TY - JOUR

T1 - Quantum quench across a holographic critical point

AU - Basu, Pallab

AU - Das, Sumit R.

PY - 2012

Y1 - 2012

N2 - 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 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* which is later than the time when (m c 2 - m 2) or J hits zero. In the critical region, t*, 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.

AB - 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 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* which is later than the time when (m c 2 - m 2) or J hits zero. In the critical region, t*, 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.

KW - AdS-CFT Correspondence

KW - Black Holes in String Theory

KW - Holography and condensed matter physics (AdS/CMT)

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U2 - 10.1007/JHEP01(2012)103

DO - 10.1007/JHEP01(2012)103

M3 - Article

AN - SCOPUS:84863393530

SN - 1126-6708

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 1

M1 - 103

ER -