Nachtergaele, Bruno
Overview
Works:  50 works in 63 publications in 1 language and 394 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Collector, Editor, Contributor, Other 
Classifications:  QC20.7.N6, 531 
Publication Timeline
.
Most widely held works by
Bruno Nachtergaele
Nonlinear phenomena in fluids, solids, and other complex systems : proceedings of the Second Latin American Workshop on Nonlinear
Phenomena, Santiago, Chile, September 614, 1990 by
Patricio Cordero(
Book
)
10 editions published between 1991 and 2014 in English and held by 206 WorldCat member libraries worldwide
This book contains short courses in current topics in nonlinear physics given by distinguished professionals in their fields. These include: nonlinear fluid dynamics, transition to turbulence, quantum hall effect, cellular automata and neural networks, phase transitions. These courses are up to date and are aimed at a wide audience, in particular to graduate students and researchers in the field of nonlinear physics
10 editions published between 1991 and 2014 in English and held by 206 WorldCat member libraries worldwide
This book contains short courses in current topics in nonlinear physics given by distinguished professionals in their fields. These include: nonlinear fluid dynamics, transition to turbulence, quantum hall effect, cellular automata and neural networks, phase transitions. These courses are up to date and are aimed at a wide audience, in particular to graduate students and researchers in the field of nonlinear physics
Statistical Mechanics : Selecta of Elliott H. Lieb by
Bruno Nachtergaele(
)
1 edition published in 2004 in English and held by 66 WorldCat member libraries worldwide
In Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with realistic forces. Elliott Lieb is a mathematical physicist who meets the challenge of statistical mechanics head on, taking nothing for granted and not being content until the purported consequences have been shown, by rigorous analysis, to follow from the premises. The present volume contains a selection of his contributions to the field, in particular papers dealing with general properties of Coulomb systems, phase transitions in systems with a continuous symmetry, lattice crystals, and entropy inequalities. It also includes work on classical thermodynamics, a discipline that, despite many claims to the contrary, is logically independent of statistical mechanics and deserves a rigorous and unambiguous foundation of its own. The articles in this volume have been carefully annotated by the editors
1 edition published in 2004 in English and held by 66 WorldCat member libraries worldwide
In Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with realistic forces. Elliott Lieb is a mathematical physicist who meets the challenge of statistical mechanics head on, taking nothing for granted and not being content until the purported consequences have been shown, by rigorous analysis, to follow from the premises. The present volume contains a selection of his contributions to the field, in particular papers dealing with general properties of Coulomb systems, phase transitions in systems with a continuous symmetry, lattice crystals, and entropy inequalities. It also includes work on classical thermodynamics, a discipline that, despite many claims to the contrary, is logically independent of statistical mechanics and deserves a rigorous and unambiguous foundation of its own. The articles in this volume have been carefully annotated by the editors
Linear algebra as an introduction to abstract mathematics by
Bruno Nachtergaele(
Book
)
5 editions published between 2015 and 2016 in English and held by 64 WorldCat member libraries worldwide
5 editions published between 2015 and 2016 in English and held by 64 WorldCat member libraries worldwide
Condensed Matter Physics and Exactly Soluble Models : Selecta of Elliott H. Lieb(
)
in English and held by 6 WorldCat member libraries worldwide
in English and held by 6 WorldCat member libraries worldwide
Statistical Mechanics : Selecta of Elliott H. Lieb(
)
in English and held by 6 WorldCat member libraries worldwide
in English and held by 6 WorldCat member libraries worldwide
A direct proof of dimerization in a family of SU(n)invariant quantum spin chains by
Bruno Nachtergaele(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Entanglement Dynamics of Disordered Quantum XY Chains by
Houssam AbdulRahman(
)
1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide
Spectral Gap and Edge Excitations of dDimensional PVBS Models on HalfSpaces by Michael Bishop(
)
1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide
NonEquilibrium States of a Photon Cavity Pumped by an Atomic Beam by
Bruno Nachtergaele(
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
Droplet Excitations for the Spin1/2 XXZ Chain with Kink Boundary Conditions by
Bruno Nachtergaele(
)
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
The Complete Set of Infinite Volume Ground States for Kitaev's Abelian Quantum Double Models by Matthew Cha(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Much Ado About Something: Why LiebRobinson bounds are useful by
Bruno Nachtergaele(
)
1 edition published in 2011 in Undetermined and held by 1 WorldCat member library worldwide
This is a short review on the applications of LiebRobinson bounds for a general readership of mathematical physicists
1 edition published in 2011 in Undetermined and held by 1 WorldCat member library worldwide
This is a short review on the applications of LiebRobinson bounds for a general readership of mathematical physicists
Locality Estimates for Quantum Spin Systems by
Bruno Nachtergaele(
)
1 edition published in 2007 in Undetermined and held by 1 WorldCat member library worldwide
We review some recent results that express or rely on the locality properties of the dynamics of quantum spin systems. In particular, we present a slightly sharper version of the recently obtained LiebRobinson bound on the group velocity for such systems on a large class of metric graphs. Using this bound we provide expressions of the quasilocality of the dynamics in various forms, present a proof of the Exponential Clustering Theorem, and discuss a multidimensional LiebSchultzMattis Theorem
1 edition published in 2007 in Undetermined and held by 1 WorldCat member library worldwide
We review some recent results that express or rely on the locality properties of the dynamics of quantum spin systems. In particular, we present a slightly sharper version of the recently obtained LiebRobinson bound on the group velocity for such systems on a large class of metric graphs. Using this bound we provide expressions of the quasilocality of the dynamics in various forms, present a proof of the Exponential Clustering Theorem, and discuss a multidimensional LiebSchultzMattis Theorem
Quantum Spin Systems by
Bruno Nachtergaele(
)
1 edition published in 2004 in Undetermined and held by 1 WorldCat member library worldwide
This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formulating problems and results in quantum spin systems is described. Then, three short sections are devoted to Spontaneaous Symmetry Breaking, Phase transitions, and Dynamcis
1 edition published in 2004 in Undetermined and held by 1 WorldCat member library worldwide
This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formulating problems and results in quantum spin systems is described. Then, three short sections are devoted to Spontaneaous Symmetry Breaking, Phase transitions, and Dynamcis
LiebRobinson bounds and the existence of infinite system dynamics by
Bruno Nachtergaele(
)
1 edition published in 2009 in Undetermined and held by 1 WorldCat member library worldwide
We present a recent result on the existence of the dynamics in the thermodynamic limit of a class of anharmonic quantum oscillator lattices, which was obtained using LiebRobinson bounds
1 edition published in 2009 in Undetermined and held by 1 WorldCat member library worldwide
We present a recent result on the existence of the dynamics in the thermodynamic limit of a class of anharmonic quantum oscillator lattices, which was obtained using LiebRobinson bounds
Interfaces and droplets in quantum lattice models by
Bruno Nachtergaele(
)
1 edition published in 2000 in Undetermined and held by 1 WorldCat member library worldwide
This paper is a short review of recent results on interface states in the FalicovKimball model and the ferromagnetic XXZ Heisenberg model. More specifically, we discuss the following topics: 1) The existence of interfaces in quantum lattice models that can be considered as perturbations of classical models. 2) The rigidity of the 111 interface in the threedimensional FalicovKimball model at sufficiently low temperatures. 3) The lowlying excitations and the scaling of the gap in the 111 interface ground state in the ferromagnetic XXZ Heisenberg model in three dimensions. 4) The existence of droplet states in the XXZ chain and their properties
1 edition published in 2000 in Undetermined and held by 1 WorldCat member library worldwide
This paper is a short review of recent results on interface states in the FalicovKimball model and the ferromagnetic XXZ Heisenberg model. More specifically, we discuss the following topics: 1) The existence of interfaces in quantum lattice models that can be considered as perturbations of classical models. 2) The rigidity of the 111 interface in the threedimensional FalicovKimball model at sufficiently low temperatures. 3) The lowlying excitations and the scaling of the gap in the 111 interface ground state in the ferromagnetic XXZ Heisenberg model in three dimensions. 4) The existence of droplet states in the XXZ chain and their properties
Mathematical fluid dynamics(
Book
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
Ferromagnetic Ordering of Energy Levels by
Bruno Nachtergaele(
)
1 edition published in 2003 in Undetermined and held by 1 WorldCat member library worldwide
We study a natural conjecture regarding ferromagnetic ordering of energy levels in the Heisenberg model which complements the LiebMattis Theorem of 1962 for antiferromagnets: for ferromagnetic Heisenberg models the lowest energies in each subspace of fixed total spin are strictly ordered according to the total spin, with the lowest, i.e., the ground state, belonging to the maximal total spin subspace. Our main result is a proof of this conjecture for the spin1/2 Heisenberg XXX and XXZ ferromagnets in one dimension. Our proof has two main ingredients. The first is an extension of a result of Koma and Nachtergaele which shows that monotonicity as a function of the total spin follows from the monotonicity of the ground state energy in each total spin subspace as a function of the length of the chain. For the second part of the proof we use the TemperleyLieb algebra to calculate, in a suitable basis, the matrix elements of the Hamiltonian restricted to each subspace of the highest weight vectors with a given total spin. We then show that the positivity properties of these matrix elements imply the necessary monotonicity in the volume. Our method also shows that the first excited state of the XXX ferromagnet on any finite tree has one less than maximal total spin
1 edition published in 2003 in Undetermined and held by 1 WorldCat member library worldwide
We study a natural conjecture regarding ferromagnetic ordering of energy levels in the Heisenberg model which complements the LiebMattis Theorem of 1962 for antiferromagnets: for ferromagnetic Heisenberg models the lowest energies in each subspace of fixed total spin are strictly ordered according to the total spin, with the lowest, i.e., the ground state, belonging to the maximal total spin subspace. Our main result is a proof of this conjecture for the spin1/2 Heisenberg XXX and XXZ ferromagnets in one dimension. Our proof has two main ingredients. The first is an extension of a result of Koma and Nachtergaele which shows that monotonicity as a function of the total spin follows from the monotonicity of the ground state energy in each total spin subspace as a function of the length of the chain. For the second part of the proof we use the TemperleyLieb algebra to calculate, in a suitable basis, the matrix elements of the Hamiltonian restricted to each subspace of the highest weight vectors with a given total spin. We then show that the positivity properties of these matrix elements imply the necessary monotonicity in the volume. Our method also shows that the first excited state of the XXX ferromagnet on any finite tree has one less than maximal total spin
Droplet States in the XXZ Heisenberg Chain by
Bruno Nachtergaele(
)
1 edition published in 2000 in Undetermined and held by 1 WorldCat member library worldwide
We consider the ground states of the ferromagnetic XXZ chain with spin up boundary conditions in sectors with a fixed number of down spins. This forces the existence of a droplet of down spins in the system. We find the exact energy and the states that describe these droplets in the limit of an infinite number of down spins. We prove that there is a gap in the spectrum above the droplet states. As the XXZ Hamiltonian has a gap above the fully magnetized ground states as well, this means that the droplet states (for sufficiently large droplets) form an isolated band. The width of this band tends to zero in the limit of infinitely large droplets. We also prove the analogous results for finite chains with periodic boundary conditions and for the infinite chain
1 edition published in 2000 in Undetermined and held by 1 WorldCat member library worldwide
We consider the ground states of the ferromagnetic XXZ chain with spin up boundary conditions in sectors with a fixed number of down spins. This forces the existence of a droplet of down spins in the system. We find the exact energy and the states that describe these droplets in the limit of an infinite number of down spins. We prove that there is a gap in the spectrum above the droplet states. As the XXZ Hamiltonian has a gap above the fully magnetized ground states as well, this means that the droplet states (for sufficiently large droplets) form an isolated band. The width of this band tends to zero in the limit of infinitely large droplets. We also prove the analogous results for finite chains with periodic boundary conditions and for the infinite chain
LiebRobinson Bounds and Existence of the Thermodynamic Limit for a Class of Irreversible Quantum Dynamics by
Bruno Nachtergaele(
)
1 edition published in 2011 in Undetermined and held by 1 WorldCat member library worldwide
We prove LiebRobinson bounds and the existence of the thermodynamic limit for a general class of irreversible dynamics for quantum lattice systems with timedependent generators that satisfy a suitable decay condition in space
1 edition published in 2011 in Undetermined and held by 1 WorldCat member library worldwide
We prove LiebRobinson bounds and the existence of the thermodynamic limit for a general class of irreversible dynamics for quantum lattice systems with timedependent generators that satisfy a suitable decay condition in space
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Related Identities
 Cordero, Patricio Other Author Editor
 Fundación Andes (Chile)
 Benguria, Rafael D.
 Yngvason, Jakob Collector
 Solovej, Jan Philip Collector
 Schilling, Anne (Mathematician)
 Lankham, Isaiah Author
 SpringerLink (Online service) Other
 Sims, Robert Contributor
 Young, Amanda Contributor
Useful Links
Alternative Names
Bruno Nachtergaele Belgian mathematician and physicist
Bruno Nachtergaele Belgisch wiskundige
Bruno Nachtergaele belgischer Mathematiker und Physiker
Nachtergaele, B.
Nachtergaele, B. (Bruno)
Nachtergaele, Bruno
Nachtergaele, Bruno L. Z. 1962
Nachtergaele, Bruno Leo Zulma 1962
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