SciPost Phys. 9, 079 (2020) ·
published 23 November 2020
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We study the quantum dynamics of Bose-Einstein condensates when the
scattering length is modulated periodically or quasi-periodically in time
within the Bogoliubov framework. For the periodically driven case, we consider
two protocols where the modulation is a square-wave or a sine-wave. In both
protocols for each fixed momentum, there are heating and non-heating phases,
and a phase boundary between them. The two phases are distinguished by whether
the number of excited particles grows exponentially or not. For the
quasi-periodically driven case, we again consider two protocols: the
square-wave quasi-periodicity, where the excitations are generated for almost
all parameters as an analog of the Fibonacci-type quasi-crystal; and the
sine-wave quasi-periodicity, where there is a finite measure parameter regime
for the non-heating phase. We also plot the analogs of the Hofstadter butterfly
for both protocols.
SciPost Phys. 8, 094 (2020) ·
published 26 June 2020
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The Sachdev-Ye-Kitaev model is an $N$-modes fermionic model with infinite
range random interactions. In this work, we study the thermal R\'enyi entropy
for a subsystem of the SYK model using the path-integral formalism in the
large-$N$ limit. The results are consistent with exact diagonalization [1] and
can be well approximated by thermal entropy with an effective temperature [2]
when subsystem size $M\leq N/2$. We also consider generalizations of the SYK
model with quadratic random hopping term or $U(1)$ charge conservation.
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