1,724,152 research outputs found
Lagrangian dynamics for classical, Brownian and quantum mechanical particles
No full textIn the framework of Nelson’s stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton’s principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical‐like equations
Lagrange Lemma and the optimal control of diffusions II : nonlinear Lagrange functionals
No full textIn (Kosmol, 1991; Kosmol and Pavon, 1993) a new elementary approach to optimal control problems relying on the Lagrange lemma was described which appears to be technically, and conceptually, much simpler than existing methods, and, furthermore, provides a unified variational approach. In (Kosmol and Pavon, 1992) this method was further clarified and developed for linear Lagrangefunctionals. We devote this second paper to nonlinear Lagrangefunctionals. The power
of this approach is here clearly demonstrated. In particular, it is shown that the nonlinear Lagrange functional induced
by the value function of the problem is just one of the many functionals which may effectively be employed to solve
control problems, see Examples 1 and 2 in Section 3. Moreover, in our approach, we can deal in the same framework with problems with state constraints, or nonsmooth problems. Hence, the Lagrange functionals approach provides new tools to solve control problems which may be readily applied even when existing approaches fail
The Algebraic Riccati Inequality: Parametrization of Solutions, Tightest Local Frames and Generalized Feedback Matrices
No full textExtending on previous work by Faurre, Scherer and Pavon, a parametrization of the symmetric solutions of the algebraic Riccati inequality is established. This is then applied
to derive new results on tightest local frames, and on generalized feedback matrices that arise in stochastic realization theory
Quantum Schroedinger bridges
No full textElaborating on M. Pavon, J. Math. Phys. 40 (1999), 5565-5577, we develop a simplified version of a variational principle within Nelson stochastic mechan- ics that produces the von Neumann wave packet reduction after a position measurement. This stochastic control problem parallels, with a different kine- matics, the problem of the Schr ̈odinger bridge. This gives a profound meaning to what was observed by Schr ̈odinger in 1931 concerning Schr ̈odinger bridges: “Merkwu ̈rdige Analogien zur Quantenmechanik, die mir sehr des Hindenkens wert erscheinen”
On the well-posedness of multivariate spectrum approximation and convergence of high-resolution spectral estimators
No full textIn this paper, we establish the well-posedness of the generalized moment problems recently studied by Byrnes-Georgiou-Lindquist and coworkers, and by Ferrante-Pavon-Ramponi. We then apply these continuity results to prove almost sure convergence of a sequence of high-resolution spectral estimators indexed by the sample size
On the well-posedness of multivariate spectrum approximation and convergence of high-resolution spectral estimators
No full textIn this paper, we establish the well-posedness of the generalized moment problems recently studied by Byrnes-Georgiou-Lindquist and coworkers, and by Ferrante-Pavon-Ramponi. We then apply these continuity results to prove the almost sure convergence of a sequence of high-resolution spectral estimators indexed by the sample size
Stochastic mechanics and the Feynman integral
No full textThe Feynman integral is given a stochastic interpretation in the framework of Nelson’s stochastic mechanics employing a time-symmetric variant of Nelson’s kinematics recently developed by the author
Mægtige Middelalder: Martin Pavon - Kalundborg Vor Frue, bygningskunst og Hviderne
No full textI denne episode er jeg i Kalundborg. Her taler jeg med Martin Pavon, museumsinspektør på Museum Vestsjælland om den fantastiske Kalundborg Vor Frue kirke. Kirken er fra omkring år 1200, og den er en del af Hvideslægtens netværk af kirker i Midt- og Vestsjælland. I episoden fortæller Martin både om kirkens enestående konstruktion, og om Hviderne, og deres rolle i udformningen af kirken. Og så kan man se billeder af kirken på Mægtige Middelalders Instagram og Facebook profiler. Så lyt med, og bliv klogere på dette pragtfulde bygningsværk fra middelalderens Vestsjælland.<br/
Mægtige Middelalder: Martin Pavon - Kalundborg Vor Frue, bygningskunst og Hviderne
No full textI denne episode er jeg i Kalundborg. Her taler jeg med Martin Pavon, museumsinspektør på Museum Vestsjælland om den fantastiske Kalundborg Vor Frue kirke. Kirken er fra omkring år 1200, og den er en del af Hvideslægtens netværk af kirker i Midt- og Vestsjælland. I episoden fortæller Martin både om kirkens enestående konstruktion, og om Hviderne, og deres rolle i udformningen af kirken. Og så kan man se billeder af kirken på Mægtige Middelalders Instagram og Facebook profiler. Så lyt med, og bliv klogere på dette pragtfulde bygningsværk fra middelalderens Vestsjælland.<br/
Mægtige Middelalder: Martin Pavon - Kalundborg Vor Frue, bygningskunst og Hviderne
No full textI denne episode er jeg i Kalundborg. Her taler jeg med Martin Pavon, museumsinspektør på Museum Vestsjælland om den fantastiske Kalundborg Vor Frue kirke. Kirken er fra omkring år 1200, og den er en del af Hvideslægtens netværk af kirker i Midt- og Vestsjælland. I episoden fortæller Martin både om kirkens enestående konstruktion, og om Hviderne, og deres rolle i udformningen af kirken. Og så kan man se billeder af kirken på Mægtige Middelalders Instagram og Facebook profiler. Så lyt med, og bliv klogere på dette pragtfulde bygningsværk fra middelalderens Vestsjælland.<br/
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