Related papers: The Quantum Reduced Action In Higher Dimensions
Using the framework of Nambu's generalised mechanics, we obtain a new description of constrained Hamiltonian dynamics, involving the introduction of another degree of freedom in phase space, and the necessity of defining the action integral…
The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an $N$-particle…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs…
Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB…
One can introduce so-called {\em Plain Mechanics} having an {\bf operator realization}. Then the set of one-dimension representations of this operator realization may be identified with the Classical Mechanics. Different irreducible…
The wave-particle duality and its probabilistic interpretation are at the heart of quantum mechanics. Here we show that, in some standard contexts like the double slit experiment, a deterministic interpretation can be provided. This…
Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized…
When an observable is measured on an evolving coherent quantum system twice, the first measurement generally alters the statistics of the second one, which is known as measurement back-action. We introduce, and push to its theoretical and…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…
Quantum Action Principle formulated earlier is used as a ground for a probabilistic interpretation of one-particle relativistic quantum mechanics. In this new approach the probability "flows" in the Minkowsky space being dependent on an…
This article is devoted to the study of lower semicontinuous solutions of Hamilton-Jacobi equations with convex Hamiltonians in a gradient variable. Such Hamiltonians appear in the optimal control theory. We present a necessary and…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic…
Quantum state diffusion shows how stochastic interaction with the environment may cause localisation of the wave-function, and thereby demonstrates that quantum mechanics need not invoke a separate axiom of measurement to explain the…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
We discuss a systematic construction of dimensionless quantum-mechanical equations. The process reduces the number of independent model parameters to a minimum and, at the same time, provides the natural units of length, energy, etc. in a…
Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their…
Refined are the known descriptions of particle behavior with the help of Hamilton function in the phase space of coordinates and their multiple derivatives. This entails existing of circumstances when at closer distances gravitational…