Related papers: Non-uniqueness of the third post-Newtonian binary …
We present new family of exact analytic solutions for three anyons in a harmonic potential (or in free space) in terms of generalized harmonics on $S^3$, which supplement the known solutions. The new solutions satisfy the hard-core…
We investigate point-line geometries whose singular subspaces correspond to binary equidistant codes. The main result is a description of automorphisms of these geometries. In some important cases, automorphisms induced by non-monomial…
We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in [25]. This mechanism is based on shadowing of pseudo-orbits generated by two dynamics: an `outer dynamics', given by…
Building on the relativistic Hamiltonian of Sonnleitner and Barnett arXiv:1806.00234 and its post-Newtonian extensions by Schwartz and Giuilini arXiv:1908.06929, we investigate composite atomic systems in dynamical gravitational…
Normal forms of Hamiltonian are very important to analyze the nonlinear stability of a dynamical system in the vicinity of invariant objects. This paper presents the normalization of Hamiltonian and the analysis of nonlinear stability of…
In contrast to Hermitian systems, eigenstates of non-Hermitian ones are in general nonorthogonal. This feature is most pronounced at exceptional points where several eigenstates are linearly dependent. In this work we show that near this…
The spectral, dynamical and topological properties of physical systems described by non-Hermitian (including $\mathcal{PT}$-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here…
Reliable predictions of general relativity theory are extracted using approximation methods. Among these, the powerful post-Newtonian approximation provides us with our best insights into the problems of motion and gravitational radiation…
To date, the second-order post-Newtonian (2PN) Hamiltonian has been known in closed analytic form only for systems of up to three point masses. In this paper, we present an analytic expression for the general $N$-body 2PN Hamiltonian in the…
Atom-dimer scattering below the three-body break-up threshold is studied for a system of three identical bosons. The atom-dimer scattering length and the energy of the most weakly-bound three-body state are shown to be strongly correlated.…
We reconsider the Hamiltonian reduction of the action for three dimensional AdS supergravity and $W_3$ higher spin AdS gravity in the Chern-Simons formulation under asymptotically anti-de Sitter boundary conditions. We show that the…
Two recent examples of non-Abelian discrete symmetries (S_3 and A_4) in understanding neutrino masses and mixing are discussed.
The energy of a compact binary system at the fifth post-Newtonian order is explicitly computed in the post-Minkowskian approximation by means of the Effective Field Theory approach. This result allows to determine, for the first time beyond…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
We consider a macroscopic model describing a system of self-gravitating particles. We study the existence and uniqueness of non-negative stationary solutions and allude the differences to results obtained from classical gravitational…
Exceptional points (EPs) has seen substantial advances in both experiment and theory. However, in quantum systems, higher-order exceptional points remain of great interest and possess numerous intriguing properties yet to be fully explored.…
The equations of motion of nonspinning compact binary systems at the third post-Newtonian (PN) order in massless scalar-tensor theories have recently been obtained. In the present paper, we complete this work by computing at 3PN order the…
The purpose of this paper is to analyze in detail the Hamiltonian formulation for the compact Gowdy models coupled to massless scalar fields as a necessary first step towards their quantization. We will pay special attention to the coupling…
We study binary mergers in bootstrapped Newtonian gravity, where higher-order couplings are added to the non-relativistic Lagrangian for the Newtonian potential. In this theory, the Arnowitt-Deser-Misner (ADM) mass differs from both the…
The $\nu_\mu \to \nu_e$ oscillation probability over short baseline ($\lesssim 1$~km) would be negligible in case the mixing matrix for three active neutrinos is unitary. However, in case of non-unitary mixing of three neutrinos, this…