M. V. Berry and N. L. Balazs. Evolution of Semiclassical Quantum States in Phase Space. J. Phys. A 12 (1979), 625--642. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Semi-classical Propagation on |log h|-Time-Scales - De Bièvre, Robert (2002) (Correct)
....or periodic orbits, for example) these estimates tend to break down on much shorter time scales that are only logarithmic in h. A good understanding of the quantum dynamics on as long a time scale as possible is important in quantum chaos, and has attracted considerable attention in this context [BB] [CC] OTH] TH] but not much is known rigorously. In the case of certain chaotic quantum maps, it was shown in [DB] and [BDB1] BDB2] that already on the relatively short logarithmic time scale, interesting phenomena occur. Here we want to address this same question in the context of a ....
Berry, M. V., Balasz N.L., Evolution of semi-classical quantum states in phase space, J. Phys. A 12, 625-642 (1979)
The Classical Limit of Quantum Theory - Werner (1995) (Correct)
....of functions on phase space. f) In the limit, i=h times a commutator should become the Poisson bracket of the limits. g) The quantum mechanical time evolution should converge (uniformly in finite time intervals) to the classical Hamiltonian evolution. h) Equilibrium states (canonical Gibbs states) and partition functions of quantum theory should converge to their classical counterparts. On the other hand, we can distinguish in the literature the following approaches to the classical limit, each of which naturally has a considerable overlap of results and applications with the ....
....wave functions do correspond to (a subclass of ) convergent states in our approach (see Section 4.8) Their limits are measures supported by Lagrangian manifolds in phase space, hence they have a curious intermediate position between point measures and general measures. B) Wigner functions. Wig,BB,Bru,BCSS,Ara] It is often claimed that quantum mechanics has an equivalent reformulation in terms of Wigner s phase space distribution functions. The classical limit could then be stated very simply in terms of these functions. However, the premise is only partly correct. Since the Wigner ....
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M.V. Berry and N.L. Balazs: "Evolution of semiclassical quantum states in phase space", J.Phys. A12(1979) 625--642
Classical Limit of the Matrix Elements on. . . - Ripamonti (1998) (Correct)
....W n;n k (A; OE) tend to ffi (A Gamma A 0 )e Gammaik DeltaOE in the sense of distributions, i.e. lim n 1; 0 n A W n;n k (A; OE) ffi (A Gamma A 0 )e Gammaik DeltaOE : 1.3) Formula 1. 3, for k = 0, has been proved in great generality by stationary phase arguments in [By] and [BB]; however the complete mathematical details for the general assertion 1.1 have been so far obtained (see [R] only when H is the harmonic oscillator, by proving directly 1.3 in the Bargmann representation. The proof has been subsequently simplified in [DBR] using the anti Wick quantization, always ....
M.V.Berry e N.L.Balazs, Evolution of semiclassical quantum states in phase space, J. Phys. A 12 (1979), 625-642.
Quantum Maps As Privileged Semiclassical Chaotic Models - Voros (Correct)
....Such issues can be wholly addressed within the framework of quantum maps U with integer time steps T . Various indications exist that if the classical system has a Lyapunov exponent 0, then the quantum corrections to U sc in eq. 3) of order h 2 or higher) may grow with time like e t [12, 13]. A critical time could then appear as early as the log time or Ehrenfest time T = Gamma1 log( h Gamma1 ) However, rigorous semiclassical results only consist of upper bounds (not actual estimates) for the growth of those quantum corrections [13] On the contrary, some long time ....
M.V. Berry and N.L. Balazs, Evolution of semiclassical quantum states in phase space, J. Phys. A 12, 625--642 (1979).
A Scaling Theory of Bifurcations in the Symmetric Weak-Noise.. - Maier, Stein (1996) (4 citations) (Correct)
....all points (y; p y ) at constant x is obtained by intersecting the Lagrangian manifold with the hyperplane x = const, the manifold itself becomes increasingly whorled with each passage through a focus. The formation of convolutions in Lagrangian manifolds was first considered by Berry and Balazs [5] (in a time dependent context) and the progression in Fig. 6 resembles the figures in their paper. Geometrically, the linear to cubic transition at each successive focus corresponds to the creation of a fold [12] One can fit the shape of the manifold near the l th focus, i.e. near (x; y; p y ) ....
M. V. Berry and N. L. Balazs. Evolution of Semiclassical Quantum States in Phase Space. J. Phys. A 12 (1979), 625--642.
A Scaling Theory of Bifurcations in the - Symmetric Weak-Noise Escape (Correct)
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M. V. Berry and N. L. Balazs. Evolution of Semiclassical Quantum States in Phase Space. J. Phys. A 12 (1979), 625--642.
Geometric Properties Of Eigenfunctions - Jakobson, Nadirashvili, Toth (Correct)
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N. Balacz and M. Berry. Evolution of semiclassical quantum states in phase space. J. Phys. A 12(5)(1979), 625-642.
A Scaling Theory of Bifurcations in the Symmetric Weak-Noise.. - Maier, Stein (1996) (4 citations) (Correct)
No context found.
M. V. Berry and N. L. Balazs. Evolution of Semiclassical Quantum States in Phase Space. J. Phys. A 12 (1979), 625--642.
Stochastic Solution to Quantum Dynamics - John, Wilson (1994) (Correct)
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Berry, M. V.; and Balazs, N. L.: Evolution of Semiclassical Quantum States in Phase Space. J. Phys. A: Math. Gen., vol. 12, no. 5, 1979, pp. 625--642.
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