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This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…

The classic brachistrochrone problem is standard material in intermediate mechanics. Many variations exist including some accessible to introductory students. While a quantitative solution isn't feasible in introductory classes, qualitative…

In these notes I will briefly summarize our knowledge about the dark matter problem, and emphasize the corresponding dynamical aspects. This covers a wide area of research, so I have been selective, and have concentrated on the subject of…

The aim of these lectures is to provide (experimental particle physics Ph.D.) students with an introduction to some of the core concepts and methods of QCD that are relevant in an LHC context.

It is the goal of this thesis to revisit and revise the problem of black hole formation and evolution in semiclassical gravity -- a theory in which spacetime is treated classically, while matter admits a quantum description, coupling to…

This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.

We study electron spin decoherence in a two-electron double quantum dot due to the hyperfine interaction, under spin-echo conditions as studied in recent experiments. We develop a semi-classical model for the interaction between the…

We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…

We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…

We explore the possibility of avoiding cosmological singularity with a bounce solution in the early Universe. The main finding is that simple and well-known semiclassical correction, which describes the mixing of radiation and gravity in…

Observational evidence and theoretical motivation for dark matter are presented and connections to the CMB and BBN are made. Problems for baryonic and neutrino dark matter are summarized. Emphasis is placed on the prospects for…

We study quantum particles in interaction with a force-carrying field, in the quasi-classical limit. This limit is characterized by the field having a very large number of excitations (it is therefore macroscopic), while the particles…

We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…

Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…

We give a simple, semianalytic theory of the development of the hadronic and neutrino/muon components of a cascade induced by a primary which produces hadrons at the initial interaction. The main purpose of the theory is to allow the user…

The aim of this note is two-fold. In the first part of the paper we are going to investigate an inverse problem related to additive energy. In the second, we investigate how dense a subset of a finite structure can be for a given additive…

The physics of matter in the condensed state is concerned with problems in which the number of constituent particles is vastly greater than can be easily comprehended. The inherent physical limitations of the human mind are fundamental and…

This is a brief reminder, with extensions, from a different angle and for a less specialized audience, of my presentation at WGMP32 in July 2013, to which I refer for more details on the topics hinted at in the title, mainly deformation…

Work in closed quantum systems is usually defined by a two-point measurement. This definition of work is compatible with quantum fluctuation theorems but it fundamentally differs from its classical counterpart. In this paper, we study the…

We present here our considerations concerning the problem of classical consistency of pseudoclassical models touched upon in a recent comment on our paper "New pseudoclassical model for Weyl particle".