scholarly journals Localization-delocalization transitions in a two-dimensional quantum percolation model: von Neumann entropy studies

2009 ◽  
Vol 80 (17) ◽  
Author(s):  
Longyan Gong ◽  
Peiqing Tong
Keyword(s):  
Percolation Model ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Von Neumann ◽  
Quantum Percolation

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

ENTANGLEMENT IN ONE-AND TWO-DIMENSIONAL ANDERSON MODELS WITH LONG-RANGE CORRELATED-DISORDER

2009 ◽  
Vol 07 (05) ◽  
pp. 959-968
Author(s):  
Z. Z. GUO ◽  
Z. G. XUAN ◽  
Y. S. ZHANG ◽  
XIAOWEI WU
Keyword(s):  
Long Range ◽  
Ground State ◽  
Two Dimensions ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Correlation Effects ◽  
Von Neumann ◽  
Range Correlation ◽  
The Difference ◽  
Anderson Models

The ground state entanglement in one- and two-dimensional Anderson models are studied with consideration of the long-range correlation effects and using the measures of concurrence and von Neumann entropy. We compare the effects of the long-range power-law correlation for the on-site energies on entanglement with the uncorrelated cases. We demonstrate the existence of the band structure of the entanglement. The intraband and interband jumping phenomena of the entanglement are also reported and explained to as the localization-delocalization transition of the system. We also demonstrated the difference between the results of one- and two-dimensions. Our results show that the correlation of the on-site energies increases the entanglement.

scholarly journals Islands in multiverse models

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Sergio E. Aguilar-Gutierrez ◽  
Aidan Chatwin-Davies ◽  
Thomas Hertog ◽  
Natalia Pinzani-Fokeeva ◽  
Brandon Robinson
Keyword(s):  
Saddle Point ◽  
Quantum Cosmology ◽  
Von Neumann Entropy ◽  
Coarse Grain ◽  
Two Dimensional ◽  
Dilaton Gravity ◽  
False Vacuum ◽  
Von Neumann ◽  
Eternal Inflation ◽  
Linear Dilaton

Abstract We consider multiverse models in two-dimensional linear dilaton-gravity theories as toy models of false vacuum eternal inflation. Coupling conformal matter we calculate the Von Neumann entropy of subregions. When these are sufficiently large we find that an island develops covering most of the rest of the multiverse, leading to a Page-like transition. This resonates with a description of multiverse models in semiclassical quantum cosmology, where a measure for local predictions is given by saddle point geometries which coarse-grain over any structure associated with eternal inflation beyond one’s patch.

Quantum transmittance and resonance in the two-dimensional quantum percolation model

1992 ◽  
Author(s):  
Indra Dasgupta ◽  
Tanusri Saha ◽  
Abhijit Mookerjee ◽  
Bikas N. Chakrabarti
Keyword(s):  
Percolation Model ◽  
Two Dimensional ◽  
Quantum Percolation

IS THERE A DELOCALISATION TRANSITION IN A TWO-DIMENSIONAL MODEL FOR QUANTUM PERCOLATION?

1992 ◽  
Vol 06 (13) ◽  
pp. 817-821 ◽  
Author(s):  
INDRA DASGUPTA ◽  
TANUSRI SAHA ◽  
ABHIJIT MOOKERJEE ◽  
B. K. CHAKRABARTI
Keyword(s):  
Finite Size ◽  
Two Dimensions ◽  
Percolation Model ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Dimensional Model ◽  
Recursion Method ◽  
Quantum Percolation ◽  
Two Dimensional Model

We estimate the transmittance of the quantum percolation model of Eggarter and Kirkpatrick (1972) on the square lattice of various sizes using the vector recursion method. We note from finite size scaling that there is no delocalisation transition for any degree of disorder in two dimensions.

Analysis of stochastic resonances in a two-dimensional quantum percolation model

1993 ◽  
Vol 47 (6) ◽  
pp. 3097-3104 ◽  
Author(s):  
Indra Dasgupta ◽  
Tanusri Saha ◽  
Abhijit Mookerjee
Keyword(s):  
Percolation Model ◽  
Two Dimensional ◽  
Quantum Percolation
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