Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.

American Journal of PhysicsMay 23, 20165 citations

Perturbation Theories Based on the Density Matrix Renormalization Group

Sheng Guo

Jan 1, 20180 citations

Renormalization Group Theory

U. Köbler, A. Hoser

Springer series in materials scienceNov 6, 200911 citations

Boundary entropy under ambient RG flow in the AdS/BCFT model

Yoshiki Sato

We discuss the change of the boundary entropy under an ambient renormalization group flow. We use conformal perturbation theory to calculate the change of the boundary entropy for $d$ -dimensional BCFTs between two nearby fixed points. We also use the ${\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}$ model to calculate the boundary entropy. We show that the boundary entropy can increase under the ambient renormalization group flow both in conformal perturbation theory and the ${\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}$ model. In a special case, the change of the boundary entropy in the ${\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}$ model reduces to that of the conformal perturbation theory.We discuss the change of the boundary entropy under an ambient renormalization group flow. We use conformal perturbation theory to calculate the change of the boundary entropy for $d$-dimensional BCFTs between two nearby fixed points. We also use the ${\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}$ model to calculate the boundary entropy. We show that the boundary entropy can increase under the ambient renormalization group flow both in conformal perturbation theory and the ${\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}$ model. In a special case, the change of the boundary entropy in the ${\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}$ model reduces to that of the conformal perturbation theory.

arXiv:2004.04929Physical review. D/Physical review. D.Jun 2, 202015 citations

We discuss the change of the boundary entropy under an ambient renormalization group flow. We use conformal perturbation theory to calculate the change of the boundary entropy for

d

-dimensional BCFTs between two nearby fixed points. We also use the

{\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}

model to calculate the boundary entropy. We show that the boundary entropy can increase under the ambient renormalization group flow both in conformal perturbation theory and the

{\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}

model. In a special case, the change of the boundary entropy in the

{\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}

model reduces to that of the conformal perturbation theory.