Related papers: A note on Liouville theory
We introduce a numerical method to obtain approximate eigenvalues for some problems of Sturm-Liouville type. As an application, we consider an infinite square well in one dimension in which the mass is a function of the position. Two…
In this paper, we establish a Liouville type theorem for the homogeneous dual fractional parabolic equation \begin{equation} \partial^\alpha_t u(x,t)+(-\Delta)^s u(x,t) = 0\ \ \mbox{in}\ \ \mathbb{R}^n\times\mathbb{R} . \end{equation} where…
Using a coupling for the weighted sum of independent random variables and the explicit expression of the transition semigroup of Ornstein-Uhlenbeck processes driven by compound Poisson processes, we establish the existence of a successful…
Using the Observable form of Maxwell's equations, we reveal that effective parameters at materials boundaries emerge naturally as anisotropic transfer functions. The complexity of the boundary dictates the order of these functions.…
The quantum-classical Liouville equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this equation in the mapping basis leads to a continuous description of discrete quantum…
We are interested by the behaviour of a 1D single heavy particle, interacting with an environment made of very fast particles in a thermal state. Assuming that the interactions are instantaneous, we construct an appropriate quantum jump…
In this paper, we address exponential ergodicity for L\'{e}vy driven Langevin dynamics with singular potentials, which can be used to model the time evolution of a molecular system consisting of $N$ particles moving in $\R^d$ and subject to…
For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…
Dynamics of active deformable particles in an external Poiseuille flow is investigated. In order to make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical…
The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The…
We investigate the qualitative properties of positive solutions to mixed local-nonlocal equations with indefinite nonlinearities, emphasizing the interaction between classical and fractional Laplacians. We first establish maximum principles…
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…
We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…
The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case.…
We derive exact expressions for the forces and torques between biaxial molecules interacting via the RE-squared potential, a recent variant of the Gay-Berne potential. Moreover, efficient routines have been provided for rigid body MD…
In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum…
The expression of the free energy density of a classical crystalline system as a gradient expansion in terms of a set of order parameters is developed using classical density functional theory. The goal here is to extend and complete an…
The space-noncommutativity adapted to the Liouville black hole theory is studied in the present work. Among our contributions, we present the solutions of noncommutative Liouville Black hole equations of motion and find their classical…
We provide some Liouville theorems for ancient nonnegative solutions of the heat equation on a complete non-compact Riemannian manifold with Ricci curvature bounded from below. We determine growth conditions ensuring triviality of the…
We compute the critical behaviour of three-dimensional scalar theories using a new exact non-perturbative evolution equation. Our values for the critical exponents agree well with previous precision estimates.