Related papers: Continuous eigenfunctions of the transfer operator…
In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…
Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators
Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we…
We consider a family of potentials f, derived from the Hofbauer potentials, on the symbolic space Omega=\{0,1\}^\mathbb{N} and the shift mapping $\sigma$ acting on it. A Ruelle operator framework is employed to show there is a phase…
Dyson's model in infinite dimensions is a system of Brownian particles interacting via a logarithmic potential with an inverse temperature of $ \beta = 2$. The stochastic process is given as a solution to an infinite-dimensional stochastic…
If $\mathcal{A}$ is a finite set (alphabet), the shift dynamical system consists of the space $\mathcal{A}^{\mathbb{N}}$ of sequences with entries in $\mathcal{A}$, along with the left shift operator $S$. Closed $S$-invariant subsets are…
The interplay of quantum statistics, interactions and temperature is studied within the framework of the bosonic two-component theory with repulsive delta-function interaction in one dimension. We numerically solve the thermodynamic Bethe…
We introduce sufficient conditions on discrete singular integral operators for their maximal truncations to satisfy a sparse bound. The latter imply a range of quantitative weighted inequalities, which are new. As an application, we prove…
We extend results on quadratic pressure and convergence of Gibbs mesures from previous joined work of the authors to the Curie-Weiss-Potts model. We define the notion of equilibrium state for the quadratic pressure and show that under some…
Based on the functional-discrete technique (FD-method), an algorithm for eigenvalue transmission problems with discontinuous flux and integrable potential is developed. The case of the potential as a function belonging to the functional…
Near a quantum critical point (QCP) in a metal, strong Fermion-Fermion interactions mediated by soft collective bosons give rise to two competing phenomena: non-Fermi liquid behavior and superconductivity that deviates from conventional BCS…
We consider a one-dimensional system of Brownian particles that repel each other through a logarithmic potential. We study two formulations for the system and the relation between them. The first, Dyson's Brownian motion model, has an…
We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators.
We consider here a class of groupoids obtained via an equivalence relation (the subgroupoids of pair groupoids). We generalize to Haar Systems in these groupoids some results related to entropy and pressure which are well known in…
We study very smooth functions on the real line, namely Schwartz functions, that satisfy a finite identity relating their translates and a single modulation. Concretely, we assume there is a nontrivial linear combination of translates of…
Let $\bigl\{X_k\bigr\}_{k \in \mathbb{Z}} \in \mathbb{L}^2(\mathcal{T})$ be a stationary process with associated lag operators ${\boldsymbol{\cal C}}_h$. Uniform asymptotic expansions of the corresponding empirical eigenvalues and…
We present experimental results on eigenfunctions of a wave chaotic system in the continuous crossover regime between time-reversal symmetric and time-reversal symmetry-broken states. The statistical properties of the eigenfunctions of a…
In this study, singular diffusion operator with jump conditions is considered. Integral representations have been derived for solutions that satisfy boundary conditions and jump conditions. Some properties of eigenvalues and eigenfunctions…
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
A general principle of modern statistical physics is that divergences of either thermodynamic or transport properties are only possible if the correlation length diverges. We show by explicit calculation that the thermopower in the quantum…