相关论文: Geometry of the high energy limit of differential …
This paper deals with systems of spherical particles immersed in a viscous fluid. Two aspects are studied, namely the controllability of such systems, with particular attention to the case of one active particle and either one or two…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…
We construct explicit examples of spontaneous energy generation and non-uniqueness for the compressible Euler system, with and without pressure, by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. The…
We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting)…
An explicit dynamical model for non relativistic quantum mechanics with an effective gravitational interaction is proposed, which, as being well defined, allows in principle for the evaluation of every physical quantity. Its non unitary…
A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to…
Finite, bound, many-body systems, where the interaction operator, $V=\sum v_{ij}$, is local and happens to strongly dominate the kinetic energy operator, $T=\sum t_i$, display a classical limit from diagonalizing $V$ alone, hence a clear…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
We consider a class of spin-type discrete systems and analyze their continuum limit as the lattice spacing goes to zero. Under standard coerciveness and growth assumptions together with an additional head-to-tail symmetry condition, we…
We have computed the low energy quantum states and low frequency dynamical susceptibility of complex quantum spin systems in the limit of strong interactions, obtaining exact results for system sizes enormously larger than accessible…
We consider Laplacians with non unitary twists acting on sections of flat vector bundles over compact hyperbolic surfaces. These non self-adjoint Laplacians have discrete spectrum inside a parabola in the complex plane. For representations…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators,…
Generic properties of the strength function (local density of states (LDOS)) and chaotic eigenstates are analyzed for isolated systems of interacting particles. Both random matrix models and dynamical systems are considered in the unique…
A unified treatment for the existence of free energy in several random energy models is presented. If the sequence of distributions associated with the particle systems obeys a large deviation principle, then the free energy exists almost…
The behavior of spin-1/2 particle in a weak static gravitational field is considered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysen transformation providing also the simple form for the momentum and spin polarization…
A novel method for deriving energy conditions in stable field theories is described. In a local classical theory with one spatial dimension, a local energy condition always exists. For a relativistic field theory, one obtains the dominant…
Can classical systems be described analytically at all orders in their interaction strength? For periodic and approximately periodic systems, the answer is yes, as we show in this work. Our analytical approach, which we call the…
Classical description of relativistic pointlike particle with intrinsic degrees of freedom such as isospin or colour is proposed. It is based on the Lagrangian of general form defined on the tangent bundle over a principal fibre bundle. It…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…