Related papers: Quantum Riemann-Hilbert problems for the resolved …
The no-boundary proposal is a theory of the initial conditions of the universe formulated in semi-classical gravity, and relying on the existence of regular (complex) solutions of the equations of motion. We show by explicit computation…
We consider the Cahn-Hilliard equation on a manifold with conical singularities and show the existence of bounded imaginary powers for suitable closed extensions of the bilaplacian. Combining results and methods from singular analysis with…
We quantize a compactified version of the trigonometric Ruijse\-naars-Schneider particle model with a phase space that is symplectomorphic to the complex projective space CP^N. The quantum Hamiltonian is realized as a discrete difference…
We prove the crepant resolution conjecture for Donaldson-Thomas invariants of hard Lefschetz CY3 orbifolds, formulated by Bryan-Cadman-Young, interpreting the statement as an equality of rational functions. In order to do so, we show that…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
The solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions $a,b,A,B$. The functions $a(k)$ and $b(k)$ are…
We formulate large $N$ duality of $\mathrm{U}(N)$ refined Chern-Simons theory with a torus knot/link in $S^3$. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string…
This paper concerns the cohomological aspects of Donaldson-Thomas theory for Jacobi algebras and the associated cohomological Hall algebra, introduced by Kontsevich and Soibelman. We prove the Hodge-theoretic categorification of the…
In the present work, the results obtained in [1] about the revivals of a relativistic fermion wave function on a torus are considerably enlarged. In fact, all the possible quantum states exhibiting revivals are fully characterized. The…
In recent work, Benjamin Schumacher and Michael D. Westmoreland investigate a version of quantum mechanics which they call modal quantum theory. This theory is obtained by instantiating the mathematical framework of Hilbert spaces with a…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
The $\alpha'$-complete cosmology developed by Hohm and Zwiebach classifies the ${\rm O}(d,d;{\mathbb R})$ invariant theories involving metric, $b$-field and dilaton that only depend on time, to all orders in $\alpha'$. Some of these…
Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimization problem can be transformed into an unconstrained problem…
For even dimensional conformal manifolds several new conformally invariant objects were found recently: invariant differential complexes related to, but distinct from, the de Rham complex (these are elliptic in the case of Riemannian…
In this paper, we study the prescribed $Q$-curvature problem on closed four-dimensional Riemannian manifolds when the total integral of the $Q$-curvature is a positive integer multiple of the one of the four-dimensional round sphere. This…
We consider three dimensional gravity with a positive cosmological constant and non- zero gravitational Chern-Simons term. This theory has inflating de Sitter solutions and local metric degrees of freedom. The Euclidean signature partition…
The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component…
The new method of solving quantum mechanical problems is proposed. The finite, i.e. cut off, Hilbert space is algebraically implemented in the computer code with states represented by lists of variable length. Complete numerical solution of…
In this paper we quantize the $N$-dimensional classical Hamiltonian system $H= \frac{|q|}{2(\eta + |q|)} p^2-\frac{k}{\eta +|q|}$, that can be regarded as a deformation of the Coulomb problem with coupling constant $k$, that it is smoothly…
We establish a new perturbation theory for orthogonal polynomials using a Riemann--Hilbert approach and consider applications in numerical linear algebra and random matrix theory. This new approach shows that the orthogonal polynomials with…