Inverse kinetic theory for quantum hydrodynamic equations

@article{Tessarotto2007InverseKT,
  title={Inverse kinetic theory for quantum hydrodynamic equations},
  author={Massimo Tessarotto and Marco Ellero and Piero Nicolini},
  journal={Physical Review A},
  year={2007},
  volume={75},
  pages={012105}
}
We propose a solution for the inverse kinetic theory for quantum hydrodynamic equations associated to the non-relativistic Schr\"{o}dinger equation. It is shown that an inverse kinetic equation of the form of the Vlasov equation can be non-uniquely determined under suitable mathematical prescriptions. 
Quantum theory of extended particle dynamics in the presence of EM radiation-reaction
In this paper a trajectory-based relativistic quantum wave equation is established for extended charged spinless particles subject to the action of the electromagnetic (EM) radiation-reaction (RR)Expand
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart ofExpand
Hamiltonian Structure of the Schrödinger Classical Dynamical System
The connection between quantum mechanics and classical statistical mechanics has motivated in the past the representation of the Schrödinger quantum-wave equation in terms of “projections” onto theExpand
Mathematical properties of the Navier-Stokes dynamical system for incompressible Newtonian fluids
The connection between fluid dynamics and classical statistical mechanics has motivated in the past mathematical investigations of the incompressible Navier–Stokes (NS) equations (INSE) by means ofExpand
Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity
TLDR
The CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical) g-quantization, and the quantum state ψ is proven to fulfill generalized Heisenberg inequalities. Expand
An exact pressure evolution equation for the incompressible Navier-Stokes equations
In this paper the issue of the determination of the fluid pressure in incompressible fluids is addressed, with particular reference to the search of algorithms which permit to advance in time theExpand
The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of theExpand
Microscopic statistical description of incompressible Navier-Stokes granular fluids
Abstract.Based on the recently established Master kinetic equation and related Master constant H-theorem which describe the statistical behavior of the Boltzmann-Sinai classical dynamical system forExpand
The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system
In this investigation, exact particular realizations are sought for the microscopic statistical description which is associated with the classical dynamical system (CDS) formed by N identical smoothExpand
Entropic force, noncommutative gravity, and ungravity
After recalling the basic concepts of gravity as an emergent phenomenon, we analyze the recent derivation of Newton's law in terms of entropic force proposed by Verlinde. By reviewing some points ofExpand
...
1
2
...

References

SHOWING 1-10 OF 45 REFERENCES
Hydrodynamic equations for mixed quantum states. I. General formulation
Quantum-mechanical hydrodynamic equations are considered for mixed quantum states, and the corresponding equations for pure quantum states are derived as a particular case. A generalization of theExpand
The quantum hydrodynamic model for semiconductors in thermal equilibrium
Abstract. The thermal equilibrium states of the quantum hydrodynamic model are analyzed. We show existence of solutions, perform the classical limit and investigate the uniqueness of the solutions.Expand
Closure conditions for classical and quantum moment hierarchies in the small-temperature limit
Abstract We analyze closure conditions in the small initial temperature limit for classical and quantum mechanical moment hierarchies of corresponding collisionless kinetic equations. Euler equationsExpand
Hydrodynamic equations for mixed quantum states. II. Coupled electronic states
A hydrodynamic approach is developed to describe nonadiabatic nuclear dynamics. We derive a hierarchy of hydrodynamic equations which are equivalent to the exact quantum Liouville equation forExpand
Navier-Stokes Analog of Quantum Mechanics
Bohm's formulation of quantum mechanics as a modified set of Hamilton-Jacobi equations is rewritten as a quantum-mechanical Navier-Stokes equation.
Quantum hydrodynamics, Wigner transforms, the classical limit
We analyse the classical limit of the quantum hydrodynamic equations as the Planck constant tends to zero. The equations have the form of an Euler system with a constant pressure and a dispersiveExpand
Quantum dynamics for dissipative systems: A hydrodynamic perspective
This paper explores the hydrodynamic description of quantum densities evolving under the effects of dissipation. For illustration, we refer to analytical solutions for a harmonic system and MarkovianExpand
On the quantum correction for thermodynamic equilibrium
The probability of a configuration is given in classical theory by the Boltzmann formula exp [— V/hT] where V is the potential energy of this configuration. For high temperatures this of course alsoExpand
Inequivalence between the Schrödinger equation and the Madelung hydrodynamic equations.
  • Wallstrom
  • Physics, Medicine
  • Physical review. A, Atomic, molecular, and optical physics
  • 1994
TLDR
This paper proves that this is incorrect: to recover the Schroedinger equation, one must add by hand a quantization condition, as in the old quantum theory. Expand
Foundations of quantum mechanics: non-relativistic theory
The objective of this paper is to axiomatically derive quantum mechanics from three basic axioms. In this paper, the Schrodinger equation for a characteristic function is first obtained and from itExpand
...
1
2
3
4
5
...