Related papers: Quantum Potential and Symmetries in Extended Phase…
In a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schr\"odinger quantum mechanics by an…
The composition of the quantum potential and its role in the breakdown of classical symplectic symmetry in quantum mechanics is investigated. General expressions are derived for the quantum potential in both configuration space and momentum…
We suggest an extension of the Hilbert Phase Space formalism, which appears to be naturally suited for application to the dissipative (open) quantum systems, such as those described by the non-stationary (time-dependent) Hamiltonians…
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…
We introduce a numerical method to simulate nonlinear open quantum dynamics of a particle in situations where its state undergoes significant expansion in phase space while generating small quantum features at the phase-space Planck scale.…
The three-dimensional potential equation, motivated by representations of quantum mechanics, is investigated in four different scenarios: (i) In the usual Euclidean space $\mathbb{E}_{3}$ where the potential is singular but invariant under…
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\log\rho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum…
The talk is devoted to the "extended phase space" approach to Quantum Geometrodynamics. The premises that have led to the formulation of this approach are briefly reviewed, namely, non-trivial topology of the Universe which implies the…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
We use the quantum potential approach to analyse the quantum cosmological model of the universe. The quantum potential arises from exact solutions of the full Wheeler-De Witt equation.
Using the symplectic tomography map, both for the probability distributions in classical phase space and for the Wigner functions of its quantum counterpart, we discuss a notion of Lyapunov exponent for quantum dynamics. Because the…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
It is known that the Schroedinger equation may be derived from a hydrodynamic model in which the Lagrangian position coordinates of a continuum of particles represent the quantum state. Using Routh\s method of ignorable coordinates it is…
A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential,…
The standard formulation of Quantum Mechanics violates locality of interactions and the action reaction principle. An alternative formulation in an extended phase space could preserve both principles, but Bell's theorems show that a…