240 research outputs found
Classical limit of the quantum Zeno effect
The evolution of a quantum system subjected to infinitely many measurements
in a finite time interval is confined in a proper subspace of the Hilbert
space. This phenomenon is called "quantum Zeno effect": a particle under
intensive observation does not evolve. This effect is at variance with the
classical evolution, which obviously is not affected by any observations. By a
semiclassical analysis we will show that the quantum Zeno effect vanishes at
all orders, when the Planck constant tends to zero, and thus it is a purely
quantum phenomenon without classical analog, at the same level of tunneling.Comment: 10 pages, 2 figure
Mean-Field- and Classical Limit of Many-Body Schr\"odinger Dynamics for Bosons
We present a new proof of the convergence of the N-particle Schroedinger
dynamics for bosons towards the dynamics generated by the Hartree equation in
the mean-field limit. For a restricted class of two-body interactions, we
obtain convergence estimates uniform in the Planck constant , up to an
exponentially small remainder. For h=0, the classical dynamics in the
mean-field limit is given by the Vlasov equation.Comment: Latex 2e, 18 page
On the Convergence of the WKB Series for the Angular Momentum Operator
In this paper we prove a recent conjecture [Robnik M and Salasnich L 1997 J.
Phys. A: Math. Gen. 30 1719] about the convergence of the WKB series for the
angular momentum operator. We demonstrate that the WKB algorithm for the
angular momentum gives the exact quantization formula if all orders are summed.Comment: latex, 9 pages, no figures, to be published in Journal of Physics A:
Math. and Ge
Deterministic spin models with a glassy phase transition
We consider the infinite-range deterministic spin models with Hamiltonian
, where is the quantization of a
chaotic map of the torus. The mean field (TAP) equations are derived by summing
the high temperature expansion. They predict a glassy phase transition at the
critical temperature .Comment: 8 pages, no figures, RevTex forma
On a Watson-like Uniqueness Theorem and Gevrey Expansions
We present a maximal class of analytic functions, elements of which are in
one-to-one correspondence with their asymptotic expansions. In recent decades
it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.),
that the formal power series solutions of a wide range of systems of ordinary
(even non-linear) analytic differential equations are in fact the Gevrey
expansions for the regular solutions. Watson's uniqueness theorem belongs to
the foundations of this new theory. This paper contains a discussion of an
extension of Watson's uniqueness theorem for classes of functions which admit a
Gevrey expansion in angular regions of the complex plane with opening less than
or equal to (\frac \pi k,) where (k) is the order of the Gevrey expansion. We
present conditions which ensure uniqueness and which suggest an extension of
Watson's representation theorem. These results may be applied for solutions of
certain classes of differential equations to obtain the best accuracy estimate
for the deviation of a solution from a finite sum of the corresponding Gevrey
expansion.Comment: 18 pages, 4 figure
A map from 1d Quantum Field Theory to Quantum Chaos on a 2d Torus
Dynamics of a class of quantum field models on 1d lattice in Heisenberg
picture is mapped into a class of `quantum chaotic' one-body systems on
configurational 2d torus (or 2d lattice) in Schr\" odinger picture. Continuum
field limit of the former corresponds to quasi-classical limit of the latter.Comment: 4 pages in REVTeX, 1 eps-figure include
symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
Consider in , , the operator family . \ds
H_0= a^\ast_1a_1+... +a^\ast_da_d+d/2 is the quantum harmonic oscillator with
rational frequencies, a symmetric bounded potential, and a real
coupling constant. We show that if , being an explicitly
determined constant, the spectrum of is real and discrete. Moreover we
show that the operator \ds H(g)=a^\ast_1 a_1+a^\ast_2a_2+ig a^\ast_2a_1 has
real discrete spectrum but is not diagonalizable.Comment: 20 page
Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval
The upper bound for asymptotic behavior of the coefficients of expansion of
the evolution operator kernel in powers of the time interval \Dt was
obtained. It is found that for the nonpolynomial potentials the coefficients
may increase as . But increasing may be more slow if the contributions with
opposite signs cancel each other. Particularly, it is not excluded that for
number of the potentials the expansion is convergent. For the polynomial
potentials \Dt-expansion is certainly asymptotic one. The coefficients
increase in this case as , where is the order of
the polynom. It means that the point \Dt=0 is singular point of the kernel.Comment: 12 pp., LaTe
Resummation of Nonalternating Divergent Perturbative Expansions
A method for the resummation of nonalternating divergent perturbation series
is described. The procedure constitutes a generalization of the Borel-Pad\'{e}
method. Of crucial importance is a special integration contour in the complex
plane. Nonperturbative imaginary contributions can be inferred from the purely
real perturbative coefficients. A connection is drawn from the quantum field
theoretic problem of resummation to divergent perturbative expansions in other
areas of physics.Comment: 5 pages, LaTeX, 2 tables, 1 figure; discussion of the Carleman
criterion added; version to appear in Phys. Rev.
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