We review several properties of thermal states of spin Hamiltonians with short range interactions. In particular, we focus on those aspects in which the application of tools coming from quantum information theory has been specially... more
We review several properties of thermal states of spin Hamiltonians with short range interactions. In particular, we focus on those aspects in which the application of tools coming from quantum information theory has been specially successful in the recent years. This comprises the study of the correlations at finite and zero temperature, the stability against distant and/or weak perturbations, the locality of temperature and their classical simulatability. For the case of states with a finite correlation length, we overview the results on their energy distribution and the equivalence of the canonical and microcanonical ensemble.
A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of... more
A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of...
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In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath... more
In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.
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We show that the physical mechanism for the equilibration of closed quantum systems is dephasing, and identify the energy scales that determine the equilibration timescale of a given observable. For realistic physical systems (e.g those... more
We show that the physical mechanism for the equilibration of closed quantum systems is dephasing, and identify the energy scales that determine the equilibration timescale of a given observable. For realistic physical systems (e.g those with local Hamiltonians), our arguments imply timescales that do not increase with the system size, in contrast to previously known upper bounds. In particular we show that, for such Hamiltonians, the matrix representation of local observables in the energy basis is banded, and that this property is crucial in order to derive equilibration times that are non-negligible in macroscopic systems. Finally, we give an intuitive interpretation to recent theorems on equilibration time-scale.
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Absence of thermalization | Introductory words 2 / 19 Old questions and new contributions How do quantum mechanics and statistical mechanics go together? Absence of thermalization | Setup and terminology 3 / 19
The equilibration of the double proton transfer in porphine is demonstrated using a model system Hamiltonian. This highly coherent process could be witnessed experimentally using state-of-the-art femtosecond spectroscopy.
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Christian Gogolin, Markus P. Müller, and Jens Eisert 1 Institute for Physics and Astronomy, Potsdam University, 14476 Potsdam, Germany 2 Fakultät für Physik und Astronomie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany 3... more
Christian Gogolin, Markus P. Müller, and Jens Eisert 1 Institute for Physics and Astronomy, Potsdam University, 14476 Potsdam, Germany 2 Fakultät für Physik und Astronomie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany 3 Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK 4 Institute of Mathematics, Technical University of Berlin, 10623 Berlin, Germany 5 Institute for Advanced Study Berlin, 14193 Berlin, Germany
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems,made up ofmicroscopic particles, in terms of a small number ofmacroscopic quantities, such... more
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems,made up ofmicroscopic particles, in terms of a small number ofmacroscopic quantities, such aswork and entropy. As systems get ever smaller, fluctuations of these quantities become increasingly relevant, prompting the development of stochastic thermodynamics. Recently we have seen a surge of interest in exploring the quantum regime, where the origin offluctuations is quantum rather than thermal.Many questions, such as the role of entanglement and the emergence of thermalisation, lie wide open. Answering these questionsmay lead to the development of quantumheat engines and refrigerators, as well as to vitally needed simple descriptions of quantummany-body systems.
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Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a... more
Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and always vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic situation of non-Markovian quantum Brownian motion.
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Thermodynamics is one of the most successful physical theories ever formulated. Though it was initially developed to deal with steam engines and, in particular, the problem of conversion of heat into mechanical work, it has prevailed even... more
Thermodynamics is one of the most successful physical theories ever formulated. Though it was initially developed to deal with steam engines and, in particular, the problem of conversion of heat into mechanical work, it has prevailed even after the scientific revolutions of relativity and quantum mechanics. Despite its wide range of applicability, it is known that the laws of thermodynamics break down when systems are correlated with their environments. In the presence of correlations, anomalous heat flows from cold to hot baths become possible, as well as memory erasure accompanied by work extraction instead of heat dissipation. Here, we generalize thermodynamics to physical scenarios which allow presence of correlations, including those where strong correlations are present. We exploit the connection between information and physics, and introduce a consistent redefinition of heat dissipation by systematically accounting for the information flow from system to bath in terms of the ...
There is a renewed interest in the derivation of statistical mechanics from the dynamics of closed quantum systems. A central part of this program is to understand how far-from-equilibrium closed quantum system can behave as if relaxing... more
There is a renewed interest in the derivation of statistical mechanics from the dynamics of closed quantum systems. A central part of this program is to understand how far-from-equilibrium closed quantum system can behave as if relaxing to a stable equilibrium. Equilibration dynamics has been traditionally studied with a focus on the so-called quenches of large-scale many-body systems. Alternatively, we consider here the equilibration of a molecular model system describing the double proton transfer reaction in porphine. Using numerical simulations, we show that equilibration in this context indeed takes place and does so very rapidly ($\sim \!\! 200$fs) for initial states induced by pump-dump laser pulse control with energies well above the synchronous tunneling barrier.
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In this paper we propose a framework for simulating thermal particle production in condensed matter systems. The procedure we describe can be realized by means of a quantum quench of a parameter in the model. In order to support this... more
In this paper we propose a framework for simulating thermal particle production in condensed matter systems. The procedure we describe can be realized by means of a quantum quench of a parameter in the model. In order to support this claim, we study quadratic fermionic systems in one and two dimensions by means of analytical and numerical techniques. In particular, we are able to show that a class of observables associated to Unruh--de Witt detectors are very relevant for this type of setup and that exhibit approximate thermalization.
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How much work can be extracted from a heat bath using a thermal machine operating at the quantum level? In this work, we establish a framework of work extraction in the presence of quantum correlations as they naturally emerge in quantum... more
How much work can be extracted from a heat bath using a thermal machine operating at the quantum level? In this work, we establish a framework of work extraction in the presence of quantum correlations as they naturally emerge in quantum thermodynamics beyond the weak-coupling regime. Quantum correlations and entanglement, as they are ubiquitously encountered when putting systems into contact with a bath, emerge as a limitation to work extraction, rather than as an advantage. We bring together concepts of quantum thermodynamics with those of non-equilibrium dynamics, in a rigorous but physically motivated approach. We discuss various limits that relate to known results and put our work into context of approaches to finite-time quantum thermodynamics.
This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of temperature, which has been an open problem in the... more
This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of temperature, which has been an open problem in the context of nanoscale systems. Technically, we derive a truncation formula for thermal states. The truncation error is exactly given by a generalized covariance. For this covariance we prove exponential clustering of correlations above a universal critical temperature. The proof builds on a percolation argument originally used to approximate thermal states by matrix-product operators. As a corollary we obtain that above a the critical temperature, thermal states are stable against distant Hamiltonian perturbations and we obtain a model independent upper bound on critical temperatures, such as the Curie temperature. Moreover, our results imply that above the critical temperature local expectation values can be approximated efficiently in the error an...
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We study the signatures of rotational and phase symmetry breaking in small rotating clouds of trapped ultracold Bose atoms by looking at rigorously defined condensate wave function. Rotational symmetry breaking occurs in narrow frequency... more
We study the signatures of rotational and phase symmetry breaking in small rotating clouds of trapped ultracold Bose atoms by looking at rigorously defined condensate wave function. Rotational symmetry breaking occurs in narrow frequency windows, where energy degeneracy between the lowest energy states of different total angular momentum takes place. This leads to a complex condensate wave function that exhibits vortices clearly seen as holes in the density, as well as characteristic local phase patterns, reflecting the appearance of vorticities. Phase symmetry (or gauge symmetry) breaking, on the other hand, is clearly manifested in the interference of two independent rotating clouds.
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In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath... more
In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified ...
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Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and... more
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations.Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed am...