Related papers: Quantum Systems at The Brink: Properties of Atomic…
In the present paper we study two challenging problems for helium-type systems. Existence of eigenvalues at thresholds and the asymptotic behavior of the corresponding eigenfunctions. Since the usual methods for addressing these problems…
The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non--relativistic quantum mechanics. The long--range part of pair potentials is assumed to be pure Coulomb and no restriction…
The competition between the tendency of magnetic moments to order at low temperatures, and the tendency of conduction electrons to shield these moments, can result in a phase transition that takes place at zero Kelvin, the quantum critical…
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…
It is well known that $N$-electron atoms undergoes unbinding for a critical charge of the nucleus $Z_c$, i.e. the atom has eigenstates for the case $Z> Z_c$ and it has no bound states for $Z<Z_c$. In the present paper we derive upper bound…
We study a system in which the quantum dynamics of electrons depend on the particle density in their neighborhood. For any on-site repulsive interaction, we show that the exact two-body and three-body ground states are bound states. We also…
One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, i.e., below the essential spectrum, is well understood, the situation of zero energy bound states at the edge…
The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non-relativistic quantum mechanics. The long-range part of pair potentials is assumed to be pure Coulomb and no restriction…
A variational technique to describe the ground and scattering states below the break-up threshold for a three-nucleon system is developed. The method consists in expanding the wave function in terms of correlated Harmonic Hyperspherical…
The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…
Transition states or quantum states of zero energy appear at the boundary between the discrete part of the spectrum of negative energies and the continuum part of positive energy states. As such, transition states can be regarded as a…
In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length…
This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…
As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition at some critical Z_c. We investigate whether the electrons remain bound when Z=Z_c and whether the radius of the system stays…
Quantum critical systems out of equilibrium are of extensive interest, but are difficult to study theoretically. We consider here the steady state limit of a single electron transistor, which is attached to ferromagnetic leads and subjected…
We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and characterize the support of the limiting distributions. Such results are known for particles with positions on a…
Topological properties of quantum systems are one of the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have…
We discuss how the thermalization of an elementary quantum system is modified when the system is placed in an environment out of thermal equilibrium. To this aim we provide a detailed investigation of the dynamics of an atomic system placed…
A remarkable feature of atomic ground states is that they are observed to be radiationless in nature, despite (from a classical viewpoint) typically involving charged particles in accelerated motions. The simple hydrogen atom is a case in…
We present rigorous results for quantum systems with both bound and continuum states subjected to an arbitrary strength time-periodic field. We prove that the wave function takes the form of a sum of time-periodic resonant states with…