Derivation of the Landau–Pekar equations in a many-body mean-field limit
Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 240, 383–417.
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Abstract
We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.
Publishing Year
Date Published
2021-02-26
Journal Title
Archive for Rational Mechanics and Analysis
Publisher
Springer Nature
Acknowledgement
Financial support by the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (Grant Agreement
No 694227; N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the
Deutsche Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral
Theory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.
gratefully acknowledges support from the NCCRSwissMAP and would like to thank Simone
Rademacher and Benjamin Schlein for interesting discussions about the time-evolution of
the polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for
extensive discussions about the Fröhlich polaron.
Volume
240
Page
383-417
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eISSN
IST-REx-ID
Cite this
Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 2021;240:383-417. doi:10.1007/s00205-021-01616-9
Leopold, N. K., Mitrouskas, D. J., & Seiringer, R. (2021). Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01616-9
Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01616-9.
N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar equations in a many-body mean-field limit,” Archive for Rational Mechanics and Analysis, vol. 240. Springer Nature, pp. 383–417, 2021.
Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 240, 383–417.
Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” Archive for Rational Mechanics and Analysis, vol. 240, Springer Nature, 2021, pp. 383–417, doi:10.1007/s00205-021-01616-9.
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