## 8 Citations

### Stochastic Variational Method for Viscous Hydrodynamics

- PhysicsPhysics
- 2022

In this short review, we focus on some of the subjects, related to J. Cleymans’ pioneering contribution of statistical approaches to the particle production process in heavy-ion collisions. We…

### Analytic continuation of stochastic mechanics

- MathematicsJournal of Mathematical Physics
- 2022

We study a (relativistic) Wiener process on a complexified (pseudo-)Riemannian manifold. Using Nelson’s stochastic quantization procedure, we derive three equivalent descriptions for this problem. If…

### Viscous control of minimum uncertainty state in hydrodynamics

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

A minimum uncertainty state for position and momentum of a fluid element is obtained. We consider a general fluid described by the Navier–Stokes–Korteweg (NSK) equation, which reproduces the…

### Viscous control of minimum uncertainty state

- Physics
- 2021

A minimum uncertainty state for position and momentum is obtained in quantum viscous hydrodynamics which is defined through the Navier-Stokes-Korteweg (NSK) equation. This state is the generalization…

### Poisson bracket operator

- Physics, MathematicsPhysical Review A
- 2021

We introduce the Poisson bracket operator which is an alternative quantum counterpart of the Poisson bracket. This operator is defined using the operator derivative formulated in quantum analysis and…

### Uncertainty Relations in Hydrodynamics

- PhysicsWater
- 2020

The qualitative behaviors of uncertainty relations in hydrodynamics are numerically studied for fluids with low Reynolds numbers in 1+1 dimensional system. We first give a review for the formulation…

### Maupertuis-Hamilton least action principle in the space of variational parameters for Schrödinger dynamics; A dual time-dependent variational principle

- MathematicsJournal of Physics Communications
- 2020

Time-dependent variational principle (TDVP) provides powerful methods in solving the time-dependent Schröinger equation. As such Kan developed a TDVP (Kan 1981 Phys. Rev. A 24, 2831) and found that…

### Variational formulation of compressible hydrodynamics in curved spacetime and symmetry of stress tensor

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The…

## References

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- Physics
- 1993

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### Variational formulation of compressible hydrodynamics in curved spacetime and symmetry of stress tensor

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The…

### Derivation of the Schrodinger equation from Newtonian mechanics

- Physics, Mathematics
- 1966

We examine the hypothesis that every particle of mass $m$ is subject to a Brownian motion with diffusion coefficient $\frac{\ensuremath{\hbar}}{2m}$ and no friction. The influence of an external…

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- Mathematics
- 1985

We present the main results of a variational calculus for Markovian stochastic processes which allows us to characterize the dynamics of probabilistic systems by extremal properties for some…

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- Physics
- 1952

By re-expressing the generalized SchrOdinger equation in its coordinate represenration in terms of amplitude and phase of the state vector, a quantum-mechanical change of a system can be made to…