Related papers: Geometry and symmetries of multi-particle systems
Quantum statistical correlations and momentum distributions are calculated for a spherically symmetric, three-dimensionally expanding finite fireballs, for non-relativistic expansions applying plane-wave approximation. The new concepts of…
We illustrate how non-relativistic quantum mechanics may be recovered from a dynamical Weyl geometry on configuration space and an `ensemble' of trajectories (or `worlds'). The theory, which is free of a physical wavefunction, is presented…
We propose a formulation of quantum mechanics in three dimensions with spherical symmetry for a finite level system whose dynamics is not governed by a differential equation of motion. The wavefunction is written as an infinite sum in a…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
We present an equation-free dynamic renormalization approach to the computational study of coarse-grained, self-similar dynamic behavior in multidimensional particle systems. The approach is aimed at problems for which evolution equations…
The temporal evolution of quantum statistical properties of an interacting atom-radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes-Cummings model. To…
A generic aggregate forming system in two dimensions (2D) is studied using canonical ensemble constant temperature molecular dynamics simulation. The aggregates form due to the competition between short range attraction and long range…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited numerically. When the wave complex amplitudes are independent, with a gaussian distribution, the quasilinear approximation is found to always…
We introduce a topological quantum number -- coined dynamical topological order parameter (DTOP) -- that is dynamically defined in the real-time evolution of a quantum many-body system and represented by a momentum space winding number of…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
We present a relativistic quantum mechanics of a point mass with absolute thermodynamic time and temperature, combined to a single complex parameter of evolution. In this theory, the geometric time is introduced as one of space-time…
A single mechanism, endemic to the standard model of physics, is proposed to explain wavefunction collapse, classical motion, dissipation, equilibration, and the transition from pure quantum mechanics through open system decoherence to the…
In this work it is shown that there is an inherent nonlinear evolution in the dynamics of the so-called generalized coherent states. To show this, the immersion of a classical manifold into the Hilbert space of quantum mechanics is…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application…
A monitored quantum system undergoing a cyclic evolution of the parameters governing its Hamiltonian accumulates a geometric phase that depends on the quantum trajectory followed by the system on its evolution. The phase value will be…
The question that guides our discussion is how did the geometry and particles come into being. The present theory reveals primordial deeper structures underlying fundamental concepts of contemporary physics. We begin with a drastic revision…