@article{DoerriesLoosKlapp2021,
  author    = {D{\"o}rries, Timo and Loos, Sarah Anna Marie and Klapp, Sabine H. L.},
  title     = {Correlation functions of non-Markovian systems out of equilibrium},
  series = {Journal of statistical mechanics: theory and experiment : JSTAT},
  journal   = {Journal of statistical mechanics: theory and experiment : JSTAT},
  number    = {3},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1742-5468},
  doi       = {10.1088/1742-5468/abdead},
  pages     = {36},
  year      = {2021},
  abstract  = {This paper is concerned with correlation functions of stochastic systems with memory, a prominent example being a molecule or colloid moving through a complex (e.g. viscoelastic) fluid environment. Analytical investigations of such systems based on non-Markovian stochastic equations are notoriously difficult. A common approximation is that of a single-exponential memory, corresponding to the introduction of one auxiliary variable coupled to the Markovian dynamics of the main variable. As a generalization, we here investigate a class of 'toy' models with altogether three degrees of freedom, giving rise to more complex forms of memory. Specifically, we consider, mainly on an analytical basis, the under- and overdamped motion of a colloidal particle coupled linearly to two auxiliary variables, where the coupling between variables can be either reciprocal or non-reciprocal. Projecting out the auxiliary variables, we obtain non-Markovian Langevin equations with friction kernels and colored noise, whose structure is similar to that of a generalized Langevin equation. For the present systems, however, the non-Markovian equations may violate the fluctuation-dissipation relation as well as detailed balance, indicating that the systems are out of equilibrium. We then study systematically the connection between the coupling topology of the underlying Markovian system and various autocorrelation functions. We demonstrate that already two auxiliary variables can generate surprisingly complex (e.g. non-monotonic or oscillatory) memory and correlation functions. Finally, we show that a minimal overdamped model with two auxiliary variables and suitable non-reciprocal coupling yields correlation functions resembling those describing hydrodynamic backflow in an optical trap.},
  language  = {en}
}
@article{AndersSaitHorsley2022,
  author    = {Anders, Janet and Sait, Connor R. J. and Horsley, Simon A. R.},
  title     = {Quantum Brownian motion for magnets},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {24},
  journal   = {New journal of physics : the open-access journal for physics},
  number    = {3},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ac4ef2},
  pages     = {21},
  year      = {2022},
  abstract  = {Spin precession in magnetic materials is commonly modelled with the classical phenomenological Landau-Lifshitz-Gilbert (LLG) equation. Based on a quantized three-dimensional spin + environment Hamiltonian, we here derive a spin operator equation of motion that describes precession and includes a general form of damping that consistently accounts for memory, coloured noise and quantum statistics. The LLG equation is recovered as its classical, Ohmic approximation. We further introduce resonant Lorentzian system-reservoir couplings that allow a systematic comparison of dynamics between Ohmic and non-Ohmic regimes. Finally, we simulate the full non-Markovian dynamics of a spin in the semi-classical limit. At low temperatures, our numerical results demonstrate a characteristic reduction and flattening of the steady state spin alignment with an external field, caused by the quantum statistics of the environment. The results provide a powerful framework to explore general three-dimensional dissipation in quantum thermodynamics.},
  language  = {en}
}
@article{GoychukKharchenko2013,
  author    = {Goychuk, I. and Kharchenko, V. O.},
  title     = {Rocking subdiffusive ratchets origin, optimization and efficiency},
  series = {Mathematical modelling of natural phenomena},
  volume    = {8},
  journal   = {Mathematical modelling of natural phenomena},
  number    = {2},
  publisher = {EDP Sciences},
  address   = {Les Ulis},
  issn      = {0973-5348},
  doi       = {10.1051/mmnp/20138210},
  pages     = {144 -- 158},
  year      = {2013},
  abstract  = {We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-inversion symmetry and driven by a time-periodic field. The anomalous transport becomes optimal for a subthreshold driving when the driving period matches a characteristic time scale of interwell transitions. It can also be optimized by varying temperature, amplitude of periodic potential and driving strength. The useful work done against a load shows a parabolic dependence on the load strength. It grows sublinearly with time and the corresponding thermodynamic efficiency decays algebraically in time because the energy supplied by the driving field scales with time linearly. However, it compares well with the efficiency of normal diffusion rocking ratchets on an appreciably long time scale.},
  language  = {en}
}