相关论文: On common energies and sumsets II
For a set $A$ of $k$ elements from an additive abelian group $G$ and a positive integer $r \leq k$, we consider the set of elements of $G$ that can be written as a sum of $h$ elements of $A$ with at least $r$ distinct elements. We denote…
We show that high energy scattering is a statistical process essentially similar to reaction-diffusion in a system made of a finite number of particles. The Balitsky-JIMWLK equations correspond to the time evolution law for the particle…
We show how in PT-symmetric 2J-level quantum systems the assumption of an upside-down symmetry (or duality) of their spectra simplifies their classification based on the non-equivalent pairwise mergers of the energy levels.
Studying the energy partioning published in nucl-th/0406056v2 we show that the presented results do not fulfill the sum rule due to energy conservation. The observed fluctuations of the energy conservation test point to a numerical problem.…
We prove a new class of low-energy decompositions which, amongst other consequences, imply that any finite set $A$ of integers may be written as $A = B \cup C$, where $B$ and $C$ are disjoint sets satisfying \[ |\{ (b_1, \dots, b_{2s}) \in…
We consider the problem of two-photon cooperative emission in systems of two-level atoms. Two physically distinct regimes are analyzed. First, we investigate the case of a small number of atoms. We study the evolution of two-photon super-…
We derive a formula that defines quantum fluctuations of energy in subsystems of a hot relativistic gas. For small subsystem sizes we find substantial increase of fluctuations compared to those known from standard thermodynamic…
We deduce from energy conservation a lower bound on the mass of any system capable of imparting a constant acceleration to a charged body. We also point out a connection between this bound and the so called dominant energy condition of…
We demonstrate that certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem and using principles of quantum mechanics. For simplicity we illustrate the method by exploring the…
We prove the validity of the $\varepsilon-\varepsilon^\beta$ property in the isoperimetric problem with double density, generalising the known properties for the case of single density. As a consequence, we derive regularity for…
The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in…
We present a counter-example to the statement that there is a linear reduction in both directionsbetween the largest common subtree and the smallest common supertrees. Moreover, we show that in general, even having of one of them, it is…
In this paper, we establish a sum rule that connects the pseudoentropy and entanglement entropy of a superposition state. Through analytical continuation of the superposition parameter, we demonstrate that the transition matrix and density…
This is the second paper devoted to energetic rigidity, in which we apply our formalism to examples in two dimensions: underconstrained random regular spring networks, vertex models, and jammed packings of soft particles. Spring networks…
We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation…
Although its practical efficiency is unquestionable, the thermodynamic tool presents a slight inconsistency from the theoretical point of view. After exposing arguments, which explain this opinion, a suggestion is put forward to solve the…
The expressions for the energy-weighted sum rule of the isoscalar and isovector coordinate operators are derived based on the second-order fluctuation of the local densities. Conventional derivation of the Thouless theorem for the…
A given subset $A$ of natural numbers is said to be complete if every element of $\N$ is the sum of distinct terms taken from $A$. This topic is strongly connected to the knapsack problem which is known to be NP complete. The main goal of…
In this paper, we present a comprehensive proof concerning the regularity of critical points for the spline energy functional on Riemannian manifolds, even for the general higher-order case. Although this result is widely acknowledged in…
We prove that any finite abelian group $G$ contains a collection of not too many subsets with a special structure, so that for every subset $A$ of $G$ with a small doubling, there is a member $F$ of the collection that is fully contained in…