Workshop on Computational Hadron Physics Hadron Physics I
![Workshop on Computational Hadron Physics, Hadron Physics I 3 Topical Workshop, Cyprus, September 14 Workshop on Computational Hadron Physics, Hadron Physics I 3 Topical Workshop, Cyprus, September 14](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-1.jpg)
![Anderson localization in 3 D E>Ecr (mobility edge) IPR is small Anderson localization in 3 D E>Ecr (mobility edge) IPR is small](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-2.jpg)
![Anderson localization in 3 D E<Ecr (mobility edge) IPR is large Anderson localization in 3 D E<Ecr (mobility edge) IPR is large](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-3.jpg)
![Eigenmodes localization is characterized by IPR B. Kramer, A. Mac. Kinnon (1993); C. Gattringer Eigenmodes localization is characterized by IPR B. Kramer, A. Mac. Kinnon (1993); C. Gattringer](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-4.jpg)
![IPR EXAMPLES IPR EXAMPLES](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-5.jpg)
![Scalars fundamental representation (j=1/2) SU(2) lattice gluodynamics Scalars fundamental representation (j=1/2) SU(2) lattice gluodynamics](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-6.jpg)
![Scalars (j=1/2) SCALING is constant in physical units Scalars (j=1/2) SCALING is constant in physical units](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-7.jpg)
![Removing center vortices we get zero string tension and zero quark condensate P. de Removing center vortices we get zero string tension and zero quark condensate P. de](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-8.jpg)
![IPR for full and vortex removed gauge field configurations for SU(2) lattice gluodynamics (fundamental IPR for full and vortex removed gauge field configurations for SU(2) lattice gluodynamics (fundamental](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-9.jpg)
![IPR for large enough l is small ? mobility edge? IPR for large enough l is small ? mobility edge?](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-10.jpg)
![Visualization of localization Time slices, intensity of color is proportional to IPR=52 IPR=1. 9 Visualization of localization Time slices, intensity of color is proportional to IPR=52 IPR=1. 9](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-11.jpg)
![Fermions overlap Dirac operator, SU(2) gluodynamics Overlap computer code was given to ITEP group Fermions overlap Dirac operator, SU(2) gluodynamics Overlap computer code was given to ITEP group](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-12.jpg)
![IPR for overlap lattice fermions before and after removing center vortices Confinement and chiral IPR for overlap lattice fermions before and after removing center vortices Confinement and chiral](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-13.jpg)
![IPR for various lattice spacings something happens at 150 Mev<l<200 Mev for all lattice IPR for various lattice spacings something happens at 150 Mev<l<200 Mev for all lattice](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-14.jpg)
![Localization volume IPR vs lattice spacing, V=const Localization volume IPR vs lattice spacing, V=const](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-15.jpg)
![Time slices for IPR=5. 13 chirality=-1 IPR=1. 45 chirality=0 Time slices for IPR=5. 13 chirality=-1 IPR=1. 45 chirality=0](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-16.jpg)
![Localization properties of overlap fermions and scalars (fundamental representation, j=1/2) are qualitatively (not quantitatively) Localization properties of overlap fermions and scalars (fundamental representation, j=1/2) are qualitatively (not quantitatively)](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-17.jpg)
![Scalars adjoint (j=1) and j=3/2 representation SU(2) lattice gluodynamics Scalars adjoint (j=1) and j=3/2 representation SU(2) lattice gluodynamics](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-18.jpg)
![fundamental adjoint Adjoint localization volume d=2? No! Additional analysis (hep-lat/0504008) show that adjoint localization fundamental adjoint Adjoint localization volume d=2? No! Additional analysis (hep-lat/0504008) show that adjoint localization](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-19.jpg)
![j=3/2 representation Or very strong localization (d=0) or localization volume very fast shrinks to j=3/2 representation Or very strong localization (d=0) or localization volume very fast shrinks to](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-20.jpg)
![Low dimensional structures in lattice gluodynamics 1. I. Horvath et al. hep-lat/0410046, heplat/0308029, Phys. Low dimensional structures in lattice gluodynamics 1. I. Horvath et al. hep-lat/0410046, heplat/0308029, Phys.](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-21.jpg)
![Summary 1. Localization of eigenfunctions of the Laplacian and Dirac operator is a manifestation Summary 1. Localization of eigenfunctions of the Laplacian and Dirac operator is a manifestation](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-22.jpg)
![Appendix Appendix](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-23.jpg)
![Removing center vortices Confinement and chiral condensate disappears after removing center vortices (P. de Removing center vortices Confinement and chiral condensate disappears after removing center vortices (P. de](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-24.jpg)
![Quark condensate Banks-Casher (1980) Result is in agreement with S. J. Hands and M. Quark condensate Banks-Casher (1980) Result is in agreement with S. J. Hands and M.](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-25.jpg)
![The action of monopoles and center vortices is singular, they exist due to energy-entropy The action of monopoles and center vortices is singular, they exist due to energy-entropy](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-26.jpg)
![Length of IR monopole cluster scales, Length of IR monopole cluster scales,](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-27.jpg)
![Monopoles have fine tuned action density: Monopoles have fine tuned action density:](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-28.jpg)
![P-VORTEX density, Area/(6*V 4), scales: P-VORTEX density, Area/(6*V 4), scales:](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-29.jpg)
![Minimal 3 D Volumes bounded by P-vortices scale Minimal 3 D Volumes bounded by P-vortices scale](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-30.jpg)
![P-VORTEX has UV divergent action density: (S-Svac)=Const. /a 2 In lattice units P-VORTEX has UV divergent action density: (S-Svac)=Const. /a 2 In lattice units](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-31.jpg)
![Monopoles belong to surfaces (center vortices). Surfaces are bounds of minimal 3 d volumes Monopoles belong to surfaces (center vortices). Surfaces are bounds of minimal 3 d volumes](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-32.jpg)
- Slides: 32
![Workshop on Computational Hadron Physics Hadron Physics I 3 Topical Workshop Cyprus September 14 Workshop on Computational Hadron Physics, Hadron Physics I 3 Topical Workshop, Cyprus, September 14](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-1.jpg)
Workshop on Computational Hadron Physics, Hadron Physics I 3 Topical Workshop, Cyprus, September 14 -17, 2005 Localization of the scalar and fermionic eigenmodes and confinement J. Greensite, F. V. Gubarev, A. V. Kovalenko, S. M. Morozov, S. Olejnik, MIP, S. V. Syritsyn, V. I. Zakharov hep-lat/0505016, hep-lat/0504008
![Anderson localization in 3 D EEcr mobility edge IPR is small Anderson localization in 3 D E>Ecr (mobility edge) IPR is small](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-2.jpg)
Anderson localization in 3 D E>Ecr (mobility edge) IPR is small
![Anderson localization in 3 D EEcr mobility edge IPR is large Anderson localization in 3 D E<Ecr (mobility edge) IPR is large](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-3.jpg)
Anderson localization in 3 D E<Ecr (mobility edge) IPR is large
![Eigenmodes localization is characterized by IPR B Kramer A Mac Kinnon 1993 C Gattringer Eigenmodes localization is characterized by IPR B. Kramer, A. Mac. Kinnon (1993); C. Gattringer](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-4.jpg)
Eigenmodes localization is characterized by IPR B. Kramer, A. Mac. Kinnon (1993); C. Gattringer et al. (2001); T. Kovacs (2003); C. Aubin et al. [MILC Collaboration] (2004), J. Greensite et al. (2005) F. Bruckmann, E. -M. Ilgenfritz (2005) (Solid state physics, lattice fermions and bosons). Talks at Lattice 2005: N. Cundy, T. De Grand, C. Gattringer, J. Greensite, J. Hetrick, I. Horvath, Y. Koma, S. Solbrig, B. Svetitsky, S. Syritsyn, M. I. P. By definition the inverse participation ratio (IPR) is:
![IPR EXAMPLES IPR EXAMPLES](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-5.jpg)
IPR EXAMPLES
![Scalars fundamental representation j12 SU2 lattice gluodynamics Scalars fundamental representation (j=1/2) SU(2) lattice gluodynamics](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-6.jpg)
Scalars fundamental representation (j=1/2) SU(2) lattice gluodynamics
![Scalars j12 SCALING is constant in physical units Scalars (j=1/2) SCALING is constant in physical units](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-7.jpg)
Scalars (j=1/2) SCALING is constant in physical units
![Removing center vortices we get zero string tension and zero quark condensate P de Removing center vortices we get zero string tension and zero quark condensate P. de](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-8.jpg)
Removing center vortices we get zero string tension and zero quark condensate P. de Forcrand M. D'Elia, Phys. Rev. Lett. 82 (1999) 4582 Z(2) gauge fixing
![IPR for full and vortex removed gauge field configurations for SU2 lattice gluodynamics fundamental IPR for full and vortex removed gauge field configurations for SU(2) lattice gluodynamics (fundamental](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-9.jpg)
IPR for full and vortex removed gauge field configurations for SU(2) lattice gluodynamics (fundamental Laplasian, j=1/2) Confinement is similar to Anderson localization?
![IPR for large enough l is small mobility edge IPR for large enough l is small ? mobility edge?](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-10.jpg)
IPR for large enough l is small ? mobility edge?
![Visualization of localization Time slices intensity of color is proportional to IPR52 IPR1 9 Visualization of localization Time slices, intensity of color is proportional to IPR=52 IPR=1. 9](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-11.jpg)
Visualization of localization Time slices, intensity of color is proportional to IPR=52 IPR=1. 9
![Fermions overlap Dirac operator SU2 gluodynamics Overlap computer code was given to ITEP group Fermions overlap Dirac operator, SU(2) gluodynamics Overlap computer code was given to ITEP group](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-12.jpg)
Fermions overlap Dirac operator, SU(2) gluodynamics Overlap computer code was given to ITEP group by G. Schierholz and T. Streuer
![IPR for overlap lattice fermions before and after removing center vortices Confinement and chiral IPR for overlap lattice fermions before and after removing center vortices Confinement and chiral](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-13.jpg)
IPR for overlap lattice fermions before and after removing center vortices Confinement and chiral condensate disappears after removing center vortices (P. de Forcrand M. d’Ellia (1999); J. Gattnar et al. (2005), what happens with localization?
![IPR for various lattice spacings something happens at 150 Mevl200 Mev for all lattice IPR for various lattice spacings something happens at 150 Mev<l<200 Mev for all lattice](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-14.jpg)
IPR for various lattice spacings something happens at 150 Mev<l<200 Mev for all lattice spacings
![Localization volume IPR vs lattice spacing Vconst Localization volume IPR vs lattice spacing, V=const](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-15.jpg)
Localization volume IPR vs lattice spacing, V=const
![Time slices for IPR5 13 chirality1 IPR1 45 chirality0 Time slices for IPR=5. 13 chirality=-1 IPR=1. 45 chirality=0](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-16.jpg)
Time slices for IPR=5. 13 chirality=-1 IPR=1. 45 chirality=0
![Localization properties of overlap fermions and scalars fundamental representation j12 are qualitatively not quantitatively Localization properties of overlap fermions and scalars (fundamental representation, j=1/2) are qualitatively (not quantitatively)](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-17.jpg)
Localization properties of overlap fermions and scalars (fundamental representation, j=1/2) are qualitatively (not quantitatively) similar
![Scalars adjoint j1 and j32 representation SU2 lattice gluodynamics Scalars adjoint (j=1) and j=3/2 representation SU(2) lattice gluodynamics](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-18.jpg)
Scalars adjoint (j=1) and j=3/2 representation SU(2) lattice gluodynamics
![fundamental adjoint Adjoint localization volume d2 No Additional analysis heplat0504008 show that adjoint localization fundamental adjoint Adjoint localization volume d=2? No! Additional analysis (hep-lat/0504008) show that adjoint localization](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-19.jpg)
fundamental adjoint Adjoint localization volume d=2? No! Additional analysis (hep-lat/0504008) show that adjoint localization volume is 4 d, but shrinks to zero in the continuum limit
![j32 representation Or very strong localization d0 or localization volume very fast shrinks to j=3/2 representation Or very strong localization (d=0) or localization volume very fast shrinks to](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-20.jpg)
j=3/2 representation Or very strong localization (d=0) or localization volume very fast shrinks to zero when a t 0
![Low dimensional structures in lattice gluodynamics 1 I Horvath et al heplat0410046 heplat0308029 Phys Low dimensional structures in lattice gluodynamics 1. I. Horvath et al. hep-lat/0410046, heplat/0308029, Phys.](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-21.jpg)
Low dimensional structures in lattice gluodynamics 1. I. Horvath et al. hep-lat/0410046, heplat/0308029, Phys. Rev. D 68: 114505, 2003 2. MILC collaboration hep-lat/0410024
![Summary 1 Localization of eigenfunctions of the Laplacian and Dirac operator is a manifestation Summary 1. Localization of eigenfunctions of the Laplacian and Dirac operator is a manifestation](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-22.jpg)
Summary 1. Localization of eigenfunctions of the Laplacian and Dirac operator is a manifestation of the possible existence of low dimentional objects in the QCD vacuum. 2. The density of the states is in physical units, while the localization volume of the modes tends to zero in physical units “Fine tuning phenomenon” hep-lat/0505016.
![Appendix Appendix](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-23.jpg)
Appendix
![Removing center vortices Confinement and chiral condensate disappears after removing center vortices P de Removing center vortices Confinement and chiral condensate disappears after removing center vortices (P. de](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-24.jpg)
Removing center vortices Confinement and chiral condensate disappears after removing center vortices (P. de Forcrand M. d’Ellia (1999); J. Gattnar et al. (2005), what happens with localization? Topological charge disappears
![Quark condensate BanksCasher 1980 Result is in agreement with S J Hands and M Quark condensate Banks-Casher (1980) Result is in agreement with S. J. Hands and M.](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-25.jpg)
Quark condensate Banks-Casher (1980) Result is in agreement with S. J. Hands and M. Teper (1990), (Wilson fermions)
![The action of monopoles and center vortices is singular they exist due to energyentropy The action of monopoles and center vortices is singular, they exist due to energy-entropy](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-26.jpg)
The action of monopoles and center vortices is singular, they exist due to energy-entropy balance (the entropy of lines and surfaces is also singular) Monopoles Center vortices 3 D volumes
![Length of IR monopole cluster scales Length of IR monopole cluster scales,](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-27.jpg)
Length of IR monopole cluster scales,
![Monopoles have fine tuned action density Monopoles have fine tuned action density:](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-28.jpg)
Monopoles have fine tuned action density:
![PVORTEX density Area6V 4 scales P-VORTEX density, Area/(6*V 4), scales:](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-29.jpg)
P-VORTEX density, Area/(6*V 4), scales:
![Minimal 3 D Volumes bounded by Pvortices scale Minimal 3 D Volumes bounded by P-vortices scale](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-30.jpg)
Minimal 3 D Volumes bounded by P-vortices scale
![PVORTEX has UV divergent action density SSvacConst a 2 In lattice units P-VORTEX has UV divergent action density: (S-Svac)=Const. /a 2 In lattice units](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-31.jpg)
P-VORTEX has UV divergent action density: (S-Svac)=Const. /a 2 In lattice units
![Monopoles belong to surfaces center vortices Surfaces are bounds of minimal 3 d volumes Monopoles belong to surfaces (center vortices). Surfaces are bounds of minimal 3 d volumes](https://slidetodoc.com/presentation_image/57f90a9948bc8453ce34fdf15a95e619/image-32.jpg)
Monopoles belong to surfaces (center vortices). Surfaces are bounds of minimal 3 d volumes in Z(2) Landau gauge 3 D analogue: monopole center vortex 3 d volume Minimal 3 d volume corresponds to minimal surface spanned on center vortex
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