Zobrazeno 1 - 10
of 196
pro vyhledávání: '"Hundertmark, Dirk"'
Autor:
Hundertmark, Dirk, Kovarik, Hynek
We consider eigenvalues of the Pauli operator in $\mathbb R^3$ embedded in the continuous spectrum. In our main result we prove the absence of such eigenvalues above a threshold which depends on the asymptotic behavior of the magnetic and electric fi
Externí odkaz:
http://arxiv.org/abs/2312.04995
Publikováno v:
INdAM Meeting: Quantum Mathematics Workshop (2023)
We present a method to calculate the asymptotic behavior of eigenfunctions of Schr\"odinger operators that also works at the threshold of the essential spectrum. It can be viewed as a higher order correction to the well-known WKB method which does ne
Externí odkaz:
http://arxiv.org/abs/2210.16356
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 of the es
Externí odkaz:
http://arxiv.org/abs/2107.14128
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 ionization threshold. For atomic systems at the critical nuclear char
Externí odkaz:
http://arxiv.org/abs/2012.12748
Autor:
Hundertmark, Dirk, Kovařík, Hynek
Publikováno v:
In Journal of Functional Analysis 15 February 2024 286(4)
In this work we provide results on the long time localisation in space (dynamical localisation) of certain two-dimensional magnetic quantum systems. The underlying Hamiltonian may have the form $H=H_0+W$, where $H_0$ is rotationally symmetric, has de
Externí odkaz:
http://arxiv.org/abs/2006.00134
We consider a molecule in the Born-Oppenheimer approximation interacting with a plate of infinite thickness, i.e, a half--space, which is perfectly conducting or dielectric. It is well--known in the physics literature that in this case the atom or mo
Externí odkaz:
http://arxiv.org/abs/2004.04771
We prove local and global well-posedness results for the Gabitov-Turitsyn or dispersion managed nonlinear Schr\"odinger equation with a large class of nonlinearities and arbitrary average dispersion on $L^2(\mathbb{R})$ and $H^1(\mathbb{R})$. Moreove
Externí odkaz:
http://arxiv.org/abs/2003.09076
We study sufficient conditions for the absence of positive eigenvalues of magnetic Schr\"odinger operators in $\mathbb{R}^d,\, d\geq 2$. In our main result we prove the absence of eigenvalues above certain threshold energy which depends explicitly on
Externí odkaz:
http://arxiv.org/abs/2003.07294
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
Externí odkaz:
http://arxiv.org/abs/1908.05016