Publications related to Lattice (group)

Mean value theorems for collections of lattices with a prescribed group of symmetries

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

Transition to chaos in extended systems and their quantum impurity models

Camille Didier Georges Aron

Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis-Cummings model ...

Bristol2024

Mapping orthorhombic domains with geometrical phase analysis in rare-earth nickelate heterostructures

Duncan Thomas Lindsay Alexander, Bernat Mundet, Jean-Marc Triscone

Most perovskite oxides belong to the Pbnm space group, composed of an anisotropic unit cell, A-site antipolar displacements, and oxygen octahedral tilts. Mapping the orientation of the orthorhombic unit cell in epitaxial heterostructures that consist of at ...

Melville2024

Primary and secondary order parameters in the fully frustrated transverse-field Ising model on the square lattice

Frédéric Mila

Using quantum Monte Carlo simulations and field-theory arguments, we study the fully frustrated transversefield Ising model on the square lattice for the purpose of quantitatively relating two different order parameters to each other. We consider a "primar ...

Amer Physical Soc2024

Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Critical line of the triangular Ising antiferromagnet in a field from a C3-symmetric corner transfer matrix algorithm

Frédéric Mila, Samuel Louis Nyckees, Afonso Dos Santos Rufino, Jeanne Colbois

The corner transfer matrix renormalization group (CTMRG) algorithm has been extensively used to investigate both classical and quantum two-dimensional (2D) lattice models. The convergence of the algorithm can strongly vary from model to model depending on ...

College Pk2023

Geometric Considerations in Lattice Programming

Moritz Andreas Venzin

We provide faster algorithms and fine-grained reductions for lattice problems in general norms. ...

EPFL2023

Computer-assisted proof of kernel inequalities

Maryna Viazovska, Abhinav Kumar

This data set provides a computer-assisted proof for the kernel inequalities needed to prove universal optimality in the paper "Universal optimality of the E_8 and Leech lattices and interpolation formulas" (by Cohn, Kumar, Miller, Radchenko, and Viazovska ...

EPFL Infoscience2023

Elastocapillary menisci mediate interaction of neighboring structures at the surface of a compliant solid

John Martin Kolinski

Surface stress drives long-range elastocapillary interactions at the surface of compliant solids, where it has been observed to mediate interparticle interactions and to alter the transport of liquid drops. We show that such an elastocapillary interaction ...

2023

A type I conjecture and boundary representations of hyperbolic groups

Nicolas Monod

We establish new results on the weak containment of quasi-regular and Koopman representations of a second countable locally compact group G

G

associated with nonsingular G

G

-spaces. We deduce that any two boundary representations of a hyperbolic locally ...

WILEY2023

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Mean value theorems for collections of lattices with a prescribed group of symmetries

Transition to chaos in extended systems and their quantum impurity models

Mapping orthorhombic domains with geometrical phase analysis in rare-earth nickelate heterostructures

Primary and secondary order parameters in the fully frustrated transverse-field Ising model on the square lattice

Moments of the number of points in a bounded set for number field lattices

Critical line of the triangular Ising antiferromagnet in a field from a C3-symmetric corner transfer matrix algorithm

Geometric Considerations in Lattice Programming

Computer-assisted proof of kernel inequalities

Elastocapillary menisci mediate interaction of neighboring structures at the surface of a compliant solid

A type I conjecture and boundary representations of hyperbolic groups

Moments of the number of points in a bounded set for number field lattices

Primary and secondary order parameters in the fully frustrated transverse-field Ising model on the square lattice

Mean value theorems for collections of lattices with a prescribed group of symmetries

Critical line of the triangular Ising antiferromagnet in a field from a C3-symmetric corner transfer matrix algorithm

A type I conjecture and boundary representations of hyperbolic groups

Computer-assisted proof of kernel inequalities

Transition to chaos in extended systems and their quantum impurity models

Mapping orthorhombic domains with geometrical phase analysis in rare-earth nickelate heterostructures

Geometric Considerations in Lattice Programming

Elastocapillary menisci mediate interaction of neighboring structures at the surface of a compliant solid