Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/9310109

Minimum Uncertainty, Coherence and Squeezing in Diffusion Processes, and Stochastic Quantization

S. De Martino, Silvio De Siena, Fabrizio Illuminati, Giuseppe Vitiello

Published Oct 18, 1993• 1 citation
arXivHTMLPDF

Abstract

We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
DOI
10.48550/arxiv.hep-th/9310109

Related papers

Minimum uncertainty and squeezing in diffusion processes and stochastic quantization

Salvatore DeMartino, Silvio DeSiena, Fabrizo Illuminati +1 more

We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states. 1

•May 1, 1994•0 citations

DIFFUSION PROCESSES AND COHERENT STATES

S. De Martino, Silvio De Siena, Fabrizio Illuminati

It is shown that uncertainty relations, as well as coherent and squeezed states, are structural properties of stochastic processes with Fokker-Planck dynamics. The quantum mechanical coherent and squeezed states are explicitly constructed via Nelson stochastic quantization. The method is applied to derive new minimum uncertainty states in time-dependent oscillator potentials. 1

•Jan 1, 1994•10 citations

DIFFUSION PROCESSES AND COHERENT STATES

SALVATORE DE MARTINO, SILVIO DE SIENA, GIUSEPPE VITIELLO +1 more

It is shown that uncertanity relations, as well as coherent and squeezed states, are structural properties of stochastic processes with Fokker–Planck dynamics. The quantum mechanical coherent and squeezed states are explicitly constructed via Nelson stochastic quantization. The method is applied to derive new minimum uncertainty states in time-dependent oscillator potentials.

arXiv:cond-mat/9407100•Modern Physics Letters B•Jul 10, 1994•8 citations

Position-Momentum Uncertainty Relations in Stochastic Mechanics

Diego de Falco, S. De Martino, Silvio De Siena

A simple inequality relating the root mean square deviations of position and osmotic velocity for a diffusion process is presented and, in the framework of Nelson's stochastic mechanics, is related to the Heisenberg position-momentum uncertainty relations.

Physical Review Letters•Jul 19, 1982•41 citations

Stochastic variational approach to minimum uncertainty states

Fabrizio Illuminati, Lorenza Viola

We introduce a new variational characterization of Gaussian diffusion processes as minimum uncertainty states. We then define a variational method constrained by kinematics of diffusions and Schrodinger dynamics to seek states of local minimum uncertainty for general non-harmonic potentials.

arXiv:hep-th/9501034•Journal of Physics A Mathematical and General•May 21, 1995•9 citations

Quantum Laws in Connection with Stochastic Processes

J. C. Aron

It is shown that, with suitable conventions, Schrödinger's equation can be deduced from the lows of stochastic diffusion: uncertainty relations, concrete meaning of mass-energy equivalence, minimal constants of time and length and vanishing of negative energy also appear resulting from the basic conventions. An extension to mechanics with spin is worked out, and a model of Dirac's fluied is elaborated. Stochastic assumptions also lead to the energy states and quantum numbers of the hydrogen atom. Suggestions are made on the physical interpretation of the model, on its relation to the wave-particle dualism, and on the meaning of quantized states.

Progress of Theoretical Physics•Apr 1, 1965•6 citations
It is shown that, with suitable conventions, Schrödinger's equation can be deduced from the lows of stochastic diffusion: uncertainty relations, concrete meaning of mass-energy equivalence, minimal constants of time and length and vanishing of negative energy also appear resulting from the basic conventions. An extension to mechanics with spin is worked out, and a model of Dirac's fluied is elaborated. Stochastic assumptions also lead to the energy states and quantum numbers of the hydrogen atom. Suggestions are made on the physical interpretation of the model, on its relation to the wave-particle dualism, and on the meaning of quantized states.