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Crossover-Time in Quantum Boson and Spin Systems (Paperback, Softcover reprint of the original 1st ed. 1994)
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Crossover-Time in Quantum Boson and Spin Systems (Paperback, Softcover reprint of the original 1st ed. 1994)
Series: Lecture Notes in Physics Monographs, 21
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Total price: R1,486
Discovery Miles: 14 860
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We consider quantum dynamical systems (in general, these could be
either Hamiltonian or dissipative, but in this review we shall be
interested only in quantum Hamiltonian systems) that have, at least
formally, a classical limit. This means, in particular, that each
time-dependent quantum-mechanical expectation value X (t) has as i
cl Ii -+ 0 a limit Xi(t) -+ x1 )(t) of the corresponding classical
sys- tem. Quantum-mechanical considerations include an additional
di- mensionless parameter f = iiiconst. connected with the Planck
constant Ii. Even in the quasiclassical region where f~ 1, the dy-
namics of the quantum and classicalfunctions Xi(t) and XiCcl)(t)
will be different, in general, and quantum dynamics for expectation
val- ues may coincide with classical dynamics only for some finite
time. This characteristic time-scale, TIi., could depend on several
factors which will be discussed below, including: choice of
expectation val- ues, initial state, physical parameters and so on.
Thus, the problem arises in this connection: How to estimate the
characteristic time- scale TIi. of the validity of the
quasiclassical approximation and how to measure it in an
experiment? For rather simple integrable quan- tum systems in the
stable regions of motion of their corresponding classical phase
space, this time-scale T" usually is of order (see, for example,
[2]) const TIi. = p,li , (1.1) Q where p, is the dimensionless
parameter of nonlinearity (discussed below) and a is a constant of
the order of unity.
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