The Experts below are selected from a list of 64488 Experts worldwide ranked by ideXlab platform
Carlangelo Liverani - One of the best experts on this subject based on the ideXlab platform.
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Exponential Decay of correlations for finite horizon Sinai billiard flows
2018Co-Authors: Viviane Baladi, Mark F. Demers, Carlangelo LiveraniAbstract:We prove Exponential Decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group $$\mathcal {L}_t$$ L t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions.
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Exponential Decay of correlations for finite horizon sinai billiard flows
2015Co-Authors: Viviane Baladi, Mark F. Demers, Carlangelo LiveraniAbstract:We prove Exponential Decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L_t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions. (Revised after referees' comments.)
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Exponential Decay of correlations for piecewise cone hyperbolic contact flows
2012Co-Authors: Viviane Baladi, Carlangelo LiveraniAbstract:We prove Exponential Decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time Exponential Decay of correlations is proved for continuous-time dynamics with singularities on a manifold. Our proof combines the second author’s version (Liverani in Ann Math 159:1275–1312, 2004) of Dolgopyat’s estimates for contact flows and the first author’s work with Gouezel (J Mod Dyn 4:91–137, 2010) on piecewise hyperbolic discrete-time dynamics.
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Exponential Decay of correlations for piecewise cone hyperbolic contact flows
2011Co-Authors: Viviane Baladi, Carlangelo LiveraniAbstract:We prove Exponential Decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time Exponential Decay of correlations is proved for continuous-time dynamics with singularities on a manifold. Our proof combines the second author's version of Dolgopyat's estimates for contact flows and the first author's work with Gou\"ezel on piecewise hyperbolic discrete-time dynamics. (Presentation revised.)
Viviane Baladi - One of the best experts on this subject based on the ideXlab platform.
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Exponential Decay of correlations for finite horizon Sinai billiard flows
2018Co-Authors: Viviane Baladi, Mark F. Demers, Carlangelo LiveraniAbstract:We prove Exponential Decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group $$\mathcal {L}_t$$ L t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions.
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Exponential Decay of correlations for finite horizon sinai billiard flows
2015Co-Authors: Viviane Baladi, Mark F. Demers, Carlangelo LiveraniAbstract:We prove Exponential Decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L_t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions. (Revised after referees' comments.)
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Exponential Decay of correlations for piecewise cone hyperbolic contact flows
2012Co-Authors: Viviane Baladi, Carlangelo LiveraniAbstract:We prove Exponential Decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time Exponential Decay of correlations is proved for continuous-time dynamics with singularities on a manifold. Our proof combines the second author’s version (Liverani in Ann Math 159:1275–1312, 2004) of Dolgopyat’s estimates for contact flows and the first author’s work with Gouezel (J Mod Dyn 4:91–137, 2010) on piecewise hyperbolic discrete-time dynamics.
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Exponential Decay of correlations for piecewise cone hyperbolic contact flows
2011Co-Authors: Viviane Baladi, Carlangelo LiveraniAbstract:We prove Exponential Decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time Exponential Decay of correlations is proved for continuous-time dynamics with singularities on a manifold. Our proof combines the second author's version of Dolgopyat's estimates for contact flows and the first author's work with Gou\"ezel on piecewise hyperbolic discrete-time dynamics. (Presentation revised.)
Michał Horodecki - One of the best experts on this subject based on the ideXlab platform.
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Exponential Decay of Correlations Implies Area Law
2015Co-Authors: Fernando G. S. L. Brandão, Michał HorodeckiAbstract:We prove that a finite correlation length, i.e., Exponential Decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is Exponential in the correlation length of the state, thus reproducing as a particular case Hastings’s proof of an area law for groundstates of 1D gapped Hamiltonians. As a consequence, we show that 1D quantum states with Exponential Decay of correlations have an efficient classical approximate description as a matrix product state of polynomial bond dimension, thus giving an equivalence between injective matrix product states and states with a finite correlation length. The result can be seen as a rigorous justification, in one dimension, of the intuition that states with Exponential Decay of correlations, usually associated with non-critical phases of matter, are simple to describe. It also has implications for quantum computing: it shows that unless a pure state quantum computation involves states with long-range correlations, Decaying at most algebraically with the distance, it can be efficiently simulated classically. The proof relies on several previous tools from quantum information theory—including entanglement distillation protocols achieving the hashing bound, properties of single-shot smooth entropies, and the quantum substate theorem—and also on some newly developed ones. In particular we derive a new bound on correlations established by local random measurements, and we give a generalization to the max-entropy of a result of Hastings concerning the saturation of mutual information in multiparticle systems. The proof can also be interpreted as providing a limitation on the phenomenon of data hiding in quantum states.
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Exponential Decay of correlations implies area law
2015Co-Authors: Fernando G. S. L. Brandão, Michał HorodeckiAbstract:We prove that a finite correlation length, i.e., Exponential Decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is Exponential in the correlation length of the state, thus reproducing as a particular case Hastings’s proof of an area law for groundstates of 1D gapped Hamiltonians.
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an area law for entanglement from Exponential Decay of correlations
2013Co-Authors: Fernando G. S. L. Brandão, Michał HorodeckiAbstract:Area laws for entanglement in quantum many-body systems give useful information about their low-temperature behaviour and are tightly connected to the possibility of good numerical simulations. An intuition from quantum many-body physics suggests that an area law should hold whenever there is Exponential Decay of correlations in the system, a property found, for instance, in non-critical phases of matter. However, the existence of quantum data-hiding states—that is, states having very small correlations, yet a volume scaling of entanglement—was believed to be a serious obstruction to such an implication. Here we prove that notwithstanding the phenomenon of data hiding, one-dimensional quantum many-body states satisfying Exponential Decay of correlations always fulfil an area law. To obtain this result we combine several recent advances in quantum information theory, thus showing the usefulness of the field for addressing problems in other areas of physics.
Fernando G. S. L. Brandão - One of the best experts on this subject based on the ideXlab platform.
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Exponential Decay of Correlations Implies Area Law
2015Co-Authors: Fernando G. S. L. Brandão, Michał HorodeckiAbstract:We prove that a finite correlation length, i.e., Exponential Decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is Exponential in the correlation length of the state, thus reproducing as a particular case Hastings’s proof of an area law for groundstates of 1D gapped Hamiltonians. As a consequence, we show that 1D quantum states with Exponential Decay of correlations have an efficient classical approximate description as a matrix product state of polynomial bond dimension, thus giving an equivalence between injective matrix product states and states with a finite correlation length. The result can be seen as a rigorous justification, in one dimension, of the intuition that states with Exponential Decay of correlations, usually associated with non-critical phases of matter, are simple to describe. It also has implications for quantum computing: it shows that unless a pure state quantum computation involves states with long-range correlations, Decaying at most algebraically with the distance, it can be efficiently simulated classically. The proof relies on several previous tools from quantum information theory—including entanglement distillation protocols achieving the hashing bound, properties of single-shot smooth entropies, and the quantum substate theorem—and also on some newly developed ones. In particular we derive a new bound on correlations established by local random measurements, and we give a generalization to the max-entropy of a result of Hastings concerning the saturation of mutual information in multiparticle systems. The proof can also be interpreted as providing a limitation on the phenomenon of data hiding in quantum states.
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Exponential Decay of correlations implies area law
2015Co-Authors: Fernando G. S. L. Brandão, Michał HorodeckiAbstract:We prove that a finite correlation length, i.e., Exponential Decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is Exponential in the correlation length of the state, thus reproducing as a particular case Hastings’s proof of an area law for groundstates of 1D gapped Hamiltonians.
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an area law for entanglement from Exponential Decay of correlations
2013Co-Authors: Fernando G. S. L. Brandão, Michał HorodeckiAbstract:Area laws for entanglement in quantum many-body systems give useful information about their low-temperature behaviour and are tightly connected to the possibility of good numerical simulations. An intuition from quantum many-body physics suggests that an area law should hold whenever there is Exponential Decay of correlations in the system, a property found, for instance, in non-critical phases of matter. However, the existence of quantum data-hiding states—that is, states having very small correlations, yet a volume scaling of entanglement—was believed to be a serious obstruction to such an implication. Here we prove that notwithstanding the phenomenon of data hiding, one-dimensional quantum many-body states satisfying Exponential Decay of correlations always fulfil an area law. To obtain this result we combine several recent advances in quantum information theory, thus showing the usefulness of the field for addressing problems in other areas of physics.
Hailong Wang - One of the best experts on this subject based on the ideXlab platform.
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probing the spin pumping mechanism exchange coupling with Exponential Decay in y3fe5o12 barrier pt heterostructures
2013Co-Authors: Chunhui Du, T L Meyer, Fengyuan Yang, Patrick M. Woodward, Yong Pu, Hailong Wang, P C HammelAbstract:: It is widely believed that the mechanism for spin pumping in ferromagnet-nonmagnet bilayers is the exchange interaction between the ferromagnet and nonmagnetic material. We observe 1000-fold Exponential Decay of spin pumping from thin Y3Fe5O12 films to Pt across insulating barriers, from which Exponential Decay lengths of 0.16, 0.19, and 0.23 nm are extracted for oxide barriers having band gaps of 4.91, 3.40, and 2.36 eV, respectively. This archetypal signature of quantum tunneling through a barrier underscores the importance of exchange coupling for spin pumping and reveals its dependence on the characteristics of the barrier material.
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probing the spin pumping mechanism exchange coupling with Exponential Decay in y 3 fe 5 o 12 barrier pt heterostructures
2013Co-Authors: Hailong Wang, T L Meyer, Fengyuan Yang, Patrick M. Woodward, Pascal HammelAbstract:It is widely believed that the mechanism for spin pumping in ferromagnet-nonmagnet bilayers is the exchange interaction between the ferromagnet and nonmagnetic material. We observe 1000-fold Exponential Decay of spin pumping from thin ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ films to Pt across insulating barriers, from which Exponential Decay lengths of 0.16, 0.19, and 0.23 nm are extracted for oxide barriers having band gaps of 4.91, 3.40, and 2.36 eV, respectively. This archetypal signature of quantum tunneling through a barrier underscores the importance of exchange coupling for spin pumping and reveals its dependence on the characteristics of the barrier material.
