Related papers: Dynamic disquantization of Dirac equation
Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The…
As examples of models having interesting constraint structures, we derive a quantum mechanical model from the spatial freezing of a well known relativistic field theory - the chiral Schwinger model. We apply the Hamiltonian constraint…
The semiclassical kinetic theory of Dirac particles in the presence of external electromagnetic fields and global rotation is established. To provide the Hamiltonian formulation of Dirac particles a symplectic two-form which is a matrix in…
A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…
We present a novel approach of mapping dissipative particle dynamics (DPD) into classical molecular dynamics. By introducing the invariant volume element representing the swarm of atoms we show that the interactions between the emerging…
A model system for classical fluids out of equilibrium, referred to as DPD solid (Dissipative Particles Dynamics), is studied by analytical and simulation methods. The time evolution of a DPD particle is described by a fluctuating heat…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
A method to quantify robust performance for situations where structured parameter variations and initial state errors rather than extraneous disturbances are the main performance limiting factors is presented. The approach is based on the…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
The traditional approach to accelerator optics, based mainly on classical mechanics, is working excellently from the practical point of view. However, from the point of view of curiosity, as well as with a view to explore quantitatively the…
The diffeomorphism symmetry of general relativity leads in the canonical formulation to constraints, which encode the dynamics of the theory. These constraints satisfy a complicated algebra, known as Dirac's hypersurface deformation…
We reexamine the model of relativistic particle with higher-derivative term linear on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here.…
The kinetic equation used for the description of Dirac systems does not fully take into account two features that play an important role in the vicinity of the Dirac point: (i) the spin degree of freedom, in particular if the spin-flip…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
The dynamics of wave packets in a relativistic Dirac oscillator is compared to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the Dirac oscillator produces the entanglement of the spin with the orbital motion similar…
The weak convergence theorems of the one- and two-dimensional simple quantum walks, SQW$^{(d)}, d=1,2$, show a striking contrast to the classical counterparts, the simple random walks, SRW$^{(d)}$. The limit distributions have novel…
We show that in classical mechanics, as well as in nonrelativistic quantum mechanics the equation of the relative motion for a two-body bound system at rest can be replaced by individual dynamical equations of the same kind as the first…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
The relativistic ``no pair'' model of quantum electrodynamics uses the Dirac operator, D(A), for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A -- in the Coulomb gauge.…