相关论文: Singularity with and without disorder at AKLT poin…

The low-energy properties of a system at a critical point may have additional symmetries not present in the microscopic Hamiltonian. This letter presents the theory of a class of multicritical points that provide an interesting example of…

Under the mild trace-norm assumptions we show that the eigenvalues of a generic (non Hermitian) complex perturbation of a Jacobi matrix sequence (not necessarily real) are still distributed as the real-valued function $2\cos t$ on…

Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on…

We develop a theory of the conductance of a quantum dot connected to two leads by single-mode quantum point contacts. If the contacts are in the regime of perfect transmission, the conductance shows no Coulomb blockade oscillations as a…

This is a study of phase-coherent conduction through a ballistic point contact with disordered leads. The disorder imposes mesoscopic (sample-to-sample) fluctuations and weak-localization corrections on the conductance, and also leads to…

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of…

We present an asymptotically exact solution of a paradigmatic non-Hermitian model: the disordered interacting fermionic Hatano-Nelson model, or equivalently, the non-Hermitian spin-1/2 XXZ model. We use a renormalization group method suited…

In perturbation theory, the spectral densities of two-point functions develop non-integrable threshold singularities at higher orders. In QCD, such singularities emerge when calculating the diagrams in terms of the pole quark mass, and they…

Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…

The AKLT Hamiltonian is a particular instance of a general class of model Hamiltonians defined in lattices with coordination $z$ where each site hosts a spins $S=z/2$, interacting both with linear and non-linear exchange couplings. In two…

We consider the waveguide modelled by a $n$-dimensional infinite tube. The operator we study is the Dirichlet Laplacian perturbed by two distant perturbations. The perturbations are described by arbitrary abstract operators ''localized'' in…

We characterize a singularity in the equal-time three-point density correlations that is generic to two-dimensional interacting Fermi liquids. In momentum space where the three-point correlation is determined by two wavevectors…

We conduct a numerical study of wave localization in disordered three-dimensional non-Hermitian systems featuring exceptional points. The energy spectrum of a disordered non-Hermitian Hamiltonian, exhibiting both parity-time and…

We consider a two-dimensional equilibrium measure problem under the presence of quadratic potentials with a point charge and derive the explicit shape of the associated droplets. This particularly shows that the topology of the droplets…

A previous paper by the authors found explicit contour integral formulas for certain joint moments of the multi-species q-TAZRP (totally asymmetric zero range process), using algebraic methods. These contour integral formulas have a…

Recently, waveguide lattices with non-uniform tunneling amplitudes have been explored due to their myriad tunable properties, many of which arise from the extended nature of their eigenstates in the absence of disorder. Here, we investigate…

We show, by explicit computation, that bare lattice perturbation theory in the two-dimensional O(n) nonlinear $\sigma$ models with superinstanton boundary conditions is divergent in the limit of an infinite number of points $|\Lambda|$.…

This paper aims to show that there exist non-symmetry constraints which yield integrable Hamiltonian systems through nonlinearization of spectral problems of soliton systems, like symmetry constraints. Taking the AKNS spectral problem as an…

A singular knot is an immersed circle in $\mathbb R^{3}$ with finitely many transverse double points. The study of singular knots was initially motivated by the study of Vassiliev invariants. Namely, singular knots give rise to a decreasing…

In this paper, we discuss the recognition problem for A_k-type singularities on wave fronts. We give computable and simple criteria of these singularities, which will play a fundamental role in generalizing the authors' previous work "the…