Related papers: Spin foams, Refinement limit and Renormalization
We study the task of smoothing a circuit, i.e., ensuring that all children of a plus-gate mention the same variables. Circuits serve as the building blocks of state-of-the-art inference algorithms on discrete probabilistic graphical models…
We systematically examine various proposals which aim at increasing the accuracy in the determination of the renormalization of two-fermion lattice operators. We concentrate on three finite quantities which are particularly suitable for our…
The requirement for the absence of spontaneous symmetry breaking in the d=1 dimension has been used to optimize the regulator dependence of functional renormalization group equations in the framework of the sine-Gordon scalar field theory.…
How sensitive should machine learning models be to input changes? We tackle the question of model smoothness and show that it is a useful inductive bias which aids generalization, adversarial robustness, generative modeling and…
Finite-difference simulations of fluid dynamics and magnetohydrodynamics generally require an explicit diffusion operator, either to maintain stability by attenuating grid-scale structure, or to implement physical diffusivities such as…
The usefulness of solid-state spins in quantum technologies depends on how long they can remain in a coherent superposition of quantum states. This Colloquium discusses how first-principles simulations can predict spin dynamics for…
Spin Foam and Loop approaches to Quantum Gravity reformulate Einstein's theory of relativity in terms of connection variables. The metric properties are encoded in face bivectors/conjugate fluxes that are required to satisfy certain…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible…
In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop…
We gain tight rigorous bounds on the renormalisation fixed point function for period doubling in families of unimodal maps with degree 2 critical point. By writing the relevant eigenproblems in a modified nonlinear form, we use these…
We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of…
We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent renormalization group (RG) flow the coarse graining operation must be…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
The role of fixed degrees of freedom in soft/granular matter systems has broad applicability and theoretical interest. Here we address questions of the geometrical role that a scaffolding of fixed particles plays in tuning the threshold…
Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an…
This paper answers examines the relationship between Diffeomorphism Invariance and Background Independence. First, a review of the relationship between Background Independence, General Relativity (GR) and pre-GR theories are given. Then, a…
The spin dynamics and spin relaxation of itinerant electrons in quantum wires with spin-orbit coupling is reviewed. We give an introduction to spin dynamics, and review spin-orbit coupling mechanisms in semiconductors. The spin diffusion…
Renormalization-group theory stands, since over 40 years, as one of the pillars of modern physics. As such, there should be no remaining doubt regarding its validity. However, finite-size scaling, which derives from it, has long been poorly…
Loop quantum gravity envisions a small scale structure of spacetime that is markedly different from that of the classical spacetime continuum. This has ramifications for the excitation of matter fields and for their coupling to gravity.…