30 citations · 108 across the 16 of their papers we have counts for
16 papers
Eigenstates with Infinite Position Moments
Michal Jex
We prove necessary and sufficient conditions for the Schrödinger operators to have zero-energy bound states at the threshold of the essential spectrum such that they have bounded $…
On the ground state of lattice Schrödinger operators
Michal Jex, František Štampach
We prove necessary and sufficient conditions for lattice Schrödinger operators to have a zero energy bound state in arbitrary dimension. The two criteria are sharp, complementary,…
Classical Density Functional Theory: The Local Density Approximation
Michal Jex, Mathieu Lewin, Peter Madsen
We prove that the lowest free energy of a classical interacting system at temperature with a prescribed density profile can be approximated by the local free energy $\in…
Quantum Systems at The Brink
Dirk Hundertmark, Michal Jex, Markus Lange
We present a method to calculate the asymptotic behavior of eigenfunctions of Schrödinger operators that also works at the threshold of the essential spectrum. It can be viewed as…
Classical Density Functional Theory: Representability and Universal Bounds
Michal Jex, Mathieu Lewin, Peter S. Madsen
We provide upper and lower bounds on the lowest free energy of a classical system at given one-particle density . We study both the canonical and grand-canonical cases, assum…
Quantum Systems at the Brink: Existence of Bound States, Critical Potentials and Dimensionality
Dirk Hundertmark, Michal Jex, Markus Lange
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 under…
Quantum Systems at The Brink: Properties of Atomic Bound States at The Ionization Threshold
Dirk Hundertmark, Michal Jex, Markus Lange
We give a rigorous argument that long--range repulsion stabilizes quantum systems; ground states of such quantum systems exist even when the ground state energy is precisely at the…
Trace Hardy inequality for the Euclidean space with a cut and its applications
Monique Dauge, Michal Jex, Vladimir Lotoreichik
We obtain a trace Hardy inequality for the Euclidean space with a bounded cut , . In this novel geometric setting, the Hardy-type inequality non-typic…
Quantum Systems at The Brink. Existence and Decay Rates of Bound States at Thresholds; Atoms
Dirk Hundertmark, Michal Jex, Markus Lange
It is well known that -electron atoms undergoes unbinding for a critical charge of the nucleus , i.e. the atom has eigenstates for the case and it has no bound sta…
Quantum Systems at The Brink: Helium-type systems
Dirk Hundertmark, Michal Jex, Markus Lange
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 eigenfunctio…
The Lieb-Thirring inequality revisited
Rupert L. Frank, Dirk Hundertmark, Michal Jex +1
We provide new estimates on the best constant of the Lieb-Thirring inequality for the sum of the negative eigenvalues of Schrödinger operators, which significantly improve the so f…
On absence of bound states for weakly attractive -interactions supported on non-closed curves in
Michal Jex, Vladimir Lotoreichik
Let be a non-closed piecewise- curve, which is either bounded with two free endpoints or unbounded with one free endpoint. Let be t…
Spectral asymptotics for interaction supported by a infinite curve
Michal Jex
We consider a generalized Schrödinger operator in describing an attractive interaction in a strong coupling limit. interaction is characterized by a co…
Spectral asymptotics of a strong interaction supported by a surface
Pavel Exner, Michal jex
We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive interaction supported by a smooth surface in , either infinite and asymptoticall…
Spectral asymptotics of a strong interaction on a planar loop
Pavel Exner, Michal Jex
We consider a generalized Schrödinger operator in with an attractive strongly singular interaction of type characterized by the coupling parameter and suppor…
On the ground state of quantum graphs with attractive -coupling
Pavel Exner, Michal Jex
We study relations between the ground-state energy of a quantum graph Hamiltonian with attractive coupling at the vertices and the graph geometry. We derive a necessary and suf…