Linear and Nonlinear Dissipative Dynamics

Albeverio, 2003, Symmetrizing measures for infinite dimensional diffusions: an analytic approach, 475 Al-Rashed, 2014, Monotone Norms and Finsler Structure in Noncommutative Spaces, Infin. Dimens. Anal. Qu., 17 Baudoin, 2008, Ornstein-Uhlenbeck processes on Lie groups, J. Func. Analysis, 255, 877, 10.1016/j.jfa.2008.05.004 Baudoin, 2005, Hypoellipticity in infinite dimensions and an application in interest rate theory, Ann. Appl. Probab., 15, 1765, 10.1214/105051605000000214 Bakry, 1985, Diffusions hypercontractives, 1123, 177 Bakry, 2008, On gradient bounds for the heat kernel on the Heisenberg group, J. Func. Analysis, 255, 1905, 10.1016/j.jfa.2008.09.002 Blanchard, 2007, Quantum dynamical semigroups for finite and infinite Bose systems, J. Math. Phys., 48, 10.1063/1.2406053 Bobkov, 1999, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Func. Analysis, 163, 1, 10.1006/jfan.1998.3326 Bodineau, 2000, Hypercontractivity via spectral theory, Infin. Dimens. Anal. Qu., 3, 15, 10.1142/S0219025700000030 Carbone, 2015, Logarithmic Sobolev inequalities in non-commutative algebras, Infin. Dimens. Anal. Qu., 18, 1550011, 10.1142/S0219025715500113 Carbone, 2008, Hypercontractivity for a Quantum Ornstein–Uhlenbeck Semi-group, Probab. Theory Relat. Fields, 140, 10.1007/s00440-007-0073-2 Cipriani, 1997, Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras, J. Funct. Anal., 147, 10.1006/jfan.1996.3063 Choi, 2008, Quantum markovian semigroups on quantum spin system: Glauber dynamics, J. Korean Math. Soc., 45, 1075, 10.4134/JKMS.2008.45.4.1075 Da Prato, 1992 Dragoni, 2011, Ergodicity of Markov Semigroups with Hörmander type generators in Infinite Dimensions, J. Potential Analysis, 37, 199, 10.1007/s11118-011-9253-x Driver, 2008, Hypoelliptic heat kernel inequalities on Lie groups, Stoch. Process. Appl., 118, 368, 10.1016/j.spa.2007.04.012 Fougéres, 2012, Sub-gaussian measures and associated semilinear problems, Rev. Mat. Iberoam., 28, 10.4171/rmi/679 P. Fougéres, I. Gentil and B. Zegarliński: Application of logarithmic Sobolev inequality to Cauchy problems of reaction-diffusion equations, [hal-00987370] P. Fougéres, I. Gentil and B. Zegarliński: Ergodicity and smoothing for reaction-diffusion equations via application of logarithmic Sobolev inequality, work in progress. Fougéres, 2005, Semi-linear Problems in Infinite Dimensions, J. Func. Analysis, 228, 39, 10.1016/j.jfa.2005.06.019 Goderis, 1991, Constructing quantum dissipations and their reversible states from classical interacting spin systems, Ann. Inst. Henri Poincaré, 55, 805 Guionnet, 2003, Lectures on logarithmic Sobolev inequalities, 1801 Hebisch, 2010, Coercive inequalities on metric measure spaces, J. Func. Analysis, 258, 814, 10.1016/j.jfa.2009.05.016 J. Inglis: Coercive inequalities for generators of Hormander type, PhD Thesis, Imperial College 2010. Inglis, 2011, From U-bounds to isoperimetry with applications to H-type groups, J. Func. Analysis, 260, 76, 10.1016/j.jfa.2010.08.003 Inglis, 2009, Logarithmic Sobolev inequalities for infinite dimensional Hoermander type generators on the Heisenberg group, J. Pot. Analysis, 31, 79, 10.1007/s11118-009-9126-8 Temme, 2014, Hypercontractivity of quasi-free quantum semigroups, J. Phys. A: Math. Theor., 47, 405303, 10.1088/1751-8113/47/40/405303 Kastoryano, 2013, Quantum logarithmic Sobolev inequalities and rapid mixing, J. Math. Phys., 54, 10.1063/1.4804995 Kontis, 2016, Markov semigroups with hypocoercive-type generator in Infinite Dimensions I: Ergodicity and Smoothing, J. Func. Analysis, 270, 3173, 10.1016/j.jfa.2016.02.005 Ługiewicz, 2007, Coercive inequalities for Hörmander type generators in infinite dimensions, J. Func. Anal., 247, 438, 10.1016/j.jfa.2007.03.006 Olkiewicz, 2013, Nonlinear Markov semigroups on C*-algebras, Infin. Dimens. Anal. Qu., 16, 1350004, 10.1142/S0219025713500045 Ługiewicz, 2010, Ergodic properties of diffusion-type quantum dynamical semigroups, J. Phys. A: Math. Theor., 43, 425207, 10.1088/1751-8113/43/42/425207 Lihu, 2010, Existence and Exponential mixing of infinite white α-stable Systems with unbounded interactions, Electronic J. Probab., 15, 1994, 10.1214/EJP.v15-831 Li, 2006, Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg, J. Func. Analysis, 236, 369, 10.1016/j.jfa.2006.02.016 Liggett, 1999 Taku Matsui: Interacting Particle Systems on Non-Commutative Spaces, pp.115–124 in M. Fannes, C. Maes and A. Verbeure (Eds.), On Three Levels: Micro-, Meso and Macro-phenomena in Physics, Plenum (1994), Proceedings of the ASI/ARW Workshop in Leuven, 19–23 July 1993; Purification and uniqueness of quantum Gibbs states, Commun. Math. Phys. 162 (1994), 321–332. V. P. Maslov: Nonlinear averages in economics, Mathematical Notes, 2005 – Springer; Nonlinear averaging axioms in financial mathematics and stock price dynamics, Theory of Probability & Its Applications, 2004 – SIAM; Quantum economics, Russian J. Math. Phys. 2006. Majewski, 1998, Dissipative dynamics for quantum spin systems on a lattice, J. Phys. A: Math. Gen., 31, 2045, 10.1088/0305-4470/31/8/015 Olkiewicz, 2008, Dynamics of microcavity polaritions in the Markovian limit, Phys. Lett., A 372, 3176, 10.1016/j.physleta.2008.01.071 Olkiewicz, 1999, Hypercontractivity in Non-commutative Lp spaces, J. Func. Analysis, 161, 246, 10.1006/jfan.1998.3342 Papageorgiou, 2014, The Logarithmic Sobolev Inequality for Gibbs measures on infinite product of Heisenberg groups, Markov Processes Relat. Fields, 20, 705 Park, 2000, Construction of Dirichlet forms on standard forms of von Neumann algebras, Infin. Dimens. Anal. Qu., 3 Röckner, 1999, Lp-analysis of finite and infinite dimensional diffusion operators, Stochastic PDE's and Kolmogorov's equations in infinite dimensions, vol. 1715, 65 Stroock, 1992, The equivalence of the logarithmic Sobolev inequality and the Dobrushin–Shlosman mixing condition, Commun. Math. Phys., 144, 303, 10.1007/BF02101094 Xu, 2008, Nonlinear problems in infinite interacting particle systems, Infin. Dimens. Anal. Qu., 11, 179, 10.1142/S0219025708003063 Xu, 2009, Ergodicity of the finite and infinite dimensional α-stable Systems, J. Stoch. Analysis Appl., 27, 797, 10.1080/07362990902976629 F. Zak: Exponential ergodicity of infinite system of interacting diffusions, preprint. Zegarliński, 1990, On log-Sobolev inequalities for infinite lattice systems, Lett. Math. Phys., 20, 173, 10.1007/BF00398360 Zegarliński, 2011, Analysis on Extended Heisenberg Group, Annales de la Faculté des Sciences de Toulouse, XX, 379, 10.5802/afst.1296 B. Zegarliński: Crystallographic Groups of Hörmander Fields. I, http://arxiv.org/abs/1306.6453hal-01160736 Zegarliński, 2002, 241 Zegarliński, 2010, Linear and nonlinear concentration phenomena, Markov Processes Relat. Fields, 16, 753 Bouten, 1954, Applications of quantum stochastic processes in quantum optics, 277 L. Gallardo and M. Yor: Some remarkable properties of the Dunkl martingales, in Lecture Notes in Mathematics, 2006, 1874/2006, 337–356, http://dx.doi.org/doi:10.1007/978-3-540-35513-7_21 Rösler, 2003, Dunkl Operators: Theory and Applications, in Lecture Notes in Math. 1817, 93