Quantum-Classical Hybrid System. Int J Theor Phys 58, 1676–1686 (2019). https://doi.org/10.1007/s10773-019-04065-z

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  • DOI: https://doi.org/10.1007/s10773-019-04065-z

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