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Related papers: On the Existence of the Dynamics for Anharmonic Qu…

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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.

Mathematical Physics · Physics 2017-08-23 Bruno Nachtergaele

We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems.

Mathematical Physics · Physics 2009-02-03 Bruno Nachtergaele , Hillel Raz , Benjamin Schlein , Robert Sims

For a class of infinite lattices of interacting anharmonic oscillators, we study the existence of the dynamics, together with Lieb-Robinson bounds, in a suitable algebra of observables

Mathematical Physics · Physics 2009-04-20 Laurent Amour , Pierre Levy-Bruhl , Jean Nourrigat

We supply the mathematical arguments required to complete the proofs of two previously published results: Lieb-Robinson bounds for the dynamics of quantum lattice systems with unbounded on-site terms in the Hamiltonian and the existence of…

Mathematical Physics · Physics 2014-10-31 Bruno Nachtergaele , Robert Sims

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.

Mathematical Physics · Physics 2012-03-13 Bruno Nachtergaele , Anna Vershynina , Valentin A. Zagrebnov

We prove locality estimates, in the form of Lieb-Robinson bounds, for classical oscillator systems defined on a lattice. Our results hold for the harmonic system and a variety of anharmonic perturbations with long range interactions. The…

Mathematical Physics · Physics 2015-05-13 Hillel Raz , Robert Sims

We consider the dynamics of systems of lattice bosons with infinitely many degrees of freedom. We show that their dynamics defines a group of automorphisms on a $C^*$--algebra introduced by Buchholz, which extends the resolvent algebra of…

Mathematical Physics · Physics 2025-06-13 Andreas Deuchert , Jonas Lampart , Marius Lemm

We discuss the properties of two open quantum systems with a general class of irreversible quantum dynamics. First we study Lieb-Robinson bounds in a quantum lattice systems. The time-dependent generator of the dynamics of the system is of…

Mathematical Physics · Physics 2013-02-15 Anna Vershynina

We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical…

Quantum Physics · Physics 2022-11-22 Zongping Gong , Ryusuke Hamazaki

We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle Hamiltonian. This leads to a many-body localized regime of excited states with…

Mathematical Physics · Physics 2022-10-13 Houssam Abdul-Rahman , Robert Sims , Günter Stolz

We study many-body properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the…

Mathematical Physics · Physics 2012-12-24 Bruno Nachtergaele , Robert Sims , Günter Stolz

We propose an exactly soluble W*-dynamical system generated by repeated harmonic perturbations of the one-mode quantum oscillator. In the present paper we deal with the case of isolated system. Although dynamics is Hamiltonian and…

Functional Analysis · Mathematics 2014-04-14 Hiroshi Tamura , Valentin Zagrebnov

We construct C*-dynamical systems for the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, as well on more general structures. Our approach allows…

Operator Algebras · Mathematics 2025-12-19 T. D. H. van Nuland , C. J. F. van de Ven

Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of…

Mathematical Physics · Physics 2017-05-24 Detlev Buchholz

Lieb-Robinson bounds show that the speed of propagation of information under the Heisenberg dynamics in a wide class of non-relativistic quantum lattice systems is essentially bounded. We review work of the past dozen years that has turned…

Mathematical Physics · Physics 2019-06-25 Bruno Nachtergaele , Robert Sims , Amanda Young

The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially…

Quantum Physics · Physics 2010-03-03 M. Cramer , A. Serafini , J. Eisert

We study monitored quantum dynamics of infinite-range interacting bosonic systems in the thermodynamic limit. We show that under semiclassical assumptions, the quantum fluctuations along single monitored trajectories adopt a deterministic…

Quantum Physics · Physics 2025-09-22 Zejian Li , Anna Delmonte , Rosario Fazio

Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…

Dynamical Systems · Mathematics 2019-09-30 Jason J. Bramburger

Open quantum-system dynamics can follow exponential decay, non-exponential relaxation, or oscillatory dynamics, depending on the system-environment coupling. We study a lattice with a boundary defect that transitions between these regimes,…

For classical lattice systems, the Dobrushin-Lanford-Ruelle theory of boundary conditions states that the restriction of a global equilibrium state to a subsystem can be obtained as an integral over equilibrium states of the subsystem…

Condensed Matter · Physics 2007-05-23 M. Fannes , R. F. Werner
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