Related papers: Exact Renormalization Scheme for Quantum Anosov Ma…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
We establish the first quantitative Berry-Esseen bounds for edge eigenvector statistics in random regular graphs. For any $d$-regular graph on $N$ vertices with fixed $d \geq 3$ and deterministic unit vector $\mathbf{q} \perp \mathbf{e}$,…
We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization…
We consider the eigenvalue pair correlation problem for certain integrable quantum maps on the 2-sphere. The classical maps are time one maps of Hamiltonian flows of perfect Morse functions. The quantizations are unitary operators on spaces…
We develop a universal distributional calculus for regulated volumes of metrics that are singular along hypersurfaces. When the hypersurface is a conformal infinity we give simple integrated distribution expressions for the divergences and…
Detailed knowledge of the primordial power spectrum of curvature perturbations is essential both in order to elucidate the physical mechanism (`inflation') which generated it, and for estimating the cosmological parameters from observations…
We construct a general renormalization group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show…
The requirement that the quantum partition function be invariant under a renormalization group transformation results in a wide class of exact renormalization group equations, differing in the form of the kernel. Physical quantities should…
A generalization of the on-mass-shell scheme of UV renormalization (the OMS-bar scheme) to the case of presence of unstable fundamental particles (like W and Z bosons) is proposed. Its basic ingredients are as follows: (i) the renormalized…
We present a renormalization scheme which simplifies the dynamics of an important class of interacting multi-qubit systems. We show that a wide class of M+1 qubit systems can be reduced to an equivalent n+1 qubit system with n equal to, or…
Exact Renormalization Group techniques are applied to supersymmetric models in order to get some insights into the low energy effective actions of such theories. Starting from the ultra-violet finite mass deformed N=4 supersymmetric…
The exact renormalization group equation for pure quantum gravity is used to derive the non-perturbative $\Fbeta$-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert…
We consider the half-wave maps equation $$ \partial_t \mathbf{u} = \mathbf{u} \times |D| \mathbf{u} $$ for $\mathbf{u} : \mathbb{R} \times \mathbb{T} \to \mathbb{S}^2$, where $\mathbb{T}=\mathbb{R}/2 \pi \mathbb{Z}$ is the one-dimensional…
Based on our recent work on the discretization of the radial AdS$_2$ geometry of extremal BH horizons,we present a toy model for the chaotic unitary evolution of infalling single particle wave packets. We construct explicitly the…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
We quantize the regularity properties of classical graphs that determine spin models for singly-generated Yang-Baxter planar algebras, including the Kauffman polynomial, and construct explicit examples. A source of examples comes from…
Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…