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Integrability versus chaos in the steady state of many-body open quantum systems.
Physical Review EThe Lindblad description of an open quantum system gives rise to two types of integrability, since the nonequilibrium steady state can be integrable independently of the Liouvillian.
Josef Richter, Lucas Sá, Masudul Haque
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Integration in finite terms of non-liouvillian functions
ACM Communications in Computer Algebra, 2011Definition: We call a differential field (F,D) = (C(t1, . . . , tn), D) admissible, if 1. all ti are algebraically independent over C, 2.Const(F ) = C, and 3. for each ti and Fi−1 := C(t1, . . . , ti−1) either (a) ti is a Liouvillian monomial over Fi−1, i.e.
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Corrections and complements to “Liouvillian integration of the Lotka-Volterra system”
Qualitative Theory of Dynamical Systems, 2004In the original paper [the author, Qual. Theory Dyn. Syst. 2, No. 2, 307--358 (2002; Zbl 1084.34001)] the author described all possible values of the non-zero parameters \(A\), \(B\), and \(C\) for which the vector field \( x(Cy+z)\partial/\partial x + y(Az+x)\partial/\partial y + z(Bx+y)\partial/\partial z \) admits a homogeneous Liouvillian first ...
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
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Multidisciplinary standards of care and recent progress in pancreatic ductal adenocarcinoma
Ca-A Cancer Journal for Clinicians, 2020Aaron J Grossberg +2 more
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Liouvillian and analytic integrability of the quadratic vector fields having an invariant ellipse
Acta Mathematica Sinica. English series, 2014J. Llibre, C. Valls
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