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We provide a novel existence result for energy-variational solutions to a general class of evolutionary partial differential equations. Compared to previous works on this solution concept, the generalization is mainly twofold: a relaxation…
We find the complete set of conditions satisfied by the forward $2\to2$ scattering amplitude in unitarity and causal theories. These are based on an infinite set of energy dependent quantities -- the arcs -- which are dispersively expressed…
It is well known that (possibly non-unique) suitable field dynamics can be prescribed in spacetimes with timelike boundaries by means of appropriate boundary conditions. In Ref. [J. Math. Phys. {\bf 21}, 2802 (1980)], Wald derived a…
A recent work [arXiv:2401.04685] has merged $N$-centered ensembles of neutral and charged electronic ground states with ensembles of neutral ground and excited states, thus providing a general and in-principle exact (so-called extended…
Probability distributions and densities are derived for the excess and deficiency of the intensity or instantaneous energy (quasi-static power) associated with a $p$-dimensional random vector field. Explicit expressions for the exact…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary…
We introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schr\"odinger perturbation theory to show that, in…
In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length…
We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…
Random Quantum States are presently of interest in the fields of quantum information theory and quantum chaos. Moreover, a detailed study of their properties can shed light on some foundational issues of the quantum statistical mechanics…
We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…
The Rayleigh-Ritz procedure for determining bound-states of the Schr\"{o}dinger equation relies on spectral representation of the solution as a linear combination of the basis functions. Several possible extensions of the method to…
A system of two interacting protofields with generic parameters is unstable with respect to unceasing cycles of nonlinear squeeze (reduction) to randomly chosen centres and reverse extension which form the causally probabilistic process of…
We give a proof of the Universality Conjecture for orthogonal and symplectic ensembles of random matrices in the scaling limit for a class of weights w(x)=exp(-V(x)) where V is a polynomial, V(x)=kappa_{2m}x^{2m}+..., kappa_{2m}>0. For such…
In a quantum system, different energy eigenstates have different properties or features, allowing us define a classifier to divide them into different groups. We find that the ratio of each type of energy eigenstates in an energy shell…
The resource theory of coherence addresses the extent to which quantum properties are present in a given quantum system. While coherence has been extensively studied for individual quantum states, measures of coherence for ensembles of…
We present a relativistic correction scheme to improve the accuracy of 1s core-level binding energies calculated from Green's function theory in the $GW$ approximation, which does not add computational overhead. An element-specific…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…