Related papers: Structure of Multi-Anyon Wavefunctions
The Born rule, which is one of foundational axioms of quantum theory, states that the probability of obtain outcome $a$ for the quantum state $|\psi\rangle$ is determined by $P(a)=|\langle a|\psi\rangle|^{2}$. Despite its great success in…
Bosonic end perturbative calculations for quantum mechanical anyon systems require a regularization. I regularize by adding a specific $\delta$-function potential to the Hamiltonian. The reliability of this regularization procedure is…
We investigate the survival of symmetries in a relativistic system of two mutually interacting bosons coupled with an external field, when this field is "strongly" translation invariant in some directions and additionally remains unchanged…
The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these…
We study the well-posedness of the Hamiltonian of a system of two anyons in the magnetic gauge. We identify all the possible quadratic forms realizing such an operator for non-interacting anyons and prove their closedness and boundedness…
Solitary wave and soliton solutions of nonlinear equations are well known for physicists. A soliton is a solitary wave with some outstanding features which make it reasonable to be studied seriously in nonlinear systems. In fact most of the…
Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or a single…
We analyse the available data on the polarized asymmetries $A_1$ for proton, neutron and deuteron targets. We use a homogeneous and updated set of unpolarized structure functions to derive $g_1$ from $A_1$, and we accurately correct for the…
Accelerating electrons are known to radiate electromagnetic waves, a property that is central to the concept of many devices, from antennas to synchrotrons. While the electrodynamics of accelerating charged particles is well understood, the…
A general type of localized excitations, folded solitary waves and foldons, are defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicated ways and possess quite rich…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
The possibility of consistency between the basic quantum principles and reduction (wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for…
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional…
Matter wave interferometry is becoming an increasingly important technique in quantum metrology. However, unlike its photonic counterpart, this technique relies on the interference of particles possessing a non-zero rest mass and an…
We analyse the properties of wave functions $\psi(x,t;y,s)$ that depend at once on two time-position vectors $(x,t)$ and $(y,s)$ with different time entries $t\neq{s}$. In particular, we prove that the existence of such wave functions is…
According to Huygens' principle, all points on a wave front act as secondary sources emitting spherical waves, and the envelope of these spherical waves forms a new wave front. In the mathematical formulation of Huygens' principle, the…
Complete analysis of quantum wave functions of linear systems in an arbitrary number of dimensions is given. It is shown how one can construct a complete set of stationary quantum states of an arbitrary linear system from purely classical…
Some first principles that, we believe, could serve as foundation for quantum theory of extended particles are formulated. It is also shown that in the point-like particles limit the non-relativistic quantum mechanics can be restored. As an…
Similarities between quantum systems and analogous systems for classical waves have been used to great effect in the physics community, be it to gain an intuition for quantum systems or to anticipate novel phenomena in classical waves. This…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…