Related papers: Bender-Wu singularities
Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered the Schroedinger eigenvalue problem on an infinite domain. This paper examines the consequences of imposing the boundary conditions on a finite domain. As is the…
We determine the eigenvalues with multiplicity of each element of an alternating group in any irreducible representation. This is equivalent to determining the decomposition of cyclic representations of alternating groups into irreducibles.…
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bi-partite quantum state-space. When the…
We consider families of multiple and simple integrals of the ``Ising class'' and the linear ordinary differential equations with polynomial coefficients they are solutions of. We compare the full set of singularities given by the roots of…
We study a set of crossed 1D systems, which are coupled with each other via tunnelling at the crossings. We begin with the simplest case with no electron-electron interactions and find that besides the expected level splitting, bound states…
Quantum systems with multiple degenerate classical harmonic minima exhibit new non-perturbative phenomena which are not present for the double-well and periodic potentials. The simplest characteristic example of this family is the…
Motivated by Heilmann and Lieb's work, we discuss energy level crossings for the one-dimensional Hubbard model through the Bethe ansatz, constructing explicitly the degenerate eigenstates at the crossing points. After showing the existence…
In this article we study the propagation of Wigner measures linked to solutions of the Schr{\"o}dinger equation with potentials presenting conical singularities and show that they are transported by two different Hamiltonian flows, one over…
We establish extension theorems for separately holomorphic mappings defined on sets of the form W\setminus M with values in a complex analytic space which possesses the Hartogs extension property. Here W is a 2-fold cross of arbitrary…
The spectral properties of $su(2)$ Hamiltonians are studied for energies near the critical classical energy $\epsilon_c$ for which the corresponding classical dynamics presents hyperbolic points (HP). A general method leading to an…
We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice, and compare the relevant ground-state properties with those of the corresponding symmetry-breaking…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
We establish transportation cost inequalities (TCI) with respect to the quantum Wasserstein distance by introducing quantum extensions of well-known classical methods: first, using a non-commutative version of Ollivier's coarse Ricci…
We construct random Schr\"odinger operators, called Anderson Hamiltonians, with Dirichlet and Neumann boundary conditions for a fairly general class of singular random potentials on bounded domains. Furthermore, we construct the integrated…
The eigenstates of a quantum spin glass Hamiltonian with long-range interaction are examined from the point of view of localisation and entanglement. In particular, low particle sectors are examined and an anomalous family of eigenstates is…
We consider the asymptotic behavior of the spectrum of the Landau Hamiltonian plus a rapidly decaying potential, as the magnetic field strength, $B$, tends to infinity. After a suitable rescaling, this becomes a semiclassical problem where…
The Hamiltonian of a system of two quantum mechanical particles moving on the $d$-dimensional lattice $\Z^d$ and interacting via zero-range attractive pair potentials is considered. For the two-particle energy operator $H_{\mu}(K),$ $K\in…
Describing and achieving `unconventional' superconductivity remains a forefront challenge in quantum many-body physics. Here we use a unitary mapping, combined with the well-established properties of the attractive Hubbard model to…