arXiv subjects

Ho Tat Lam

Publications and source records attributed to Ho Tat Lam.

43 records · Page 3Linked to original sources

arXiv2018

Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK

We introduce a family of partially entangled thermal states in the SYK model that interpolates between the thermo-field double state and a pure (product) state. The states are prepared by a euclidean path integral describing the evolution over two euclidean time segments separated by a local scaling operator $\mathcal{O}$. We argue that the holographic dual of this class of states consists of two black holes with their interior regions connected via a domain wall, described by the worldline of a massive particle. We compute the size of the interior region and the entanglement entropy as a function of the scale dimension of $\mathcal{O}$ and the temperature of each black hole. We argue that the one-sided bulk reconstruction can access the interior region of the black hole.

hep-th↗

arXiv2018

Shockwave S-matrix from Schwarzian Quantum Mechanics

Schwarzian quantum mechanics describes the collective IR mode of the SYK model and captures key features of 2D black hole dynamics. Exact results for its correlation functions were obtained in JHEP {\bf 1708}, 136 (2017) [arXiv:1705.08408]. We compare these results with bulk gravity expectations. We find that the semi-classical limit of the out-of-time-order (OTO) four-point function exactly matches with the scattering amplitude obtained from the Dray-'t Hooft shockwave $\mathcal{S}$-matrix. We show that the two point function of heavy operators reduces to the semi-classical saddle-point of the Schwarzian action. We also explain a previously noted match between the OTO four point functions and 2D conformal blocks. Generalizations to higher-point functions, and applications, are discussed.

hep-th↗

arXiv2017

Conformal Basis, Optical Theorem, and the Bulk Point Singularity

We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$. Scattering amplitudes written in this basis have the same symmetry as $d$-dimensional conformal correlators. We translate the optical theorem, which is a direct consequence of unitarity, into the conformal basis. In the particular case of a tree-level exchange diagram, the optical theorem takes the form of a conformal block decomposition on the principal continuous series, with OPE coefficients being the three-point coupling written in the same basis. We further discuss the relation between the massless conformal basis and the bulk point singularity in AdS/CFT. Some three- and four-point amplitudes in (2+1) dimensions are explicitly computed in this basis to demonstrate these results.

hep-th↗

arXiv2016

Resumming the POPE at One Loop

The Pentagon Operator Product Expansion represents polygonal Wilson loops in planar $\mathcal{N}=4$ super Yang-Mills in terms of a series of flux tube excitations for finite coupling. We demonstrate how to re-sum this series at the one loop level for the hexagonal Wilson loop dual to the six-point MHV amplitude. By summing over a series of effective excitations we find expressions which integrate to logarithms and polylogarithms, reproducing the known one-loop result.

hep-th↗

arXiv2015

Symmetry Protected Topological Phases and Majorana Mode in One-dimensional Quantum Walk with Boundary

The topological phases in one-dimensional quantum walk can be classified by the coin parameters. By solving for the general exact solutions of bound states in one-dimensional quantum walk with boundaries specified by different coin parameters, we show that these bound states are Majorana modes with quasi-energy $E=0,π$. These modes are qualitatively different for different boundary conditions used. For two-boundary system with symmetric boundary conditions, the interaction energy between two Majorana bound states can be computed, as in the case of a finite wire. Suggestion of observing these modes are provided.

quant-ph↗

arXiv2015

Ramsauer effect in one-dimensional quantum walk with multiple defects

Experimental observations of quantum walks in one dimension have provided many exciting applications in quantum computing, while recent theoretical investigation of single phase defect in these system points towards interesting phenomena associated with bounds states. Here we obtain analytical solutions of quantum walk with a general quantum coin in one dimension with multiple defects, with new prediction on the condition for zero reflectance for scattering state, and the existence of an analogy to the Ramsauer effect for multiple defects. We also show the transition from the zero reflectance state to the bound state can provide a method for preparing the quantum walk in a bound state. Applications to systems similar to thin film optics are suggested.

quant-ph↗

arXiv2014

Optimization of Reliability of Network of Given Connectivity using Genetic Algorithm

Reliability is one of the important measures of how well the system meets its design objective, and mathematically is the probability that a system will perform satisfactorily for at least a given period of time. When the system is described by a connected network of N components (nodes) and their L connection (links), the reliability of the system becomes a difficult network design problem which solutions are of great practical interest in science and engineering. This paper discusses the numerical method of finding the most reliable network for a given N and L using genetic algorithm. For a given topology of the network, the reliability is numerically computed using adjacency matrix. For a search in the space of all possible topologies of the connected network with N nodes and L links, genetic operators such as mutation and crossover are applied to the adjacency matrix through a string representation. In the context of graphs, the mutation of strings in genetic algorithm corresponds to the rewiring of graphs, while crossover corresponds to the interchange of the sub-graphs. For small networks where the most reliable network can be found by exhaustive search, genetic algorithm is very efficient. For larger networks, our results not only demonstrate the efficiency of our algorithm, but also suggest that the most reliable network will have high symmetry.

physics.soc-ph↗