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We study the excitation spectrum in the dimer phase of the Shastry-Sutherland model by using an unbiased variational method that works in the thermodynamic limit. The method outputs dynamical correlation functions in all possible channels.…
Dynamical fermion mass generation is studied in the three-dimensional Thirring model reformulated as a gauge theory by introducing hidden local symmetry. The analysis by use of Schwinger-Dyson equation is shown to exhibit a critical…
The spectral localizer consists of placing the Hamiltonian in a Dirac trap. For topological insulators its spectral asymmetry is equal to the topological invariants, providing a highly efficient tool for numerical computation. Here this…
We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and…
Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions. The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is…
We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point…
Although Lorentz invariance forbids the presence of a term that tilts the energy-momentum relation in the Weyl Hamiltonian, a tilted dispersion is not forbidden and, in fact, generic for condensed matter realizations of Weyl semimetals. We…
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…
Dyadic data, where outcomes reflecting pairwise interaction among sampled units are of primary interest, arise frequently in social science research. Regression analyses with such data feature prominently in many research literatures (e.g.,…
Level statistics are a useful probe for detecting symmetries and distinguishing integrable and non-integrable systems. I show by way of several examples that level statistics detect the presence of generalized symmetries that go beyond…
We study analytically the equilibrium properties of the spherical hierarchical model in the presence of random fields. The expression for the critical line separating a paramagnetic from a ferromagnetic phase is derived. The critical…
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…
In this work, we study the non-PT symmetry phase of the Swanson Hamiltonian in the framework of the Complex Scaling Method. By constructing a bi-orthogonality relation, we apply the formalism of the response function to analyse the time…
In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…
Segregation to grain boundaries affects their cohesion, corrosion and embrittlement and plays a critical role in heterogeneous nucleation. In order to quantitatively study segregation and phase separation at grain boundaries, we derive a…
This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…
In this work, we consider a time-varying stochastic saddle point problem in which the objective is revealed sequentially, and the data distribution depends on the decision variables. Problems of this type express the distributional…
We study the phase diagram for a lattice model of a time-reversal-broken three-dimensional Weyl semimetal (WSM) in an orbital magnetic field $B$ with a flux of $p/q$ per unit cell ($0\le p \le q-1$), with minimal crystalline symmetry. We…
We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random…
We introduce and study a non-oriented first passage percolation model having a property of statistical invariance by time reversal. This model is defined in a graph having directed edges and the passage times associated with each set of…