Entanglement and the foundations of statistical mechanics

Popescu, Sandu; Short, Anthony; Winter, Andreas

doi:10.1038/nphys444

Cited by 1,035 publications

(1,544 citation statements)

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“…To be precise, these coefficients are chosen according to a Gaussian distribution with zero mean. Thus, the pure state |ψ is chosen according to the unitary invariant Haar measure [68,69] and, according to typicality [70][71][72][73][74][75], a representative of the statistical ensemble. The pure state |ψ , and each |ψ N , correspond to the limit of high temperatures β → 0.…”

Section: Dynamical Quantum Typicality a Conceptmentioning

confidence: 99%

Finite-temperature charge transport in the one-dimensional Hubbard model

et al. 2015

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We study the charge conductivity of the one-dimensional repulsive Hubbard model at finite temperature using the method of dynamical quantum typicality, focusing at half filling. This numerical approach allows us to obtain current autocorrelation functions from systems with as many as 18 sites, way beyond the range of standard exact diagonalization. Our data clearly suggest that the charge Drude weight vanishes with a power law as a function of system size. The low-frequency dependence of the conductivity is consistent with a finite dc value and thus with diffusion, despite large finite-size effects. Furthermore, we consider the mass-imbalanced Hubbard model for which the charge Drude weight decays exponentially with system size, as expected for a non-integrable model. We analyze the conductivity and diffusion constant as a function of the mass imbalance and we observe that the conductivity of the lighter component decreases exponentially fast with the mass-imbalance ratio. While in the extreme limit of immobile heavy particles, the Falicov-Kimball model, there is an effective Anderson-localization mechanism leading to a vanishing conductivity of the lighter species, we resolve finite conductivities for an inverse mass ratio of η 0.3.

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Section: Dynamical Quantum Typicality a Conceptmentioning

confidence: 99%

Finite-temperature charge transport in the one-dimensional Hubbard model

et al. 2015

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“…[17]) ‡ to get the partial fraction decomposition of the function in Eq. (22). This way one expresses the ‡ LCV whishes to thank Pierre-Yves Gaillard for pointing out this connection.…”

Section: General Casementioning

confidence: 99%

“…The Lipschitz constant of the function A (φ) = φ|A|φ has been calculated in [22] Appendix A (see also [4]) where it has been shown that |A (φ 1 ) − A (φ 2 )| ≤ 2 A op ||φ 1 − |φ 2 | where A op is the operator norm of A (maximum singular value). In our case A = |1 1| so A op = 1 and we may take η = 2 in eq.…”

Section: Random Guessmentioning

confidence: 99%

“…In this case averaging over the quantum states amounts to perform the time average 1/T T 0 a(t)dt. Another possibility that recently gained relevance for the foundation of statistical mechanics [4] is to consider ψ|A|ψ and let |ψ vary over the full unit sphere of the, say d-dimensional, Hilbert space space. This manifold is transitively acted upon by the group of all d × d unitary matrices U (d) and therefore inherits a natural invariant measure from the unique group-theoretic invariant measure over U (d) i.e., the Haar measure.…”

Section: Introductionmentioning

confidence: 99%

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Probability density of quantum expectation values

Venuti

Zanardi

2013

Physics Letters A

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Abstract. We consider the quantum expectation value A = ψ|A|ψ of an observable A over the state |ψ . We derive the exact probability distribution of A seen as a random variable when |ψ varies over the set of all pure states equipped with the Haar-induced measure. The probability density is obtained with elementary means by computing its characteristic function, both for nondegenerate and degenerate observables. To illustrate our results we compare the exact predictions for few concrete examples with the concentration bounds obtained using Levy's lemma. Finally we comment on the relevance of the central limit theorem and draw some results on an alternative statistical mechanics based on the uniform measure on the energy shell.arXiv:1202.4810v3 [quant-ph]

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“…is an exact bound for the random Lévy random processes that form the (canonical) basis of our approach, and this formally sets the accuracy of approximating the electron spin correlators via a system consisting of N = 8 nuclei [53]. Furthermore, the values of the Hyperfine interaction couplings in (7) can be randomly picked between 0 μeV and 0.09873 μeV (as we did for this analysis) without significantly impacting on the accuracy of the spin correlator measurements, i.e., the dominant source of error is the size of the spin bath which yields an error of 6%.…”

Section: Discrete Fourier Transformmentioning

confidence: 99%

The Decoherence of the Electron Spin and Meta-Stability of 13C Nuclear Spins in Diamond

Crompton

2011

Entropy

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Following the recent successful experimental manipulation of entangled 13 C atoms on the surface of Diamond, we calculate the decoherence of the electron spin in Nitrogen Vacancy NV centers of Diamond via a nonperturbative treatment of the time-dependent Greens function of a Central-Spin model in order to identify the Replica Symmetry Breaking mechanism associated with intersystem mixing between the m s = 0 sublevel of the 3 A 2 and 1 A 1 states of the NV − centers, which we identify as mediated via the meta-stability of 13 C nuclei bath processes in our calculations. Rather than the standard exciton-based calculation scheme used for quantum dots, we argue that a new scheme is needed to formally treat the Replica Symmetry Breaking of the 3 A 2 → 3 E excitations of the NV − centers, which we define by extending the existing Generalized Master Equation formalism via the use of fractional time derivatives. Our calculations allow us to accurately quantify the dangerously irrelevant scaling associated with the Replica Symmetry Breaking and provide an explanation for the experimentally observed room temperature stability of Diamond for Quantum Computing applications.

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Entanglement and the foundations of statistical mechanics

Cited by 1,035 publications

References 20 publications

Finite-temperature charge transport in the one-dimensional Hubbard model

Finite-temperature charge transport in the one-dimensional Hubbard model

Probability density of quantum expectation values

The Decoherence of the Electron Spin and Meta-Stability of 13C Nuclear Spins in Diamond

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