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Quantum Langevin dynamics of a charged particle in a magnetic field: Response function, position–velocity and velocity autocorrelation functions

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Abstract

We use the quantum Langevin equation as a starting point to study the response function, the position–velocity correlation function and the velocity autocorrelation function of a charged quantum Brownian particle in the presence of a magnetic field and linearly coupled to a heat bath via position coordinate. We study two bath models – the Ohmic bath model and the Drude bath model and make a detailed comparison in various time–temperature regimes. For both bath models, there is a competition between the cyclotron frequency and the viscous damping rate giving rise to a transition from an oscillatory to a monotonic behaviour as the damping rate is increased. In the zero point fluctuation dominated low-temperature regime, non-trivial noise correlations lead to some interesting features in this transition. We study the role of the memory time-scale which comes into play in the Drude model and study the effect of this additional time-scale. We discuss the experimental implications of our analysis in the context of experiments in cold ions.

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Authors and Affiliations

  1. Raman Research Institute, Bengaluru, 560 080, India

    Suraka Bhattacharjee & Supurna Sinha

  2. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru, 560 089, India

    Urbashi Satpathi

Authors
  1. Suraka Bhattacharjee
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  2. Urbashi Satpathi
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  3. Supurna Sinha
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Bhattacharjee, S., Satpathi, U. & Sinha, S. Quantum Langevin dynamics of a charged particle in a magnetic field: Response function, position–velocity and velocity autocorrelation functions. Pramana - J Phys 96, 53 (2022). https://doi.org/10.1007/s12043-022-02295-1

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  • DOI: https://doi.org/10.1007/s12043-022-02295-1

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