Related papers: Constrained quantum dynamics
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
The constrained structure of the duality invariant form of Maxwell theory is considered in the Hamiltonian formulation of Dirac as well as from the symplectic viewpoint. Compared to the former the latter approach is found to be more…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
One of critical components of Loop Quantum Gravity (LQG) and Cosmology (LQC) -- Thiemann regularization procedure is non-unique. Different choices of particular prescriptions lead to models which differ in both mathematical structure and…
We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Constrained molecular dynamics(CoMD) model, previously introduced for nuclear dynamics, has been extended to the atomic structure and collision calculations. Quantum effects corresponding to the Pauli and Heisenberg principle are enforced…
It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…
We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
Semiclassical mechanics of systems with first-class constraints is developed. Starting from the quantum theory, one investigates such objects as semiclassical states and observables, semiclassical inner product, semiclassical gauge…
We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the…
The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In…
Numerical methods for the 1-D Dirac equation based on operator splitting and on the quantum lattice Boltzmann (QLB) schemes are reviewed. It is shown that these discretizations fall within the class of quantum walks, i.e. discrete maps for…
We propose a new description of dynamics of autonomous mechanical systems which includes the momentum-velocity relation. This description is formulated as a variational principle of virtual action more complete than the Hamilton Principle.…
The Dirac method of canonical quantization of theories with second class constraints has to be modified if the constraints depend on time explicitly. A solution of the problem was given by Gitman and Tyutin. In the present work we propose…