@article{6358,
abstract = {We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates.},
author = {Carlen, Eric A. and Maas, Jan},
issn = {15729613},
journal = {Journal of Statistical Physics},
number = {2},
pages = {319--378},
publisher = {Springer Nature},
title = {{Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems}},
doi = {10.1007/s10955-019-02434-w},
volume = {178},
year = {2020},
}
@article{8091,
abstract = {In the setting of the fractional quantum Hall effect we study the effects of strong, repulsive two-body interaction potentials of short range. We prove that Haldane’s pseudo-potential operators, including their pre-factors, emerge as mathematically rigorous limits of such interactions when the range of the potential tends to zero while its strength tends to infinity. In a common approach the interaction potential is expanded in angular momentum eigenstates in the lowest Landau level, which amounts to taking the pre-factors to be the moments of the potential. Such a procedure is not appropriate for very strong interactions, however, in particular not in the case of hard spheres. We derive the formulas valid in the short-range case, which involve the scattering lengths of the interaction potential in different angular momentum channels rather than its moments. Our results hold for bosons and fermions alike and generalize previous results in [6], which apply to bosons in the lowest angular momentum channel. Our main theorem asserts the convergence in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after appropriate energy scalings, to Hamiltonians with contact interactions in the lowest Landau level.},
author = {Seiringer, Robert and Yngvason, Jakob},
issn = {15729613},
journal = {Journal of Statistical Physics},
pages = {448--464},
publisher = {Springer},
title = {{Emergence of Haldane pseudo-potentials in systems with short-range interactions}},
doi = {10.1007/s10955-020-02586-0},
volume = {181},
year = {2020},
}
@article{8758,
abstract = {We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.},
author = {Maas, Jan and Mielke, Alexander},
issn = {15729613},
journal = {Journal of Statistical Physics},
publisher = {Springer Nature},
title = {{Modeling of chemical reaction systems with detailed balance using gradient structures}},
doi = {10.1007/s10955-020-02663-4},
year = {2020},
}