Related papers: Proof that the Hydrogen-antihydrogen Molecule is U…
A recent claim that molecule H-antiH is unstable cannot be a proof as it is based on a wrong conjecture. This is illustrated with 4 examples, including observed natural hydrogen-antihydrogen oscillations never detected previously.
We consider the stability of three Coulomb charges $\{+1, -1, -1 \}$ with finite masses in the framework of nonrelativistic quantum mechanics. A simple physical condition on masses is derived to guarantee the absence of bound states below…
We present a simple proof of the stability of the hydrogen molecule $(M^+M^+m^-m^-)$. It does not rely on the proton-to-electron mass ratio $M/m$ being very large, and actually holds for arbitrary values of $M/m$. Some asymmetric molecules…
We sketch two rigorous proofs of the stability of the hydrogen molecule in quantum mechanics. The first one is based on an extrapolation of variational estimates of the groundstate energy of a positronium molecule to arbitrary mass ratios.…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
We discuss the stability of three- and four-particle system interacting by pure Coulomb interactions, as a function of the masses and charges of the particles. We present a certain number of general properties which allow to answer a…
Ab initio quantum chemistry reveals how the charge-antisymmetric antihydrogenic antiHH+ state, deriving from conventional positional antisymmetry of a 3-unit charge system, is hidden in the PEC (potential energy curve) of the molecular…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
We introduce an efficient scheme for the molecular dynamics of electronic systems by means of quantum Monte Carlo. The evaluation of the (Born-Oppenheimer) forces acting on the ionic positions is achieved by two main ingredients: i) the…
It is shown that the homogeneous state of the spatially separated electrons and holes in the coupled quantum wells (CQW) is instable if the layer charge density is smaller than the critical value specified by the parameters of the CQW. The…
Sufficient conditions for the wave instability in general three-component reaction-diffusion systems are derived. These conditions are expressed in terms of the Jacobian matrix of the uniform steady state of the system, and enable us to…
A survey of the stability of matter problem is given, starting with the stability of the hydrogen atom. The stablity of bulk matter with Coulomb potentials, with or without relativistic mechanics, and with or without magnetic fields is…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
We examine the stability of matter-antimatter molecules by reducing the four-body problem into a simpler two-body problem with residual interactions. We find that matter-antimatter molecules with constituents (m1+, m2-, m2bar+, m1bar-)…
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power…
The quantum mechanics of two-electron systems is reviewed, starting with the ground state of the helium atom and helium-like ions, with central charge $Z\ge 2$. For Z=1, demonstrating the stability of the negative hydrogen ion, H$^-$,…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
Coulomb bubbles, though stable against monopole displacement, are unstable at least with respect to quadrupole and octupole distortions. We show that there exists a temperature at which the pressure of the vapor filling the bubble…
We present results on the stability of quantum systems consisting of a negative charge $-q_1$ with mass $m_{1}$ and two positive charges $q_2$ and $q_3$, with masses $m_{2}$ and $m_{3}$, respectively. We show that, for given masses $m_{i}$,…