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SUMMARY:HECAP Seminar - The Simplest Linear Ramp with O(1) Thouless Time
DTSTART;VALUE=DATE-TIME:20250515T140000Z
DTEND;VALUE=DATE-TIME:20250515T150000Z
DTSTAMP;VALUE=DATE-TIME:20260518T221500Z
UID:indico-event-10999@ictp.it
DESCRIPTION:Abstract:\n\n	Black hole normal modes have intriguing connecti
 ons to logarithmic spectra\, and the spectral form factor (SFF) of E_n = l
 og n is the mod square of the Riemann zeta function (RZF). In this paper\,
  we first provide an analytic understanding of the dip-ramp-plateau struct
 ure of RZF and show that the ramp at \\beta =\\Re(s)=0 has a slope precise
 ly equal to 1. The s=1 pole of RZF can be viewed as due to a Hagedorn tran
 sition in this setting\, and Riemann's analytic continuation to Re(s)< 1 p
 rovides the quantum contribution to the truncated log n partition function
 . This perspective yields a precise definition of RZF as the ``full ramp a
 fter removal of the dip''\, and allows an unambiguous determination of the
  Thouless time. For black hole microstates\, the Thouless time is expected
  to be O(1)--remarkably\, the RZF also exhibits this behavior. To our know
 ledge\, this is the first black hole-inspired toy model that has a demonst
 rably O(1) Thouless time. In contrast\, it is O(log N) in the SYK model an
 d expected to be O(N^{#}) in supergravity fuzzballs. We trace the origins 
 of the ramp to a certain reflection property of the functional equation sa
 tisfied by RZF\, and suggest that it is a general feature of L-functions--
 we find evidence for ramps in large classes of L-functions. As an aside\, 
 we also provide an analytic determination of the slopes of (non-linear) ra
 mps that arise in power law spectra using Poisson resummation techniques.\
 n	To join via Zoom :https://zoom.us/j/91362325784\n	Meeting ID: 913 6232 5
 784\n	Passcode: 652019\n	 \n\n//indico.ictp.it/event/10999/
LOCATION:Hybrid Leonardo Building - Luigi Stasi Seminar Room and via Zoom
URL://indico.ictp.it/event/10999/
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