1, of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the 1930s. In particular, we show that the introduction of the KvN Hilbert space of complex and square integrable "wave functions" requires an enlargement of the set of the observables of ...
Statistical Mechanics Non-linear Dynamics Operator Theory Spectral Analysis Data-driven modeling 果断下单买了一本 DMD book [3]。原来量子力学的计算工具的确是普适的,不仅可以解决经典力学和流体力学的问题,还能解决更一般的数据分析问题。掐指一算,虽然我已经做了五年的计算玄学,但已经落后时代差不多十年了,所...
In this thesis we study several features of the operatorial approach to classical mechanics pionereed by Koopman and von Neumann (KvN) in the Thirties. In particular in the first part we study the role of the phases of the KvN states. We analyze, within the KvN theory, the two-slit ...
phases (in quantum and classical mechanics)In this paper we study the classical Hilbert space introduced by Koopman and von Neumann in their operatorial formulation of classical mechanics. In particular we show that the states of this Hilbert space do not spread, differently from what happens in ...
Classical mechanics (CM), like quantum mechanics (QM), can have an operatorial formulation. This was pioneered by Koopman and von Neumann (KvN) in the 1930s. They basically formalized, via the introduction of a classical Hilbert space, earlier work of Liouville who had shown that the ...
1, of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the 1930s. In particular, we show that the introduction of the KvN Hilbert space of complex and square integrable "wave functions" requires an enlargement of the set of the observables of ...
In this paper we study the classical Hilbert space introduced by Koopman and von Neumann in their operatorial formulation of classical mechanics. In particular we show that the states of this Hilbert space do not spread, differently from what happens in quantum mechanics. The role of the phases...
Koopman-von Neumann formalismQuantum mechanicsClassical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator algebra is introduced...
However, this problem is entirely overcome by resorting to von Neumann operators. Indeed, we show that the latter also allow for singular 未-like profiles of the Liouville density, thereby reproducing point particles in phase space.Francois Gay-Balmaz...