相关论文: No free lunch for effective potentials: general co…
In this paper we show that the weak representation property of a semimartingale $X$ with respect to a filtration $\mathbb{F}$ is preserved in the progressive enlargement $\mathbb{G}$ by a random time $\tau$ avoiding $\mathbb{F}$-stopping…
The $GW$ approximation is a widely used framework for studying correlated materials, but it struggles with certain limitations, such as its inability to explain pseudogap phenomena. To overcome these problems, we propose a systematic…
New models of the Fock space sector corresponding to some fixed number of electrons are introduced. These models originate from the representability theory and their practical implementation may lead to essential reduction of dimensions of…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…
Conventional theoretical and computational approaches to fully coupled quantum molecular dynamics, i.e. when both the electrons and nuclei are treated as quantum-mechanical particles, are impractical for all but the smallest chemical…
In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…
This Letter looks at the consequences of so-called 'superstrong nonlocal correlations', which are hypothetical violations of Bell/CHSH inequalities that are stronger than quantum mechanics allows, yet weak enough to prohibit…
In this paper, we define a scalar complex potential $\mathcal{S}$ for an arbitrary electromagnetic field. This potential is a modification of the two scalar potential functions introduced by E. T. Whittaker. By use of a complexified…
There exist many simple tools for jointly capturing variability and incomplete information by means of uncertainty representations. Among them are random sets, possibility distributions, probability intervals, and the more recent Ferson's…
Schroedinger (Nature, v.169, p.538 (1952)) demonstrated that, contrary to the widespread belief, charged particles may be described by real fields. Therefore the sets of solutions with real-valued charged fields are considered in the…
Interpretation of deep learning models is a very challenging problem because of their large number of parameters, complex connections between nodes, and unintelligible feature representations. Despite this, many view interpretability as a…
Theoretical studies of self-assembly processes and condensed phases in colloidal systems are often based on effective inter-particle potentials. Here we show that developing an effective potential for particles interacting with a limited…
The Burau representation enables to define many other representations of the braid group $B_n$ by the topological operation of ``cabling braids''. We show here that these representations split into copies of the Burau representation itself…
An extension of the fermionic particle--particle propagator is presented, that possesses similar algebraic properties to the single--particle Green's function. In particular, this extended two--particle Green's function satisfies Dyson's…
Neural networks leverage robust internal representations in order to generalise. Learning them is difficult, and often requires a large training set that covers the data distribution densely. We study a common setting where our task is not…
Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove an inequality involving the energy and the discriminant and apply it to deduce a result on totally positive…
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
After a brief presentation of Feynman diagrams, we criticizise the idea that Feynman diagrams can be considered to be pictures or depictions of actual physical processes. We then show that the best interpretation of the role they play in…