Related papers: Garrett approximation revisited
In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-Gordon equation. Our main result includes energy class…
A new scheme of approximation in quantum theory is proposed which is potentially applicable to arbtrary interacting systems. The method consists in in approximating the original Hamiltonian by one corresponding to a suitable exactly…
We present a new approximation technique for quantum field theory. The standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In a…
The prediction of spacetime singularities, regions of infinite curvature where classical physics breaks down, is one of the most profound challenges in General Relativity (GR). In particular, black hole solutions such as the Schwarzschild…
2-dimensional knots and links are studied in the article. The notion of parity is introduced via techniques similar to the ones used by the second named author in 1-dimensional case. By using parity new invariants are constructed and known…
Using a continued fraction ansatz we obtain an analytic approximation for a spherically symmetric black hole solution to Einsteinian Quartic Gravity (EQG), the next simplest Generalized Quasi-Topological Gravity (GQTG) after Einsteinian…
In this work, we introduce an analytical approximate black hole solution in Einstein-Cubic gravity. To obtain complete solutions, we construct the near horizon and asymptotic solutions as the first step. Then, the approximate analytic…
The problem of consistent formulation of the correspondence principle in quantum gravity is considered. The usual approach based on the use of the two-particle scattering amplitudes is shown to be in disagreement with the classical result…
Generic self-gravitating quantum solutions that are not critically dependent on the specifics of microscopic interactions are presented. The solutions incorporate curvature effects, are consistent with the universality of gravity, and have…
In an effective-field-theory framework for gravity, black-hole quasinormal mode spectra acquire corrections in quadratic-curvature, scalar-tensor extensions of general relativity. Previous calculations of such corrections were limited to…
Quantum gravity corrections to accretion onto a Schwarzschild black hole are considered in the context of asymptotically safe scenario. The possible positions of the critical points are discussed and the general conditions for critical…
The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the…
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…
We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the quantum Fourier transform and quantum addition. Embedding…
I argue that the leading quantum corrections, in powers of the energy or inverse powers of the distance, may be computed in quantum gravity through knowledge of only the low energy structure of the theory. As an example, I calculate the…
We explore similarities between the quantum wells and quantum dots used as optical gain media in semiconductor lasers. We formulate a mapping procedure which allows a simpler, often analytical, description of quantum well lasers to study…
We revisit three classical numerical methods for solving unconstrained optimal control problems - multiple shooting, single shooting, and differential dynamic programming - and examine their local convergence behaviour. In particular, we…
In this note, I review a recent approach to quantum gravity that "gravitizes" quantum mechanics by emerging geometry and gravity from complex quantum states. Drawing further insights from tensor network toy models in AdS/CFT, I propose that…
For chaotic scattering on quantum graphs, the semiclassical approximation is exact. We use this fact and employ supersymmetry, the colour-flavour transformation, and the saddle-point approximation to calculate the exact expression for the…
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…