Related papers: Quantum Talagrand-type Inequalities via Variance D…
We show that the natural directed analogues of the KKL theorem [KKL88] and the Eldan--Gross inequality [EG20] from the analysis of Boolean functions fail to hold. This is in contrast to several other isoperimetric inequalities on the…
We derive a Bell-type inequality for observables with arbitrary spectra. For the case of continuous variable systems we propose a possible experimental violation of this inequality, by using squeezed light and homodyne detection together…
We prove a version of Talagrand's concentration inequality for subordinated sub-Laplacian on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on…
In this paper, we consider a renormalization group perspective on the quantum dynamics of a particle moving in the Euclidean $\mathbb{R}^N$ space through the complex landscape provided by a disordered Hamiltonian of type $2+p$. We focus on…
In this paper we develop the theory of quantum reverse hypercontractivity inequalities and show how they can be derived from log-Sobolev inequalities. Next we prove a generalization of the Stroock-Varopoulos inequality in the…
The quantum geometric tensor (QGT) provides nontrivial bounds among physical quantities, as exemplified by the metric-curvature inequality. In this paper, we investigate various bounds for different observables through certain…
We investigate the finite-size scaling of the entanglement gap in the one dimensional long-range quantum spherical model (QSM). We focus on the weak long-range QSM, for which the thermodynamic limit is well-defined. This model exhibits a…
In this work the Vacuum Energy Density Problem or Dark Energy Problem is studied on the basis of the earlier results by the author within the scope of the Holographic Principle. It is demonstrated that the previously introduced deformed…
We consider the isoperimetric problem defined on the whole $\mathbb{R}^n$ by the Allen--Cahn energy functional. For non-degenerate double well potentials, we prove sharp quantitative stability inequalities of quadratic type which are…
We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible…
We show that the linearized higher derivative gravitational field equations are equivalent to an equilibrium condition on the entanglement entropy of small spherical regions in vacuum. This extends Jacobson's recent derivation of the…
It is shown that the use of a high power $\alpha$ of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid \textit{conservative} dynamics with a finite range of spatial Fourier modes.…
Based on a variant of the frequency function approach of Almgren, we establish an optimal bound on the vanishing order of solutions to stationary Schr\"odinger equations associated to a class of subelliptic equations with variable…
Lagrangians can differ by a total derivative without altering the equations of motion, thus encoding the same physics. This is true both classically and quantum mechanically. We show, however, that in the context of open quantum systems,…
A stochastic EDQNM approach is used to investigate self-similar decaying isotropic turbulence at high Reynolds number ($400 \leq Re_\lambda \leq 10^4$). The realistic energy spectrum functional form recently proposed by Meyers & Meneveau is…
We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing…
We identify ambiguities in the available frameworks for defining quantum, classical, and total correlations as measured by discordlike quantifiers. More specifically, we determine situations for which either classical or quantum…
In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calder\'on's and Zygmund's theory of first order…
We study sequences of solutions to the inhomogeneous Landau-Fermi-Dirac equation with Coulomb potential in which the quantum parameter converges to zero. Our main result establishes the compactness of these sequences, which allows us to…
We prove a quantitative estimate for the homogenization length scale in terms of the ellipticity ratio $\Lambda/\lambda$ of the coefficient field. This upper bound applies to high-contrast elliptic equations exhibiting near-critical…