Related papers: Effective high-temperature estimates for intermitt…
The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator valued Titchmarsh--Weyl $m$-function. This general result is applied to different self-adjoint realizations of second-order elliptic…
By using quasi--derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schr\"odinger operators with periodic singular potentials $v.$ Our results reveal a close relationship between smoothness of…
We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the system-noise coupling by random $N \times N$ Hermitian matrices, and study the spectral properties of the resulting Lindblad…
Thermal operations are an operational model of non-equilibrium quantum thermodynamics. In the absence of coherence between energy levels, exact state transition conditions under thermal operations are known in terms of a mathematical…
Using the mixed space representation (t,p) in the context of scalar field theories, we prove in a simple manner that the Feynman graphs at finite temperature are related to the corresponding zero temperature diagrams through a simple…
The transfer operator corresponding to a uniformly expanding map enjoys good spectral properties. Here it is verified that coupling yields explicit estimates that depend continuously on the expansion and distortion constants of the map. For…
In this note we prove a spectral gap for various Markov chains on various functional spaces. While proving that a spectral gap exists is relatively common, explicit estimates seems somewhat rare.These estimates are then used to apply the…
We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…
In the abstract framework of Mourre theory, the propagation of states is understood in terms of a conjugate operator $A$. A powerful estimate has long been known for Hamiltonians having a good regularity with respect to $A$ thanks to the…
For an arbitrary Hermitian period-$T$ Jacobi operator, we assume a perturbation by a Wigner-von Neumann type potential to devise subordinate solutions to the formal spectral equation for a (possibly infinite) real set, $S$, of the spectral…
We study monotone operators in reflexive Banach spaces that are invariant with respect to a group of suitable isometric isomorphisms and we show that they always admit a maximal extension which preserves the same invariance. A similar…
We propose two multiscale comparisons of graphs using heat diffusion, allowing to compare graphs without node correspondence or even with different sizes. These multiscale comparisons lead to the definition of Lipschitz-continuous empirical…
We apply thermodynamic formalism to a generalized horseshoe map. We prove that a tailored anisotropic Banach space with weighted norms yields a spectral gap for the transfer operator, implying the existence of a unique physical measure.…
We consider the unperturbed operator $H_0 : = (-i \nabla - A)^2 + W$, self-adjoint in $L^2(\R^2)$. Here $A$ is a magnetic potential which generates a constant magnetic field $b>0$, and the edge potential $W$ is a non-decreasing non constant…
We prove a spectral inequality (a specific type of uncertainty relation) for Schr\"odinger operators with confinement potentials, in particular of Shubin-type. The sensor sets are allowed to decay exponentially, where the precise allowed…
We study Lipschitz, positively homogeneous and finite suprema preserving mappings defined on a max-cone of positive elements in a normed vector lattice. We prove that the lower spectral radius of such a mapping is always a minimum value of…
Here, we develop a theory of radiative heat transfer based on an equivalent electrical network representation for the hot material slabs in an arbitrary multilayered environment with arbitrary distribution of temperatures and…
In this note we provide an explicit lower bound on the spectral gap of one-dimensional Schr\"odinger operators with non-negative bounded potentials and subject to Neumann boundary conditions.
We establish the existence of a spectral gap for the transfer operator induced on $\mathbb P^k = \mathbb P^k (\mathbb C)$ by a generic holomorphic endomorphism and a suitable continuous weight and its perturbations on various functional…
We study the spectral gap behavior of an operator obtained by summing a random permutation $M$ and a deterministic bistochastic matrix $Q$. We are interested in the asymptotic in terms of dimension. In the case where $(M,Q)$ are…