Related papers: Minimality of interval exchange transformations wi…
Broad arguments indicate that quantum gravity should have a minimal length scale. In this essay we construct a minimum length model by generalizing the time-position and energy-momentum operators while keeping much of the structure of…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
We show that for any ergodic Lebesgue measure preserving transformation $f: [0,1) \rightarrow [0,1)$ and any decreasing sequence $\{b_i\}_{i=1}^{\infty}$ of positive real numbers with divergent sum, the set…
Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple…
It is proved that almost every interval exchange transformation given by the symmetric permutation 1->m, 2->m-1,..., m-1->2, m->1, where m>1 is an odd number, is disjoint from ELF systems. The notion of ELF systems was introduced to express…
The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst…
The main focus of this article is the study of ergodicity of Interacting Particle Systems (IPS). We present a simple lemma showing that scaling time is equivalent to taking the convex combination of the transition matrix of the IPS with the…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The…
Deformations of minimal surfaces lying in constant time slices in static space-times are studied. An exact and universal formula for a change of the area of a minimal surface under shifts of nearby point-like particles is found. It allows…
We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take the L^2…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
Robinson introduced a quotient space of pairs of convex sets which share their recession cone. In this paper minimal pairs of unbounded convex sets, i.e. minimal representations of elements of Robinson's spaces are investigated. The fact…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…
We consider several fundamental properties of grand variable exponent Lebesgue spaces. Moreover, we discuss Ergodic theorems in these spaces whenever the exponent is invariant under the transformation.
We deal with the minimal Lagrangian surfaces of the Einstein-K\"ahler surface $S^2 \times S^2$, studying local geometric properties and showing that they can be locally described as Gauss maps of minimal surfaces in $S^3 \subset R^4$. We…
Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian…
We discuss the issue of parity violation in quantum gravity. In particular, we study the coupling of fermionic degrees of freedom in the presence of torsion and the physical meaning of the Immirzi parameter from the viewpoint of effective…
We prove that the number of Siegel-reduced bases for a randomly chosen $n$-dimensional lattice becomes, for $n \rightarrow \infty$, tightly concentrated around its mean. We also show that most reduced bases behave as in the worst-case…
It is shown here that symmetric hyperbolicity, which guarantees well-posedness, leads to a set of two inequalities for matrices whose elements are determined by a given theory. As a part of the calculation, carried out in a mostly-covariant…