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Keywords
(8)
Anderson Localization
High Temperature
Hyperbolic Plane
Low Temperature
Random Environment
Sigma Model
Statistical Mechanics
Random Walk
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QuasiDiffusion in a 3D Supersymmetric Hyperbolic Sigma Model
QuasiDiffusion in a 3D Supersymmetric Hyperbolic Sigma Model,10.1007/s0022001011175,Communications in Mathematical Physics,Margherita Disertori,To
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QuasiDiffusion in a 3D Supersymmetric Hyperbolic Sigma Model
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Citations: 9
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Margherita Disertori
,
Tom Spencer
,
Martin R. Zirnbauer
We study a lattice field model which qualitatively reflects the phenomenon of
Anderson localization
and delocalization for real symmetric band matrices. In this
statistical mechanics
model, the field takes values in a supermanifold based on the hyperbolic plane. Correlations in this model may be described in terms of a
random walk
in a highly correlated random environment. We prove that in three or more dimensions the model has a ‘diffusive’ phase at low temperatures. Localization is expected at high temperatures. Our analysis uses estimates on nonuniformly elliptic Green’s functions and a family of Ward identities coming from internal supersymmetry.
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 300, no. 2, pp. 435486, 2010
DOI:
10.1007/s0022001011175
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Citation Context
(3)
...They proved a quasidiffusive estimate for the twopoint correlation functions in a three dimensional supersymmetric hyperbolic nonlinear sigma model at low temperatures [
13
]...
László Erdos
,
et al.
Quantum Diffusion and Eigenfunction Delocalization in a Random Band Ma...
...Finally, we mention a recent and exciting development: in [
17
], the existence of a delocalized phase in three dimensions is proven for a supersymmetric model which is interpreted as a toy version of the Anderson model...
W. De Roeck
,
et al.
Diffusion of a Massive Quantum Particle Coupled to a QuasiFree Therma...
...We refer to [
2
] for a historical introduction and motivations...
...More recently the existence of a ‘diffusive’ phase at low temperatures (β large) has been proved for the H (22) model in three or more dimensions, see [
2
]...
...Moreover, for a one dimensional chain we recover localization for all values of β. Localization is also expected in 2D (see [
2
] Sect...
...The techniques employed in this work to prove localization are quite different from the ones used in [
2
] to prove extended states...
...4 and Appendix C in [
2
] for an introduction to supersymmetric Ward identities...
...Remark. Note that e t D ε e t corresponds to the symbol Dβ,� introduced in [
2
] Eq. (1.1)...
...where A is the generator of a random walk in a random environment in [
2
]E q. (1.1)...
...For technical reasons the above representation is more convenient when we want to prove diffusion as in [
2
] while the other is more practical when we study localization (except in the proof of Theorem 2 where we will go back to the “diffusion” representation for a while)...
...where ξ , η are odd elements and z, xy are even elements of a real Grassmann algebra (see [
2
] for more details)...
...Note that the change of coordinates (1.12) is different from the one introduced in Eq. (2.7) of [
2
]...
...There the covariance of the gaussian fields in the action is (1.7) (“diffusion” representation) and the measure (see (2.12) in [
2
] ) has a � e −t factor...
...We can go back from (1.12) to (2.7) of [
2
] by performing the change of coordinates: s → se +t ,ψ → ψe +t , ¯ ψ → ¯ ψe +t ...
...We refer to [
2
] for a more detailed exposition...
...Normalization and choice of ε j . By internal supersymmetry (see [
2
] Sect...
M. Disertori
,
et al.
Anderson Localization for a Supersymmetric Sigma Model
References
(19)
Random walk with reinforcement
(
Citations: 33
)
D Coppersmith
,
P. Diaconis
Published in 1987.
Supersymmetry in disorder and chaos
(
Citations: 508
)
K. Efetov
Published in 1997.
Asymptotic behavior of edgereinforced random walks
(
Citations: 11
)
Franz Merkl
,
Silke W. W. Rolles
Journal:
Annals of Probability  ANN PROBAB
, vol. 35, no. 2007, pp. 115140, 2007
Negative moments of characteristic polynomials of random matrices: Ingham–Siegel integral as an alternative to Hubbard–Stratonovich transformation
(
Citations: 24
)
Yan V. Fyodorov
Journal:
Nuclear Physics B  NUCL PHYS B
, vol. 621, no. 3, pp. 643674, 2002
Symmetry Classes of Disordered Fermions
(
Citations: 13
)
P. Heinzner
,
A. Huckleberry
,
M. R. Zirnbauer
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 257, no. 3, pp. 725771, 2005
Sort by:
Citations
(9)
Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model
(
Citations: 2
)
László Erdos
,
Antti Knowles
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 303, no. 2, pp. 509554, 2011
Diffusion of a Massive Quantum Particle Coupled to a QuasiFree Thermal Medium
(
Citations: 2
)
W. De Roeck
,
J. Fröhlich
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 303, no. 3, pp. 613707, 2011
Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model
(
Citations: 4
)
Laszlo Erdos
,
Antti Knowles
Published in 2010.
Universality of Wigner random matrices: a Survey of Recent Results
(
Citations: 2
)
Laszlo Erdýos
Published in 2010.
Anderson Localization for a Supersymmetric Sigma Model
M. Disertori
,
T. Spencer
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 300, no. 3, pp. 659671, 2010