430,026 research outputs found
Effective potential analytic continuation calculations of real time quantum correlation functions: Asymmetric systems
We apply the effective potential analytic continuation (EPAC) method to
one-dimensional asymmetric potential systems to obtain the real time quantum
correlation functions at various temperatures. Comparing the EPAC results with
the exact results, we find that for an asymmetric anharmonic oscillator the
EPAC results are in very good agreement with the exact ones at low temperature,
while this agreement becomes worse as the temperature increases. We also show
that the EPAC calculation for a certain type of asymmetric potentials can be
reduced to that for the corresponding symmetric potentials.Comment: RevTeX4, 13 pages, 9 eps figure
The density function for the value-distribution of Lerch zeta-functions and its applications
The probabilistic study of the value-distribution of zeta-functions is one of
the modern topics in analytic number theory. In this paper, we study a
probability density function related to the value-distribution of Lerch
zeta-functions. We prove a limit theorem with an effective error term, and
moreover, we obtain an asymptotic formula on the number of zeros of Lerch
zeta-functions on the right side of the critical line by applying the density
function.Comment: 28 page
Direct Proof of Termination of the Kohn Algorithm in the Real-Analytic Case
In 1979 J.J. Kohn gave an indirect argument via the Diederich-Forn\ae ss
Theorem showing that finite D'Angelo type implies termination of the Kohn
algorithm for a pseudoconvex domain with real-analytic boundary. We give here a
direct argument for this same implication using the stratification coming from
Catlin's notion of a boundary system as well as algebraic geometry on the ring
of real-analytic functions. We also indicate how this argument could be used in
order to compute an effective lower bound for the subelliptic gain in the
-Neumann problem in terms of the D'Angelo type, the dimension of
the space, and the level of forms provided that an effective \L ojasiewicz
inequality can be proven in the real-analytic case and slightly more
information obtained about the behavior of the sheaves of multipliers in the
Kohn algorithm.Comment: 33 page
Eulerian Statistically Preserved Structures in Passive Scalar Advection
We analyze numerically the time-dependent linear operators that govern the
dynamics of Eulerian correlation functions of a decaying passive scalar
advected by a stationary, forced 2-dimensional Navier-Stokes turbulence. We
show how to naturally discuss the dynamics in terms of effective compact
operators that display Eulerian Statistically Preserved Structures which
determine the anomalous scaling of the correlation functions. In passing we
point out a bonus of the present approach, in providing analytic predictions
for the time-dependent correlation functions in decaying turbulent transport.Comment: 10 pages, 10 figures. Submitted to Phys. Rev.
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