Alejo, Miguel A.; López, José Luis On global solutions to some non-Markovian quantum kinetic models of Fokker-Planck type. (English) Zbl 1439.35477 Z. Angew. Math. Phys. 71, No. 2, Paper No. 72, 33 p. (2020). MSC: 35Q84 35A01 35A02 35A08 35Q40 35S10 81Q99 35B45 PDFBibTeX XMLCite \textit{M. A. Alejo} and \textit{J. L. López}, Z. Angew. Math. Phys. 71, No. 2, Paper No. 72, 33 p. (2020; Zbl 1439.35477) Full Text: DOI arXiv
Li, Bin; Shen, Jie-qiong The Wigner(-Poisson)-Fokker-Planck equation with singular potential. (English) Zbl 1361.35080 Appl. Anal. 96, No. 4, 563-577 (2017). MSC: 35K55 47B44 35Q40 35R09 35B25 PDFBibTeX XMLCite \textit{B. Li} and \textit{J.-q. Shen}, Appl. Anal. 96, No. 4, 563--577 (2017; Zbl 1361.35080) Full Text: DOI
Dreher, Michael; Schnur, Johannes Large data solutions to the viscous quantum hydrodynamic model with barrier potential. (English) Zbl 1342.76141 Math. Methods Appl. Sci. 39, No. 11, 3016-3034 (2016). MSC: 76Y05 34B18 34B60 PDFBibTeX XMLCite \textit{M. Dreher} and \textit{J. Schnur}, Math. Methods Appl. Sci. 39, No. 11, 3016--3034 (2016; Zbl 1342.76141) Full Text: DOI Link
Dreher, Michael; Schnur, Johannes The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential. (English) Zbl 1310.82053 J. Math. Anal. Appl. 425, No. 2, 1113-1133 (2015). MSC: 82D37 82C70 35Q82 76Y05 35Q35 35M10 35C20 PDFBibTeX XMLCite \textit{M. Dreher} and \textit{J. Schnur}, J. Math. Anal. Appl. 425, No. 2, 1113--1133 (2015; Zbl 1310.82053) Full Text: DOI
López, José Luis; Montejo-Gámez, Jesús On the derivation and mathematical analysis of some quantum-mechanical models accounting for Fokker-Planck type dissipation: phase space, Schrödinger and hydrodynamic descriptions. (English) Zbl 1273.81143 Nanoscale Syst., Math. Model. Theory Appl. 2, 49-80 (2013). MSC: 81S22 35G30 35Q55 76Y05 81Q05 81S30 78M05 PDFBibTeX XMLCite \textit{J. L. López} and \textit{J. Montejo-Gámez}, Nanoscale Syst., Math. Model. Theory Appl. 2, 49--80 (2013; Zbl 1273.81143) Full Text: DOI
Arnold, Anton; Gamba, Irene M.; Gualdani, Maria Pia; Mischler, Stéphane; Mouhot, Clement; Sparber, Christof The Wigner-Fokker-Planck equation: stationary states and large time behavior. (English) Zbl 1253.82065 Math. Models Methods Appl. Sci. 22, No. 11, 1250034, 31 p. (2012). MSC: 82C31 82C10 35S10 74H40 81Q15 PDFBibTeX XMLCite \textit{A. Arnold} et al., Math. Models Methods Appl. Sci. 22, No. 11, Article ID 1250034, 31 p. (2012; Zbl 1253.82065) Full Text: DOI arXiv
Chen, Li; Dreher, Michael Quantum semiconductor models. (English) Zbl 1273.35003 Demuth, Michael (ed.) et al., Partial differential equations and spectral theory. Basel: Birkhäuser (ISBN 978-3-0348-0023-5/hbk; 978-3-0348-0024-2/ebook). Operator Theory: Advances and Applications 211. Advances in Partial Differential Equations, 1-72 (2011). MSC: 35-02 35K35 76Y05 35B40 65M20 PDFBibTeX XMLCite \textit{L. Chen} and \textit{M. Dreher}, Oper. Theory: Adv. Appl. 211, 1--72 (2011; Zbl 1273.35003) Full Text: DOI
Jüngel, Ansgar; López, José Luis; Montejo-Gámez, Jesús A new derivation of the quantum Navier-Stokes equations in the Wigner-Fokker-Planck approach. (English) Zbl 1238.82024 J. Stat. Phys. 145, No. 6, 1661-1673 (2011). Reviewer: Piotr Garbaczewski (Opole) MSC: 82C31 81S30 82C10 76S05 76Y05 35Q30 35Q40 PDFBibTeX XMLCite \textit{A. Jüngel} et al., J. Stat. Phys. 145, No. 6, 1661--1673 (2011; Zbl 1238.82024) Full Text: DOI
López, José Luis; Montejo-Gámez, J. On a rigorous interpretation of the quantum Schrödinger-Langevin operator in bounded domains with applications. (English) Zbl 1223.81126 J. Math. Anal. Appl. 383, No. 2, 365-378 (2011). MSC: 81S22 82C31 PDFBibTeX XMLCite \textit{J. L. López} and \textit{J. Montejo-Gámez}, J. Math. Anal. Appl. 383, No. 2, 365--378 (2011; Zbl 1223.81126) Full Text: DOI
Manzini, Chiara; Frosali, Giovanni Diffusive corrections to asymptotics of a strong-field quantum transport equation. (English) Zbl 1193.82036 Physica D 239, No. 15, 1402-1415 (2010). MSC: 82C70 82D37 35Q40 81Q05 PDFBibTeX XMLCite \textit{C. Manzini} and \textit{G. Frosali}, Physica D 239, No. 15, 1402--1415 (2010; Zbl 1193.82036) Full Text: DOI arXiv Link
Markowich, P. A.; Matevosyan, N.; Pietschmann, J.-F.; Wolfram, M.-T. On a parabolic free boundary equation modeling price formation. (English) Zbl 1183.35278 Math. Models Methods Appl. Sci. 19, No. 10, 1929-1957 (2009). Reviewer: Nikolai V. Krasnoschok (Donetsk) MSC: 35R35 35K15 91B60 PDFBibTeX XMLCite \textit{P. A. Markowich} et al., Math. Models Methods Appl. Sci. 19, No. 10, 1929--1957 (2009; Zbl 1183.35278) Full Text: DOI
Gamba, Irene M.; Jüngel, Ansgar; Vasseur, Alexis Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations. (English) Zbl 1181.35209 J. Differ. Equations 247, No. 11, 3117-3135 (2009). MSC: 35Q40 35D30 35Q35 76Y05 83C55 PDFBibTeX XMLCite \textit{I. M. Gamba} et al., J. Differ. Equations 247, No. 11, 3117--3135 (2009; Zbl 1181.35209) Full Text: DOI
Lafitte, P.; Parris, P. E.; De Bièvre, S. Normal transport properties in a metastable stationary state for a classical particle coupled to a non-Ohmic bath. (English) Zbl 1152.82021 J. Stat. Phys. 132, No. 5, 863-879 (2008). MSC: 82C70 82C41 81V05 83A05 82C40 PDFBibTeX XMLCite \textit{P. Lafitte} et al., J. Stat. Phys. 132, No. 5, 863--879 (2008; Zbl 1152.82021) Full Text: DOI arXiv
Albeverio, Sergio; Cattaneo, Laura; Mazzucchi, Sonia; Di Persio, Luca A rigorous approach to the Feynman-Vernon influence functional and its applications. I. (English) Zbl 1152.81309 J. Math. Phys. 48, No. 10, 102109, 22 p. (2007). MSC: 82C10 81S40 PDFBibTeX XMLCite \textit{S. Albeverio} et al., J. Math. Phys. 48, No. 10, 102109, 22 p. (2007; Zbl 1152.81309) Full Text: DOI Link
Chen, Li; Dreher, Michael The viscous model of quantum hydrodynamics in several dimensions. (English) Zbl 1144.35012 Math. Models Methods Appl. Sci. 17, No. 7, 1065-1093 (2007). MSC: 35B40 35Q35 76Y05 35Q40 PDFBibTeX XMLCite \textit{L. Chen} and \textit{M. Dreher}, Math. Models Methods Appl. Sci. 17, No. 7, 1065--1093 (2007; Zbl 1144.35012) Full Text: DOI
Arnold, Anton; Dhamo, Elidon; Manzini, Chiara The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive effects. (English) Zbl 1121.82031 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 24, No. 4, 645-676 (2007). MSC: 82C40 35Q40 PDFBibTeX XMLCite \textit{A. Arnold} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 24, No. 4, 645--676 (2007; Zbl 1121.82031) Full Text: DOI arXiv Numdam EuDML
Jüngel, Ansgar; Tang, Shaoqiang Numerical approximation of the viscous quantum hydrodynamic model for semiconductors. (English) Zbl 1097.82030 Appl. Numer. Math. 56, No. 7, 899-915 (2006). MSC: 82D37 82-08 76Y05 PDFBibTeX XMLCite \textit{A. Jüngel} and \textit{S. Tang}, Appl. Numer. Math. 56, No. 7, 899--915 (2006; Zbl 1097.82030) Full Text: DOI
Ben Abdallah, Naoufel; Méhats, Florian Semiclassical analysis of the Schrödinger equation with a partially confining potential. (English) Zbl 1162.35343 J. Math. Pures Appl. (9) 84, No. 5, 580-614 (2005). MSC: 35J10 35Q40 81Q20 35B25 PDFBibTeX XMLCite \textit{N. Ben Abdallah} and \textit{F. Méhats}, J. Math. Pures Appl. (9) 84, No. 5, 580--614 (2005; Zbl 1162.35343) Full Text: DOI
Arnold, A.; Sparber, C. Quantum dynamical semigroups for diffusion models with Hartree interaction. (English) Zbl 1085.82004 Commun. Math. Phys. 251, No. 1, 179-207 (2004). Reviewer: Bassano Vacchini (Milano) MSC: 82C10 47D06 47N50 47N55 82C31 PDFBibTeX XMLCite \textit{A. Arnold} and \textit{C. Sparber}, Commun. Math. Phys. 251, No. 1, 179--207 (2004; Zbl 1085.82004) Full Text: DOI arXiv
Arnold, Anton; López, José L.; Markowich, Peter A.; Soler, Juan An analysis of quantum Fokker-Planck models: a Wigner function approach. (English) Zbl 1062.35097 Rev. Mat. Iberoam. 20, No. 3, 771-814 (2004). MSC: 35Q40 82C31 35S10 82C70 PDFBibTeX XMLCite \textit{A. Arnold} et al., Rev. Mat. Iberoam. 20, No. 3, 771--814 (2004; Zbl 1062.35097) Full Text: DOI EuDML
Cañizo, José A.; López, José Luis; Nieto, Juan Global \(L^{1}\) theory and regularity for the 3D nonlinear Wigner-Poisson-Fokker-Planck system. (English) Zbl 1039.35093 J. Differ. Equations 198, No. 2, 356-373 (2004). MSC: 35Q40 81Q05 82C31 35B65 82C70 PDFBibTeX XMLCite \textit{J. A. Cañizo} et al., J. Differ. Equations 198, No. 2, 356--373 (2004; Zbl 1039.35093) Full Text: DOI