相关论文: Another proof of Gell-Mann and Low's theorem

The dependence of thermal field theory on the surface of quantization and on the velocity of the heat bath is investigated by working in general coordinates that are arbitrary linear combinations of the Minkowski coordinates. In the general…

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

Yang-Mills theories undergo a deconfining phase transition at a critical temperature. In lattice calculations the temporal Wilson loop and Z_3 order parameter show above this temperature a behavior typical of deconfinement. A quantity of…

We give a short proof of Ahlfors' theorem on covering surfaces.

The fluctuation-dissipation theorem (FDT) is very general and applies to a broad variety of different physical phenomena in condensed matter physics. With the help of the FDT and following the famous work of Caldeira and Leggett, we show…

The aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts. This technique is demonstrated through new proofs of five important theorems in parabolic unique continuation and the regularity…

We give a quite detailed overview on the proof of the Cheeger-Colding-Gromoll splitting theorem in the abstract framework of spaces with Riemannian Ricci curvature bounded from below.

We prove a quantitative theorem for Diophantine approximation by rational points on spheres. Our results are valid for arbitrary unimodular lattices and we further prove 'spiraling' results for the direction of approximates. These results…

In this paper, we present a quasi-polynomial time classical algorithm that estimates the partition function of quantum many-body systems at temperatures above the thermal phase transition point. It is known that in the worst case, the same…

Given the extreme accuracy of modern space astrometry, a precise relativistic modeling of observations is required. Concerning light propagation, the standard procedure is the solution of the null-geodesic equations. However, another…

We perform a Taylor series expansion of Tsallis distribution by assuming the Tsallis parameter $q$ close to 1. The $q$ value shows the deviation of a system from a thermalised Boltzmann distribution. By taking up to first order in $(q-1)$,…

Gallagher's ergodic theorem is a result in metric number theory. It states that the approximation of real numbers by rational numbers obeys a striking 'all or nothing' behaviour. We discuss a formalisation of this result in the Lean theorem…

Freiman's theorem asserts, roughly speaking, if that a finite set in a torsion-free abelian group has small doubling, then it can be efficiently contained in (or controlled by) a generalised arithmetic progression. This was generalised by…

The quantum no-broadcasting theorem has an analogue in modal quantum theory (MQT), a toy model based on finite fields. The failure of broadcasting in MQT is related to the failure of distributivity of the lattice of subspaces of the state…

We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of…

It has recently been claimed by De Zela that Gleason's theorem, for probability measures on the lattice of projection operators, can be extended to qubits by adding assumptions related to continuity and the existence of 'eigenstates'. This…

It is of great interest to understand the thermalization of open quantum many-body systems, and how quantum computers are able to efficiently simulate that process. A recently introduced disispative evolution, inspired by existing models of…

There has been recent debate over the use of the Boltzmann property in the kinetic equations describing dense neutrino systems such as early Universe and Supernova core. A technique developed by Bell, Rawlinson, and Sawyer utilises the…

We show an optimal version of the Rellich theorem for generalized many-body Schrodinger operators. It applies to singular potentials, in particular to a model for atoms and molecules with infinite mass and finite extent nuclei. Our proof…

In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.