Publications (53)56.9 Total impact
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ABSTRACT: We establish some general dynamical properties of lattice manybody systems that are subject to a highfrequency periodic driving. We prove that such systems have a quasiconserved extensive quantity $H_*$, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is wellapproximated by the evolution with the Hamiltonian $H_*$ up to time $\tau_*$, which is exponentially long in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where $H_*$ is ergodic, the driven system prethermalizes to a thermal state described by $H_*$ at intermediate times $t\lesssim \tau_*$, eventually heating up to an infinitetemperature state at times $t\sim \tau_*$. Our results indicate that rapidly driven manybody systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for experiments which realize topological states by periodic driving.  [Show abstract] [Hide abstract]
ABSTRACT: We consider quantum spin systems under periodic driving at high frequency $\nu$. We prove that up to an (almost) exponential time $\tau_* \sim e^{c \frac{\nu}{\log^3 \nu}}$, the system barely absorbs energy. There is an effective Hamiltonian (or Floquet) operator $\widehat D$ that is approximately conserved up to $\tau_*$, which governs time evolution. More precisely, for $t \leq \tau_*$ such that $t$ is a multiple of the period $T=1/\nu$, the real evolution of an operator $O$ is wellapproximated by $e^{i t \widehat D} O e^{i t \widehat D}$. In the recent physics literature, it has been suggested that periodic driving can be used as a tool to engineer interesting manybody Hamiltonians. The operator $\widehat D$ is such a Hamiltonian and the fact that it really does govern the evolution up to very long times confirms the validity of such a protocol.  [Show abstract] [Hide abstract]
ABSTRACT: We derive general bounds on the energy absorption rates of periodically driven manybody systems of spins or fermions on a lattice. We show that for systems with local interactions, energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological manybody states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including decay of highly energetic excitations in cold atomic and solidstate systems. We note that the bound also applies to other response functions. 
Article: Absence of manybody mobility edges
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ABSTRACT: Localization transitions as a function of temperature require a manybody mobility edge in energy, separating localized from ergodic states. We argue that this scenario is inconsistent because inclusions of the ergodic phase in the supposedly localized phase can serve as mobile bubbles that induce global delocalization. Such inclusions inevitably appear as rare fluctuations in any typical state. We conclude that the only possibility for manybody localization occurs in lattice models that are localized at all energies. Building on a close analogy with a twoparticle problem, where interactions induce delocalization, we argue why hot bubbles are mobile and do not localize upon diluting their energy. Numerical tests of our scenario show that the previously reported mobility edges cannot be distinguished from finitesize effects.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a lattice of weakly interacting quantum Markov processes. Without interaction, the dynamics at each site is relaxing exponentially to a unique stationary state. With interaction, we show that there remains a unique stationary state in the thermodynamic limit, i.e. absence of phase coexistence, and the relaxation towards it is exponentially fast for local observables. We do not assume that the quantum Markov process is reversible (detailed balance) w.r.t. a local Hamiltonian.Journal of Physics A Mathematical and Theoretical 06/2015; 48(42). DOI:10.1088/17518113/48/42/425203 · 1.58 Impact Factor 
Article: The Toom Interface Via Coupling
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ABSTRACT: We consider a one dimensional interacting particle system which describes the effective interface dynamics of the two dimensional Toom model at low temperature and noise. We prove a number of basic properties of this model. First we consider the dynamics on a half open finite interval $[1, N)$, bounding the mixing time from above by $2N$. Then we consider the model defined on the integers. Due to infinite range interaction, this is a nonFeller process that we can define starting from product Bernoulli measures with density $p \in (0, 1)$, but not from arbitrary measures. We show, under a modest technical condition, that the only possible invariant measures are those product Bernoulli measures. We further show that the unique stationary measure on $[k, \infty)$ converges weakly to a product Bernoulli measure on $\Z$ as $k \rightarrow \infty$.  [Show abstract] [Hide abstract]
ABSTRACT: 'Quasiadiabatic continuation', introduced first in the seminal work [Hastings 2004], has proven a successful technique for studying locality properties in gapped quantum lattice systems. For example, when a gapped Hamiltonian is perturbed locally in a region $S$, then the quasiadiabatic continuation describes the resulting change in the ground state by a quasilocal transformation whose strength decays 'subexponentially' with distance to $S$. Here we address the natural question whether this decay can be made exponential, with characteristic decay length roughly the correlation length $\xi$ of the ground states. We point out that (a slight generalization of) [Hamza et al. 2009] allows to do this in some cases. As applications, we improve the locality estimate in some results on topological order and we prove some exponential decay estimates in models with impurities, where some relevant correlations decay faster than one would naively infer from the global gap of the system, as one also expects in disordered systems with manybody localization.Journal of Mathematical Physics 01/2015; 56(6). DOI:10.1063/1.4922507 · 1.24 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study two popular onedimensional chains of classical anharmonic oscillators: the rotor chain and a version of the discrete nonlinear Schr\"odinger chain. We assume that the interaction between neighboring oscillators, controlled by the parameter $\epsilon >0$, is small. We rigorously establish that the thermal conductivity of the chains has a nonperturbative origin, with respect to the coupling constant $\epsilon$, and we provide strong evidence that it decays faster than any power law in $\epsilon$ as $\epsilon \rightarrow 0$. The weak coupling regime also translates into a high temperature regime, suggesting that the conductivity vanishes faster than any power of the inverse temperature.Communications on Pure and Applied Mathematics 12/2014; 68(9). DOI:10.1002/cpa.21550 · 3.13 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the possibility of ManyBody Localization in translation invariant Hamiltonian systems, which was recently brought up by several authors. A key feature of ManyBody Localized disordered systems is recovered, namely the fact that resonant spots are rare and farbetween. However, we point out that resonant spots are mobile, unlike in models with strong quenched disorder, and that these mobile spots constitute a possible mechanism for delocalization, albeit possibly only on very long timescales. In some models, this argument for delocalization can be made very explicit in first order of perturbation theory in the hopping. For models where this does not work, we present instead a nonperturbative argument that relies solely on ergodicity inside the resonant spots.Physical Review B 10/2014; 90(16). DOI:10.1103/PhysRevB.90.165137 · 3.74 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We review some recent works related to the exploration of ManyBody Localization in the absence of quenched disorder. We stress that, for systems where not all eigenstates of the Hamiltonian are expected to be localized, as it is generically the case for translation invariant systems with short range interactions, some rare large ergodic spots constitute a possible mechanism for thermalization, even though such spots occur just as well in systems with strong quenched disorder, where all eigenstates are localized. Nevertheless, we show that there is a regime of asymptotic localization for some translation invariant Hamiltonians.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the possibility of manybody localization in translation invariant Hamiltonian systems. A key feature of manybody localized disordered systems is recovered, namely the fact that resonant spots are rare and farbetween. However, we point out that resonant spots are mobile, unlike in models with quenched disorder, and that they could therefore in principle delocalize the system. The motion of these resonant spots is reminiscent of motion in kinetically constrained models, the frustration effect being caused by a mismatch of energies rather than by geometric constraints. We provide examples where, in first order in the hopping, the resonant spots are effectively trapped (analogous to a jammed phase) and therefore localization is not ruled out, but we also have examples where, despite the rareness of resonant spots, the resonant spots are not trapped and hence this obvious scenario for manybody localization is not realized. We comment on the analysis of higher orders, but we did not reach a final conclusion yet.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the possibility of manybody localization in translation invariant Hamiltonian systems. A key feature of manybody localized disordered systems is recovered, namely the fact that resonant spots are rare and farbetween. However, we point out that resonant spots are mobile, unlike in models with quenched disorder, and that they could therefore in principle delocalize the system. The motion of these resonant spots is reminiscent of motion in kinetically constrained models, the frustration effect being caused by a mismatch of energies rather than by geometric constraints. We provide examples where, in first order in the hopping, the resonant spots are effectively trapped (analogous to a jammed phase) and therefore localization is not ruled out, but we also have examples where, despite the rareness of resonant spots, the resonant spots are not trapped and hence this obvious scenario for manybody localization is not realized. We comment on the analysis of higher orders, but we did not reach a final conclusion yet.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a linear Boltzmann equation that arises in a model for quantum friction. It describes a particle that is slowed down by the emission of bosons. We study the stochastic process generated by this Boltzmann equation and we show convergence of its spatial trajectory to a multiple of Brownian motion with exponential scaling. The asymptotic position of the particle is finite in mean, even though its absolute value is typically infinite. This is contrasted to an approximation that neglects the influence of fluctuations, where the mean asymptotic position is infinite.Journal of Physics A Mathematical and Theoretical 03/2014; 47(27). DOI:10.1088/17518113/47/27/275003 · 1.58 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider generalised versions of the spinboson model at small coupling. We assume the spin (or atom) to sit at the origin \({0 \in \mathbb{R}^d}\) and the propagation speed v p of free bosons to be constant, i.e. independent of momentum. In particular, the bosons are massless. We prove detailed bounds on the mean number of bosons contained in the ball \({\{ x  \leq v_p t \}}\). In particular, we prove that, as \({t \to \infty}\) , this number tends to an asymptotic value that can be naturally identified as the mean number of bosons bound to the atom in the ground state. Physically, this means that bosons, that are not bound to the atom, are travelling outwards at a speed that is not lower than v p , hence the term ‘minimal velocity estimate’. Additionally, we prove bounds on the number of emitted bosons with low momentum (soft mode bounds). This paper is an extension of our earlier work in De Roeck and Kupiainen (Annales Henri Poincaré 14:253–311, 2013). Together with the results in De Roeck and Kupiainen (Annales Henri Poincaré 14:253–311, 2013), the bounds of the present paper suffice to prove asymptotic completeness, as we describe in De Roeck et al. (Asymptotic completeness in the massless spinboson model, 2012).Annales Henri Poincare 02/2014; 16(2). DOI:10.1007/s0002301403237 · 1.64 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasilocality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measurement induced entanglement, and still satisfying a large deviation principle.Journal of Mathematical Physics 12/2013; 56(2). DOI:10.1063/1.4906767 · 1.24 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider a quantum lattice system with infinitedimensional onsite Hilbert space, very similar to the BoseHubbard model. We investigate manybody localization in this model, induced by thermal fluctuations rather than disorder in the Hamiltonian. We provide evidence that the GreenKubo conductivity $\kappa(\beta)$, defined as the timeintegrated current autocorrelation function, decays faster than any polynomial in the inverse temperature $\beta$ as $\beta \to 0$. More precisely, we define approximations $\kappa_{\tau}(\beta)$ to $\kappa(\beta)$ by integrating the currentcurrent autocorrelation function up to a large but finite time $\tau$ and we rigorously show that $\be^{n}\kappa_{\be^{m}}(\beta)$ vanishes as $\be \to 0$, for any $n,m \in \bbN$ such that $mn$ is sufficiently large.Communications in Mathematical Physics 08/2013; 332(3). DOI:10.1007/s0022001421168 · 2.09 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the dynamics of a quantum particle hopping on a simple cubic lattice and driven by a constant external force. It is coupled to an array of identical, independent thermal reservoirs consisting of free, massless Bose fields, one at each site of the lattice. When the particle visits a site x of the lattice it can emit or absorb field quanta of the reservoir at x. Under the assumption that the coupling between the particle and the reservoirs and the driving force are sufficiently small, we establish the following results: The ergodic average over time of the state of the particle approaches a nonequilibrium steady state (NESS) describing a nonzero mean drift of the particle. Its motion around the mean drift is diffusive, and the diffusion constant and the drift velocity are related to one another by the Einstein relation.Journal of Mathematical Physics 06/2013; 55(7). DOI:10.1063/1.4881532 · 1.24 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: This paper is a companion to 'Quantum Diffusion with Drift and the Einstein Relation I' (jointly submitted to arXiv). Its purpose is to describe and prove a certain number of technical results used in 'Quantum Diffusion with Drift and the Einstein Relation I', but not proven there. Both papers concern longtime properties (diffusion, drift) of the motion of a driven quantum particle coupled to an array of thermal reservoirs. The main technical results derived in the present paper are $(1)$ an asymptotic perturbation theory applicable for small driving, and, $(2)$ the construction of timedependent correlation functions of particle observables.Journal of Mathematical Physics 06/2013; 55(7). DOI:10.1063/1.4881533 · 1.24 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider generalized versions of the massless spinboson model. Building on the recent work in 'Approach to ground state and timeindependent photon bound for massless spinboson models' (arXiv:1109.5582, Annales H. Poincare, 2012) and 'Propagation bounds and soft photon bounds for the massless spinboson model' (submitted to arXiv jointly with the present paper), we prove asymptotic completeness.Advances in Mathematics 01/2013; 268. DOI:10.1016/j.aim.2014.09.012 · 1.29 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider generalized versions of the massless spinboson model. We prove detailed bounds on the number of bosons in certain spatial regions (propagation bounds) and on the number of bosons with low momentum (soft photon bounds). This work is an extension of our earlier work in 'Approach to ground state and timeindependent photon bound for massless spinboson models' (arXiv:1109.5582, Ann. H. Poincare, 2012). Together with the results in arXiv:1109.5582, the bounds of the present paper suffice to prove asymptotic completeness, as we describe in a joint submission to arXiv: 'Asymptotic completeness for the massless spinboson model'.
Publication Stats
380  Citations  
56.90  Total Impact Points  
Top Journals
Institutions

20082014

Universität Heidelberg
 Institute of Theoretical Physics
Heidelburg, BadenWürttemberg, Germany 
University of Leuven
Louvain, Flemish, Belgium


2012

University of Cologne
 Institute of Physics
Köln, North RhineWestphalia, Germany


2009

University of Helsinki
 Department of Mathematics and Statistics
Helsinki, Uusimaa, Finland 
ETH Zurich
 Institute for Theoretical Physics
Zürich, Zurich, Switzerland


2004

University of Antwerp
Antwerpen, Flanders, Belgium
