Related papers: Hamilton-Jacobi Method and Gravitation
A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of…
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.…
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic…
In this paper, we review the discrete Hamilton--Jacobi theory from a geometric point of view. In the discrete realm, the usual geometric interpretation of the Hamilton--Jacobi theory in terms of vector fields is not straightforward. Here,…
Quantum field theory in curved spacetime is a theory wherein matter is treated fully in accord with the principles of quantum field theory, but gravity is treated classically in accord with general relativity. It is not expected to be an…
With many Hamiltonians one can naturally associate a |Psi|^2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field…
In this paper we focus on energy flows in simple quantum systems. This is achieved by concentrating on the quantum Hamilton-Jacobi equation. We show how this equation appears in the standard quantum formalism in essentially three different…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
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…
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
Fully covariant wave equations predict the existence of a class of inertial-gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical fields, but, by conforming to general…
For a general mechanical system, it is shown that each solution of the Hamilton-Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is…
Beginning with a relativistic action principle for the irrotational flow of collisionless matter, we compute higher order corrections to the Zel'dovich approximation by deriving a nonlinear Hamilton-Jacobi equation for the velocity…
A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach…
We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasi-solvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasi-solvability of…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…
We do a critical review of the Faraday-Maxwell concept of classical field and of its quantization process. With the hindsight knowledge of the essentially quantum character of the interactions, we use a naive classical model of field, based…
We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total…