Nearest-neighbor level spacings

Figure 1. The nearest neighbor level spacing distribution for various parameter of temperature a) zero temperature case b) (3 = 0.1 c) (3 = 0.01 ...

Abstract. Quantum chaos at finite-temperature is studied using a simple paradigm, two-dimensional coupled nonlinear oscillator. As an approach for the treatment of the finite-temperature a real-time finite-temperature field theory, thermofield dynamics, is used. It is found that increasing the temperature leads to a smooth transition from Poissonian to Gaussian distribution in nearest neighbor level spacing distribution. 

The nearest neighbor level spacings are defined as Si = -E)+i — Ei, where Ei are the energies of the unfolded levels, which are obtained by the following way The spectrum Ei is separated into smoothed average part and fluctuating parts. Then the number of levels below E is counted and the following staircase function is defined ... 

One of the main characteristics of the statistical properies of the spectra is the level spacing distribution (Eckhardt, 1988 Gutzwiller, 1990) function. In this work we calculate the nearest-neighbor levelspacing distribution (Eckhardt, 1988 Gutzwiller, 1990). 

Here y is the average and cr is the standard deviation of the Euclidean distances of the k nearest neighbors of each compound in the training set in the chemical descriptor space, and Z is an empirical parameter to control the significance level, with the default value of 0.5. If the distance from an external compound to its nearest neighbor in the training set is above Dc, we label its prediction unreliable. 

Figure 1. Distribution of spacings of nearest-neighbor vibrational energy levels of the vibrational states of Ar3 with A, symmetry, that of the ground vibrational state. The histogram shows the computed level spacings. The solid curve is that of a fitted Wigner distribution, and the dotted curve is that of a Poisson distribution. [Reprinted with permission from D. M. Leitner, R. S. Berry, and R. M. Whitnell,, /. Chem. Phys. 91, 3470 (1989). Copyright 1989, American Institute of Physics.]...

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