Quantum Quench across a Holographic Critical Point

We study the problem of quantum quench across a critical point in a strongly coupled field theory using AdS/CFT techniques. The model involves a probe neutral scalar field with mass-squared

m^2

in the range

-9/4 < m^2 < -3/2

in a

AdS_4

charged black brane background. For a given brane background there is a critical mass-squared,

m_c^2

such that for

m^2 < m_c^2

the scalar field condenses. The theory is critical when

m^2 = m_c^2

and the source for the dual operator vanishes. At the critical point, the radial operator for the bulk linearized problem has a zero mode. We study the dynamics of the order parameter with a time dependent source

J(t)

, or a null-time dependent bulk mass

m(u)

across the critical point. We show that in the critical region the dynamics for an initially slow variation is dominated by the zero mode : this leads to an effective description in terms of a Landau-Ginsburg type dynamics with a {\em linear} time derivative. Starting with an adiabatic initial condition in the ordered phase, we find that the order parameter drops to zero at a time

t_\star

which is later than the time when

(m_c^2-m^2)

or

J

hits zero. In the critical region,

t_\star

, and the departure of the order parameter from its adiabatic value, scale with the rate of change, with exponents determined by static critical behavior. Numerical results for the order parameter are consistent with these expectations.

Note:

30 pages, 4 figures

field theory: scalar
critical phenomena
zero mode
AdS/CFT correspondence
boundary condition
membrane model
holography
black brane
quenching
duality

References(0)

Figures(4)

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