6,415 research outputs found
Time Evolution after Double Trace Deformation
In this paper, we consider double trace deformation to single CFT, and
study time evolution after the deformation. The double trace deformation we
consider is nonlocal: composed of two local operators placed at separate
points. We study two types of local operators: one is usual local operator in
CFT, and the other is HKLL bulk local operator, which is still operator in CFT
but has properties as bulk local operator. We compute null energy and averaged
null energy in the bulk in both types of deformations. We confirmed that, with
the suitable choice of couplings, averaged null energies are negative. This
implies causal structure is modified in the bulk, from classical background. We
then calculate time evolution of entanglement entropy and entanglement Renyi
entropy after double trace deformation. We find both quantities are found to
show peculiar shockwave-like time evolution.Comment: 16 pages, 12 figures, references added, typos correcte
Butterflies from Information Metric
We study time evolution of distance between thermal states excited by local
operators, with different external couplings. We find that growth of the
distance implies growth of commutators of operators, signifying the local
excitations are scrambled. We confirm this growth of distance by holographic
computation, by evaluating volume of codimension 1 extremal volume surface. We
find that the distance increases exponentially as .
Our result implies that, in chaotic system, trajectories of excited thermal
states exhibit high sensitivity to perturbation to the Hamiltonian, and the
distance between them will be significant at the scrambling time. We also
confirm the decay of two point function of holographic Wilson loops on
thermofield double state.Comment: 10 pages, 3 figures, reference added, minor modification
Chiral phase transition in the linear sigma model within Hartree factorization in the Tsallis nonextensive statistics
We studied chiral phase transition in the linear sigma model within the
Tsallis nonextensive statistics in the case of small deviation from the
Boltzmann-Gibbs (BG) statistics. The statistics has two parameters: the
temperature and the entropic parameter . The normalized -expectation
value and the physical temperature \Tph were employed in this study. The
normalized -expectation value was expanded as a series of the value ,
where the absolute value is the measure of the deviation from the BG
statistics. We applied the Hartree factorization and the free particle
approximation, and obtained the equations for the condensate, the sigma mass,
and the pion mass. The physical temperature dependences of these quantities
were obtained numerically. We found following facts. The condensate at is
smaller than that at for . The sigma mass at is lighter than
that at for at low physical temperature, and the sigma mass at
is heavier than that at for at high physical temperature. The pion
mass at is heavier than that at for . The difference between the
pion masses at different values of is small for \Tph \le 200 MeV. That is
to say, the condensate and the sigma mass are affected by the Tsallis
nonextensive statistics of small , and the pion mass is also affected by
the statistics of small except for \Tph \le 200 MeV.Comment: 9 pages, 6 figure
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