9 citations · 32 across the 12 of their papers we have counts for
13 papers
Resonances for Atoms in Dipole approximation of non-relativistic QED
David Hasler, Markus Lange
We consider atoms or molecules coupled to the quantized electromagnetic radiation field in a dipole approximation. We show the existence of ground states and resonance states in si…
Symmetries in non-relativistic quantum electrodynamics
David Hasler, Markus Lange
We define symmetries in non-relativistic quantum electrodynamics, which have the physical interpretation of rotation, parity and time reversal symmetry. We collect transformation p…
Adiabatic Evolution of Low-Temperature Many-Body Systems
Rafael L. Greenblatt, Markus Lange, Giovanna Marcelli +1
We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependen…
Degenerate perturbation theory for models of quantum field theory with symmetries
David Hasler, Markus Lange
We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we sh…
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…
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…
Trotter product formulae for -automorphisms of quantum lattice systems
Sven Bachmann, Markus Lange
We consider the dynamics of an infinite quantum lattice system that is generated by a local interaction. If the interaction decomposes into a finite number of terms t…
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…
Exactness of linear response in the quantum Hall effect
Sven Bachmann, Wojciech De Roeck, Martin Fraas +1
In general, linear response theory expresses the relation between a driving and a physical system's response only to first order in perturbation theory. In the context of charge tr…
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…
Renormalization Analysis for Degenerate Ground States
David Hasler, Markus Lange
We consider a Hamilton operator which describes a finite dimensional quantum mechanical system with degenerate eigenvalues coupled to a field of relativistic bosons. We show that t…
On Asymptotic Expansions in Spin Boson Models
Gerhard Bräunlich, David Hasler, Markus Lange
We consider expansions of eigenvalues and eigenvectors of models of quantum field theory. For a class of models known as generalized spin boson model we prove the existence of asym…