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Holographic interpretation of renormalization group approach to singular perturbations in nonlinear differential equations

Yu Nakayama
2013 Physical Review D  
We give a holographic explanation how the renormalization group approach to singular perturbations in non-linear differential equations proposed by Chen, Goldenfeld and Oono is indeed equivalent to a renormalization  ...  group method in quantum field theories proposed by Gell-Mann and Low via AdS/CFT correspondence.  ...  We would like to thank Z. Chacko for his beautiful lecture and related discussions which stimulated this study.  ... 
doi:10.1103/physrevd.88.105006 fatcat:ef73gfsn6jbbli7gmchoohvff4

Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory

Lin-Yuan Chen, Nigel Goldenfeld, Y. Oono
1996 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary layers with technically difficult asymptotic matching, and WKB analysis  ...  In contrast to conventional methods, the renormalization group approach requires neither ad hoc assumptions about the structure of perturbation series nor the use of asymptotic matching.  ...  We are pleased to acknowledge the contribution of Glenn Paquette, who participated in the early stages of the center manifold study.  ... 
doi:10.1103/physreve.54.376 pmid:9965081 fatcat:comjdyjyhzdlhcgm5k3tnlvhcy

Global Density Profile For Particle Non-Conserving One Dimensional Transport From Renormalization Group Flows

Sutapa Mukherji, Somendra M. Bhattacharjee
2019 Scientific Reports  
A renormalization group analysis is developed here by using the location and the width of the BL as the renormalization parameters.  ...  In the continuum limit, the average particle density across the system is described by a singular differential equation involving multiple scales which lead to the formation of boundary layers (BL) or  ...  Such an approach, in an order-by-order scheme for separate scales, ultimately leads to nonphysical divergences, which need to be handled by a renormalization group (RG) analysis.  ... 
doi:10.1038/s41598-019-42011-5 pmid:30952877 pmcid:PMC6451018 fatcat:f2qhjisrbzhtrlhu7ntkogue7q

Renormalization group analysis for an asymmetric simple exclusion process

Sutapa Mukherji
2017 Physical review. E  
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process.  ...  In addition, we show a nontrivial scaling of the boundary layer width with the system size close to specific phase boundaries.  ...  The utility of the renormalisation group approach in solving various singular perturbation problems has been further elaborated later in [10] .  ... 
doi:10.1103/physreve.95.032131 pmid:28415247 fatcat:mtlrz3ctlrb57mqjitaqo6hk4y

Global Density Profile for Asymmetric Simple Exclusion Process from Renormalization Group Flows [article]

Sutapa Mukherji, Somendra M. Bhattacharjee
2018 arXiv   pre-print
A renormalization group analysis is developed here by using the location and the width of the BL as the renormalization parameters.  ...  In the continuum limit, the average particle density across the system is described by a singular differential equation involving multiple scales which lead to the formation of boundary layers (BL) or  ...  A renormalization group analysis is developed here by using the location and the width of the BL as the renormalization parameters.  ... 
arXiv:1804.08958v1 fatcat:4gidcynfxrfdzmggv33zvg343y

Renormalization Group Theory for Global Asymptotic Analysis

Lin Yuan Chen, Nigel Goldenfeld, Y. Oono
1994 Physical Review Letters  
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion.  ...  The renormalized perturbation approach may be simpler to use than other approaches, because it does not require the use of asymptotic matching, and yields practically superior approximations.  ...  An example is a caricature of the Stokes-Oseen singular boundary layer problem, which describes the low Reynolds number viscous flow past a sphere of unit radius.  ... 
doi:10.1103/physrevlett.73.1311 pmid:10056761 fatcat:6k5vvjbzlfc4teb6zhawvu4l5y

Area law and real-space renormalization

Andrew J. Ferris
2013 Physical Review B  
Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those  ...  Numerical results from the tree-tensor network and tensor renormalization-group approaches for the 2D transverse-field Ising model and 3D classical Ising model, respectively, clearly demonstrate this effect  ...  Acknowledgements I would like to thank Guifre Vidal and David Poulin for discussions.  ... 
doi:10.1103/physrevb.87.125139 fatcat:35ytr4nsnfcsporhdn6tnsgy6y

Page 554 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
The renormalization group gives the transformation rules.  ...  The resulting approach to scaling in critical phenomena is reminiscent of the Richardson cascade in turbulence.  ... 

Page 469 of Mathematical Reviews Vol. , Issue 91A [page]

1991 Mathematical Reviews  
Summary: “A renormalization-group fixed point is found, cor- responding to chaotic mixing in the Rayleigh-Taylor instability problem.  ...  We formulate a non- linear boundary value problem for a blow domain with a partially unknown boundary.  ... 

Boundary quantum critical phenomena with entanglement renormalization

G. Evenbly, R. N. C. Pfeifer, V. Picó, S. Iblisdir, L. Tagliacozzo, I. P. McCulloch, G. Vidal
2010 Physical Review B  
We extend the formalism of entanglement renormalization to the study of boundary critical phenomena.  ...  We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions.  ...  As in Wilson's renormalization-group formulation of the Kondo problem, our construction produces, as a side result, an effective chain displaying explicit separation of energy scales.  ... 
doi:10.1103/physrevb.82.161107 fatcat:f2ckxz3sfnc6vpjxk3vvwgyrca

Holographic Renormalization with Machine learning [article]

Eric Howard
2018 arXiv   pre-print
Group (RG) apparatus, an efficient tool used to deal with scaling problems in effective field theories.  ...  We employ an information-theoretic approach in a deep learning setup by introducing an artificial neural network algorithm to map and identify new physical degrees of freedom.  ...  As a neural network extracts features from complex data, its mapping to the Renormalization group can help with identify features in complex quantum many-body problems.  ... 
arXiv:1803.11056v2 fatcat:s7aliw7vtnaprivmapcbopdw4a

Holographic renormalization with machine learning

Eric Howard
2020 Figshare  
As a neural network extracts features from complex data, its mapping to the Renormalization group can help with identify features in complex quantum many-body problems.  ...  DEEP LEARNING MAPPING MODEL OF RENORMALIZATION GROUP The first step of the Renormalization Group decreasing the resolution by changing the minimum length scale from a smaller scale to a larger one.  ... 
doi:10.6084/m9.figshare.12619067 fatcat:fkffc22zubaincnnnglznbpbqm

Page 6916 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
The generalization of this approach to other systems is discussed and open problems are proposed.  ...  Summary: “Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that the renormalization group has introduced in some  ... 

Metastable Reverse-Phase Droplets within Ordered Phases: Renormalization-Group Calculation of Field and Temperature Dependence of Limiting Size [article]

Ege Eren, A. Nihat Berker
2020 arXiv   pre-print
Metastable reverse-phase droplets are calculated by renormalization-group theory by evaluating the magnetization of a droplet under magnetic field, matching the boundary condition with the reverse phase  ...  The maximal metastable droplet size and the discontinuity across the droplet boundary are thus calculated as a function of field and temperature for the Ising model in three dimensions.  ...  On the other hand, renormalization-group calculations have been applied to finite-sized systems [3] .  ... 
arXiv:2003.01359v1 fatcat:uz3oha6c7rapfnxjt6gxcjeewe

Page 4638 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
The RG approach gives the reduced equation as an RG equation (this is called the reductive renormalization group approach).  ...  Summary: “After a gentle introduction to the Stiickelberg- Petermann style (i.e. field-theoretical) renormalization group (RG) theory, its application to the study of asymptotic behaviors of differential  ... 
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