Related papers: On and Off-diagonal Sturmian operator: dynamic and…
We discuss the systematic engineering of quasicrystals in open quantum systems where quasiperiodicity is introduced through purely dissipative processes. While the resulting short-time dynamics is governed by non-Hermitian variants of the…
We study the overdetermined problem for a large family of non-local operators given by generators of subordinate Brownian motions. In particular, this family includes the fractional Laplacian, relativistic stable operators etc. We consider…
For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we…
We study a canonical class of perturbations of Dirac operators that are defined in any dimension and on any Hermitian Clifford module bundle. These operators generalize the 2-dimensional Jackiw-Rossi operator, which describes electronic…
In quasicrystals, the phason degree of freedom and the inherent anharmonic potentials lead to complex dynamics which cannot be described by the usual phonon modes of motion. We have constructed simple one-dimensional model systems, the…
We look at the work of Oleg Ivrii connected with the dimension of quasicircles for asymptotically small quasiconformality parameter $k$. We intend to make this work more easily accessible. Our main focus is the integral means spectrum…
In a recent publication we have investigated the spectrum of anomalous dimensions for arbitrary composite operators in the critical N-vector model in 4-epsilon dimensions. We could establish properties like upper and lower bounds for the…
We rigorously prove a new kind of anomalous (or sub-ballistic) Lieb-Robinson bound for the isotropic XY chain with Fibonacci external magnetic field at arbitrary coupling. It is anomalous in that the usual exponential decay in $x-vt$ is…
We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasi-Hermitian Hamiltonian are related to the symmetry generators of an…
We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of…
We present a simple method, not based on the transfer matrices, to prove vanishing of dynamical transport exponents. The method is applied to long range quasiperiodic operators.
We numerically analyze spectral properties of the Fibonacci model which is a one-dimensional quasiperiodic system. We find that the energy levels of this model have the distribution of the band widths $w$ obeys $P_B(w)\sim w^{\alpha}$…
We investigate the off-equilibrium dynamics of a classical spin system with $O(n)$ symmetry in $2< D <4$ spatial dimensions and in the limit $n\to \infty$. The system is set up in an ordered equilibrium state is and subsequently driven out…
We defend the Fock-space Hamiltonian truncation method, which allows to calculate numerically the spectrum of strongly coupled quantum field theories, by putting them in a finite volume and imposing a UV cutoff. The accuracy of the method…
We apply differential operators to modular forms on orthogonal groups $\mathrm{O}(2, \ell)$ to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are…
In this paper we introduce a method that allows one to prove uniform local results for one-dimensional discrete Schr\"odinger operators with Sturmian potentials. We apply this method to the transfer matrices in order to study the Lyapunov…
The hopping dynamics of two fermionic species with different effective masses in the one-dimensional Hubbard model driven by an external field is theoretically investigated. A multiple-time-scale asymptotic analysis of the driven asymmetric…
We obtain some necessary and sufficient conditions for the boundedness of a family of positive operators defined on symmetric cones, we then deduce off-diagonal boundedness of associated Bergman-type operators in tube domains over symmetric…
We consider discrete Schr\"odinger operators with Sturmian potentials and study the transport exponents associated with them. Under suitable assumptions on the frequency, we establish upper and lower bounds for the upper transport…
We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition.…