RIKEN-OIST mini Workshop 2019


July 5th (Fri.)

8:45 - 9:00 Registration
9:00 - 10:30  Lecture 1 - Y. Sekino (RIKEN)
"Application of operator product expansion to interacting Bose gas in 1+1 dimensions"
  (10 min break)
10:40 - 12:10  Lecture 2 - Y. Sekino (RIKEN)
"Application of operator product expansion to interacting Bose gas in 1+1 dimensions"
  (Lunch: 12:10- 13:30)
13:30 - 14:30 Lecture 3 - S. Hikami (OIST)
"Intersection Theory from Random Supermatrices for Riemann and Klein Surfaces"
  (10 min break)
14:40 - 15:10 (25+5) Talk 1 - H. Shimada (OIST)
"Exact computation of OPE in a interacting QFT with space/time anisotropy"
15:10 - 15:40 (25+5) Talk 2 - A. Mukherjee (OIST)
"Quantum out-of-equilibrium cosmology and Bound on Quantum Chaos for GUE"
15:40 - 18:00 Free discussion
18:30 - Dinner

July 6th (Sat.)

9:00 - 10:30  Lecture 4 - T. Furusawa (TIT)
"Dualities in 2+1 dimensions"
  (10 min break)
10:40 - 12:10 Lecture 5 - T. Furusawa (TIT)
"Dualities in 2+1 dimensions"
  (10 min break)
12:20 - 12:50 (25+5) Talk 3 - W. Li (OIST)
"Closed-form expression for cross-channel conformal blocks near the lightcone"
  (Lunch: 12:50- 14:00)
14:00 -  Free discussion


Invited Lecture

  • Yuta Sekino (RIKEN ):"Application of operator product expansion to interacting Bose gas in 1+1 dimensions"
     When quantum particles interact with each via an interaction potential with large scattering length, behaviors of the system is constrained by a series of relations called universal relations [1,2]. These universal relations include behaviors of correlation functions at high energy and momentum as well as the adiabatic relation, which connects the derivative of the energy with respect to the scattering length to the local pair correlation. In particular, high-energy momentum behaviors of correlation functions can be systematically derived by the operator product expansion (OPE) in quantum field theory framework [2], and these behaviors are effectively determined by few-body physics. In this lecture, we review the universal properties of resonantly interacting systems and present the application of OPE to a one-dimensional system near a resonance.
     The contents in the lecture are as follows:
    1. 1. Two-body scattering problem and universal properties near a resonance
    2. 2. Derivations of universal behaviors for static correlation functions in first quantization framework [3,4]
    3. 3. How to describe a resonant system in quantum field theory framework
    4. 4. Derivation of universal behaviors for dynamic correlation functions by OPE [5]
    [1] S. Tan, Ann. Phys. (N.Y.) 323, 2952 (2008); 323, 2971 (2008); 323, 2987 (2008).
    [2] E. Braaten, in The BCS-BEC Crossover and the Unitary Fermi Gas, Lecture Note in Physics, edited by W. Zwerger (Springer, Berlin, 2012), Chap. 6.
    [3] M. Olshanii and V. Dunjko, Phys. Rev. Lett. 91, 090401 (2003).
    [4] Y. Sekino, S. Tan, and Y. Nishida, Phys. Rev. A 97, 013621 (2018).
    [5] Y. Sekino, PhD thesis.
  • Shinobu Hikami (OIST):"Intersection Theory from Random Supermatrices for Riemann and Klein Surfaces"
     The approach to the intersection theory of moduli space of Riemann surface from the random supermatrix theory is presented. The intersection numbers with boundaries are reconsidered. The intersection theory of Klein surfaces, which are generalization of Riemann surfaces to surfaces with boundaries or non-orientable surfaces, is discussed from a random supermatrix theory. The generalization of the moduli space of p-spin curve is considered for positive and negative integer numbers p from the super matrices. This is a joint work with Edouard Brezin.
  • Takuya Furusawa (TIT):"Dualities in 2+1 dimensions"
     In the last few years, many dualities in three dimensions are unearthed and intensively studied [1]. They are applied to many attractive subjects in condensed matter physics, such as the fractional quantum Hall state at half filling, deconfined criticality and surface states of strongly-correlated topological insulators. In this talk, we overview these recent developments in the three-dimensional dualities. We begin with reviewing the three-dimensional dualities, such as the particle-vortex dualities and the boson-fermion duality and derive a web of dualities from the boson-fermion duality, which includes the particle-vortex dualities [2,3]. Finally, we explain its application to the fractional quantum Hall states at the half filling [4].
    [1] T. Senthil, D. T. Son, C. Wang, C. Xu, arXiv:1810.05174 (2018).
    [2] A. Karch, D. Tong, Phys. Rev. X 6, 031043 (2016).
    [3] N. Seiberg, T. Senthil, C. Wang, E. Witten, Annals of Phys. 374, 395–433 (2016).
    [4] D. T. Son, Phys. Rev. X 5, 031027 (2015).

Oral Presentation

  • Hidehiko Shimada (OIST):"Exact computation of OPE in a interacting QFT with space/time anisotropy"
     I will discuss an interacting QFT with space/time anisotropy (z=2) where some OPE coefficients can be computed exactly. The talk is based on a work in preparation with Hirohiko Shimada(Tsuyama Tech. Coll.)
  • Arkaprava Mukherjee (OIST):"Quantum out-of-equilibrium cosmology and Bound on Quantum Chaos for GUE"
     The one to one correspondence between the conduction phenomena in electrical wires with impurity and the scattering events responsible for particle production during stochastic inflation and reheating implemented under a closed quantum mechanical system in early universe cosmology leads to derivation of quantum corrected version of the Fokker–Planck equation without dissipation and its fourth order corrected analytical solution for the probability distribution profile responsible for studying the dynamical features of the particle creation events in the stochastic inflation and reheating stage of the universe. The quantum corrected Fokker–Planck equation describe the particle creation phenomena for Dirac delta scatterer. Also Itô, Stratonovich prescription and the explicit role of finite temperature effective potential for solving the probability distribution profile suggest quantum nature of particle production event.
     Particle production phenomena can be used to describe the quantum description of randomness involved in the dynamics. The measure of the stochastic non-linearity (randomness or chaos) arising in the stochastic inflation and reheating epoch of the universe(Lyapunov Exponent) has been studied . Quantum chaos in a closed system have a more strong measure, Spectral Form Factor .From principles of Random Matrix Theory (RMT) with Gaussian Unitary Ensemble (GUE), we give a measure of quantum chaos by Spectral From Factor (SFF) appearing from the computation of two point Out of Time Order Correlation function (OTOC) expressed in terms of square of the commutator bracket of quantum operators which are separated in time scale. We also provide a bound on the measure of quantum chaos, −1/N (1 − 1/π) ≤ SFF ≤ 0 and 0 ≤ SFF ≤ 1/πN, valid for thermal systems with large and small number of degrees of freedom respectively. We have studied both the early and late behaviour of SFF(quantum chaos) to check the validity and applicability of our derived bound. Based on the appropriate physical arguments we give a precise mathematical derivation to establish this alternative strict bound of quantum chaos.
    1. https://link.springer.com/article/10.1140%2Fepjc%2Fs10052-019-6751-2
    2. https://link.springer.com/article/10.1007%2FJHEP05%282019%29149
  • Wenliang Li (OIST):"Closed-form expression for cross-channel conformal blocks near the lightcone"
     In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point functions of identical scalars. Based on the nonperturbative pole structure in spin of Lorentzian inversion, we propose a natural basis function for cross-channel conformal blocks. In this new basis, we find a closed-form expression for crossed conformal blocks in terms of the Kampe de Feriet function, which applies to intermediate states of arbitrary spin in general dimensions. The conserved-current blocks take a particularly simple form. It is straightforward to compute the Lorentzian inversion of our general expression. Our approach and results may shed light on the complete analytic expression of conformal blocks.