WorldCat Identities

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
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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 6-14, 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
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
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

Condensed Matter Physics and Exactly Soluble Models : Selecta of Elliott H. Lieb( )

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

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

Entanglement Dynamics of Disordered Quantum XY Chains by Houssam Abdul-Rahman( )

1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide

Spectral Gap and Edge Excitations of d-Dimensional PVBS Models on Half-Spaces by Michael Bishop( )

1 edition published in 2016 in English and held by 2 WorldCat member libraries worldwide

Non-Equilibrium 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

Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions by Bruno Nachtergaele( )

1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide

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

Much Ado About Something: Why Lieb-Robinson 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 Lieb-Robinson 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 Lieb-Robinson bound on the group velocity for such systems on a large class of metric graphs. Using this bound we provide expressions of the quasi-locality of the dynamics in various forms, present a proof of the Exponential Clustering Theorem, and discuss a multi-dimensional Lieb-Schultz-Mattis 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
Lieb-Robinson 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 Lieb--Robinson 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 Falicov-Kimball 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 three-dimensional Falicov-Kimball model at sufficiently low temperatures. 3) The low-lying 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

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 Lieb-Mattis 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 spin-1/2 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 Temperley-Lieb 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
Lieb-Robinson 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 Lieb-Robinson bounds and the existence of the thermodynamic limit for a general class of irreversible dynamics for quantum lattice systems with time-dependent generators that satisfy a suitable decay condition in space
 
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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-

Languages
English (25)