70,754 research outputs found
The Widom-Dyson constant for the gap probability in random matrix theory
In this paper we consider an asymptotic question in the theory of the
Gaussian Unitary Ensemble of random matrices. In the bulk scaling limit, the
probability that there are no eigenvalues in the interval (0,2s) is given by
P_s=det(I-K_s), where K_s is the trace-class operator with kernel
K_s(x,y)={sin(x-y)}/{\pi(x-y)} acting on L^2(0,2s). We are interested
particularly in the behavior of P_s as s tends to infinity...Comment: 31 pages, 4 figure
Localization of Macroscopic Object Induced by the Factorization of Internal Adiabatic Motion
To account for the phenomenon of quantum decoherence of a macroscopic object,
such as the localization and disappearance of interference, we invoke the
adiabatic quantum entanglement between its collective states(such as that of
the center-of-mass (C.M)) and its inner states based on our recent
investigation. Under the adiabatic limit that motion of C.M dose not excite the
transition of inner states, it is shown that the wave function of the
macroscopic object can be written as an entangled state with correlation
between adiabatic inner states and quasi-classical motion configurations of the
C.M. Since the adiabatic inner states are factorized with respect to each parts
composing the macroscopic object, this adiabatic separation can induce the
quantum decoherence. This observation thus provides us with a possible solution
to the Schroedinger cat paradoxComment: Revtex4,23 pages,1figur
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