Two-body continuum states in noninteger geometry

Padé Phenomenology for Two-Body Bound States

Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions

This paper addresses the problem of consistent energy-based coupling of atomistic and continuum models of materials, limited to zero-temperature statics of simple crystals. It has been widely recognized that the most practical coupled methods exhibit large errors on the atomistic/continuum interface (which are often attributed to spurious forces called “ghost forces”). There are only few existi...

The Volume of Two-Qubit States by Information Geometry

Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled states with fixed purity. We show that the usage of the classical Fisher metric on phase space probability representation of quantum states gives the same qu...

Applications of Lobachevsky Geometry to the Relativistic Two-Body Problem

In this talk we consider the geometrical basis for the reduction of the relativistic 2-body problem, much like the non-relativistic one, to describing the motion of an effective particle in an external field. It is shown that this possibility is deeply related with the Lobachevsky geometry. The concept of relativistic reduced mass and effective relativistic particle is discussed using this geom...

Random walks in noninteger dimension

One can define a random walk on a hypercubic lattice in a space of integer dimension D. For such a process formulas can be derived that express the probability of certain events, such as the chance of returning to the origin after a given number of time steps. These formulas are physically meaningful for integer values of D. However, these formulas are unacceptable as probabilities when continu...