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The crystal structure of high-pressure solid hydrogen remains a fundamental open problem. Although the research frontier has mostly shifted toward ultra-high pressure phases above 400 GPa, we show that even the broken symmetry phase…
The qualitative behavior of charged particles in a vacuum is given by Earnshaw's Theorem which states that there is no steady configuration of charged particles in a vacuum which is asymptotically stable to perturbations. In a viscous…
In this paper, we are concerned with the instability and stability of a quasi-linear hyperbolic-parabolic system modeling vascular networks. Under the assumption that the pressure satisfies $\frac{\nu P'(\bar\rho)}{\gamma \bar\rho} <…
Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium…
Given a bulk scalar field with sufficient self-interactions in a higher dimensional spacetime, it is shown that the continuous symmetries in four dimensions, induced by the topological structure of the compact manifold, naturally lead to…
The position and momentum probability densities of a multidimensional quantum system are fully characterized by means of the radial expectation values $\langle r^\alpha \rangle$ and $\left\langle p^\alpha \right\rangle$, respectively. These…
We consider the Hamiltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to an external potential. The stationary solutions of the system are a Coulomb…
Quantum mechanics is considered to arise from an underlying classical structure (``hidden variable theory'', ``sub-quantum mechanics''), where quantum fluctuations follow from a physical noise mechanism. The stability of the hydrogen ground…
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…
For monopoles with nonvanishing Higgs potential it is shown that with respect to "Brandt-Neri-Coleman type" variations (a) the stability problem reduces to that of a pure gauge theory on the two-sphere (b) each topological sector admits…
Controllable nonlinear quantum interactions are a much sought after target for modern quantum technologies. They are typically difficult and costly to engineer for bespoke purposes. However controllable nonlinearities may have always been…
We present an alternative, univocal characterization of the continuous transition from atomic to molecular shape in the Coulomb system constituted by two identical particles and a third particle with the opposite charge, as the mass ratio…
This paper proves the existence of unstable shocks of the Burgers-Hilbert equation conjectured in arXiv:2006.05568. More precisely, we construct smooth initial data with finite $H^9$-norm such that the solution in self-similar coordinates…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the…
We show that every quaternion-K\"ahler manifold of negative scalar curvature is stable as an Einstein manifold and therefore scalar curvature rigid. In particular, this implies that every irreducible nonpositive Einstein manifold of special…
The stability of dynamical systems against perturbations (variations in initial conditions/model parameters) is a property referred to as structural stability. The study of sensitivity to perturbation is essential because in experiment…
We consider the zero mass limit of a relativistic Thomas-Fermi-Weizsaecker model of atoms and molecules. We find bounds for the critical nuclear charges that ensure stability.
Extension of particle symmetry implies new conserved charges and the lightest particles, possessing such charges, should be stable. Created in early Universe, stable charged heavy leptons and quarks can exist and, hidden in elusive atoms…
There have been several existence results for the standing waves of FitzHugh-Nagumo equations. Such waves are the connecting orbits of an autonomous second-order Lagrangian system and the corresponding kinetic energy is an indefinite…