Renormalization Group in Quantum Mechanics

Polónyi, János

doi:10.1006/aphy.1996.0133

Cited by 22 publications

(18 citation statements)

References 9 publications

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“…differs from (18) in that here, the inverse is that of a 2N m × 2N m matrixD(t , t ) as opposed to an operatorD(t, t ) acting on time-dependent functions. The physical origin of the difference is that while ( 18) contains the full information about the harmonic dynamics, the (25) encodes a "stroboscope physics", the dynamics at the time scales t j − t j−1 [67].…”

Section: Discrete Observation Timesmentioning

confidence: 99%

Macroscopic Limit of Quantum Systems

Polónyi

2021

Universe

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Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed for the average of an observable over a large set of independent microscopical systems, and the deterministic classical laws can be recovered in all practical purposes, owing to the largeness of Avogadro’s number. This result refers to the observed system without considering the measuring apparatus. The emergence of a classical trajectory is followed qualitatively in Wilson’s cloud chamber.

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Section: Discrete Observation Timesmentioning

confidence: 99%

Macroscopic Limit of Quantum Systems

Polónyi

2021

Universe

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“…differs from (10) that here the inverse is that of a 2N m × 2N m matrix D(t ℓ , t ℓ ′ ) as opposed to an operator D(t, t ′ ) acting on time-dependent functions. The physical origin of the difference is that while (10) contains the full information about the harmonic dynamics the (17) encodes a "stroboscope physics", the dynamics at the time scales t j − t j−1 [42].…”

Section: Discrete Observation Timesmentioning

confidence: 99%

Macroscopic limit of quantum systems

Polónyi¹

2021

Preprint

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The classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed and the deterministic classical laws can be recovered in all practical purposes owing to the largeness of Avogadro's number. The emergence of a classical trajectory is followed qualitatively in Wilson's cloud chamber.

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“…The Gaussian integration yields eq.8, which leads to continuous but nowhere differentiable trajectories in quantum mechanics for d = 1 [22], finite, cut-off independent discontinuities and non-trivial phase structure for d = 2 [12], and Dirac delta singularities in higher dimensions [23]. It is a complicated dynamical issue, whether smoothness prevails for certain observables in quantum field theory.…”

Section: Phase Structurementioning

confidence: 99%