Built on

L. Leviandier, M. Lombardi, R. Jost and J. P. Pique, “Fourier Transform: A Tool to Measure Statistical Level Properties in Very Complex Spectra,” Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
S. Sachdev and J. Ye, “Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet,” Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
J. J. M. Verbaarschot and I. Zahed, “Spectral density of the QCD Dirac operator near zero virtuality,” Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
E. Brezin, S. Hikami and A. Zee, “Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem,” Nucl. Phys. B 464
1996
Earlier work this paper cites.
E. Brézin and S. Hikami, “Spectral form factor in a random matrix theory,” Phys. Rev. E 55
1997
Earlier work this paper cites.
J. K. Erickson, G. W. Semenoff and K. Zarembo, “Wilson loops in N=4 supersymmetric Yang-Mills theory,” Nucl. Phys. B 582
2000
Earlier work this paper cites.
N. Drukker and D. J. Gross, “An Exact prediction of N=4 SUSYM theory for string theory,” J. Math. Phys. 42
2001
Earlier work this paper cites.
G. Akemann and P. H. Damgaard, “Wilson loops in N N =4 supersymmetric Yang-Mills theory from random matrix theory,” Phys. Lett. B 513
2002
Earlier work this paper cites.
M. L. Mehta, Random Matrices
2004
Earlier work this paper cites.
S. Kawamoto, T. Kuroki and A. Miwa, “Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence,” Phys. Rev. D 79
Original
2009
Earlier work this paper cites.

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2018

Spectral form factor and semi-circle law in the time direction

Okuyama, Kazumi

Understand

We study the time derivative of the connected part of spectral form factor, which we call the slope of ramp, in Gaussian matrix model.

We find a closed formula of the slope of ramp at finite $N$ with non-zero inverse temperature.
Using this exact result, we confirm numerically that the slope of ramp exhibits a semi-circle law as a function of time.

Built on

L. Leviandier, M. Lombardi, R. Jost and J. P. Pique, “Fourier Transform: A Tool to Measure Statistical Level Properties in Very Complex Spectra,” Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
S. Sachdev and J. Ye, “Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet,” Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
J. J. M. Verbaarschot and I. Zahed, “Spectral density of the QCD Dirac operator near zero virtuality,” Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
E. Brezin, S. Hikami and A. Zee, “Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem,” Nucl. Phys. B 464
1996
Earlier work this paper cites.
E. Brézin and S. Hikami, “Spectral form factor in a random matrix theory,” Phys. Rev. E 55
1997
Earlier work this paper cites.
J. K. Erickson, G. W. Semenoff and K. Zarembo, “Wilson loops in N=4 supersymmetric Yang-Mills theory,” Nucl. Phys. B 582
2000
Earlier work this paper cites.
N. Drukker and D. J. Gross, “An Exact prediction of N=4 SUSYM theory for string theory,” J. Math. Phys. 42
2001
Earlier work this paper cites.
G. Akemann and P. H. Damgaard, “Wilson loops in N N =4 supersymmetric Yang-Mills theory from random matrix theory,” Phys. Lett. B 513
2002
Earlier work this paper cites.
M. L. Mehta, Random Matrices
2004
Earlier work this paper cites.
S. Kawamoto, T. Kuroki and A. Miwa, “Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence,” Phys. Rev. D 79
Original
2009
Earlier work this paper cites.