Thermal correlation functions in CFT and factorization

We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in d dimensions in terms of the c-anomaly coefficient. By including α′ corrections to the black brane background, we reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula. When the dimensions satisfy ∆i = ∆j + ∆k, the thermal 3-point function satisfies a factorization property. We argue that in d > 2 factorization is a reflection of the semiclassical regime.

Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory

The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for classical and semiclassical stochastic oscillators in a natural and unified manner by using the eigenfunctions of the Koopman operator of the system. We show that the proposed definition gives appropriate values of the phase and amplitude for strongly stochastic limit-cycle oscillators, excitable systems undergoing noise-induced oscillations, and also for quantum limit-cycle oscillators in the semiclassical regime.

Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems

We study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale $$\hbar = N^{-1/3}$$ ħ = N - 1 / 3 in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for the k particle Husimi measure. Further estimates are derived to obtain the weak compactness of the Husimi measure, and in addition uniform estimates for the remainder terms in the hierarchy are derived in order to show that in the semiclassical regime the weak limit of the Husimi measure is exactly the solution of the Vlasov equation.

Confinement on ℝ3 × 𝕊1 and double-string collapse

We study confining strings in $$ \mathcal{N} $$ N = 1 supersymmetric SU(Nc) Yang-Mills theory in the semiclassical regime on ℝ1,2× 𝕊1. Static quarks are expected to be confined by double strings composed of two domain walls — which are lines in ℝ2 — rather than by a single flux tube. Each domain wall carries part of the quarks’ chromoelectric flux. We numerically study this mechanism and find that double-string confinement holds for strings of all N-alities, except for those between fundamental quarks. We show that, for Nc≥ 5, the two domain walls confining unit N-ality quarks attract and form non-BPS bound states, collapsing to a single flux line. We determine the N-ality dependence of the string tensions for 2 ≤ Nc≤ 10. Compared to known scaling laws, we find a weaker, almost flat N-ality dependence, which is qualitatively explained by the properties of BPS domain walls. We also quantitatively study the behavior of confining strings upon increasing the 𝕊1 size by including the effect of virtual “W-bosons” and show that the qualitative features of double-string confinement persist.

Computing quantum dynamics in the semiclassical regime

The semiclassically scaled time-dependent multi-particle Schrödinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This paper reviews and studies numerical approaches that are robust to the small semiclassical parameter. We present and analyse variationally evolving Gaussian wave packets, Hagedorn’s semiclassical wave packets, continuous superpositions of both thawed and frozen Gaussians, and Wigner function approaches to the direct computation of expectation values of observables. Making good use of classical mechanics is essential for all these approaches. The arising aspects of time integration and high-dimensional quadrature are also discussed.