Energy Diffusion in Harmonic System with Conservative Noise

Basile, Giada; Olla, Stefano

doi:10.1007/s10955-013-0908-4

Cited by 11 publications

(26 citation statements)

References 30 publications

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“…This condition can be shown to be satisfied by W (x) in (13). We also note that (63) can be written as…”

Section: Luttinger Model With An External Field: Proof Of Theorem 21mentioning

confidence: 85%

“…To anticipate the properties of a final steady state in this set-up we consider first a system of length L > 0 in contact with infinite reservoirs at its left and right boundaries with different fixed chemical potentials or temperatures (µ L , T L ) and (µ R , T R ), respectively. The coupling between system and reservoirs is done stochastically for classical systems [10][11][12][13][14][15], and for quantum systems one uses Lindblad-type operators [7][8][9]16]. Such a system will in general approach a steady state for fixed L. We can then define the electrical conductivity σ as the ratio of the steady particle current I to the average gradient (µ L − µ R ) L:…”

Section: Introductionmentioning

confidence: 99%

“…In this case the system obeys Fourier's law. This has been shown, so far, only for classical systems with non-momentum conserving stochasticity in the bulk dynamics [13,14].2. α = 1 (perfect conductivity).…”

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confidence: 96%

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Steady States and Universal Conductance in a Quenched Luttinger Model

Langmann

Lebowitz

Mastropietro

et al. 2016

Commun. Math. Phys.

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We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian H λ with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian H λ ′ which differs from H λ by the strength of the interaction. Asymptotically in time, as t → ∞, after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference µ + − µ − between right-(+) and left-(−) moving fermions obtained from the two-point correlation function. Both I and µ + − µ − depend on λ and λ ′ . Only for the case λ = λ ′ = 0 does µ + − µ − equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, G = I (µ + − µ − ), has a universal value equal to the conductance quantum e 2 h for the spinless case.

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“…This condition can be shown to be satisfied by W (x) in (13). We also note that (63) can be written as…”

Section: Luttinger Model With An External Field: Proof Of Theorem 21mentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

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Steady States and Universal Conductance in a Quenched Luttinger Model

Langmann

Lebowitz

Mastropietro

et al. 2016

Commun. Math. Phys.

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“…By general probabilistic arguments, one expects that this distribution satisfies a partial differential equation as in (10) [27], which our results confirm. Previous works deriving diffusion from static impurities in microscopic models using precise mathematical arguments include [33][34][35] for classical systems and [36] for a noninteracting quantum system. As far as we know, there are no such previous rigorous results for interacting quantum systems.…”

mentioning

confidence: 99%

Diffusive Heat Waves in Random Conformal Field Theory

Langmann

Moosavi

2019

Phys. Rev. Lett.

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We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in onedimensional quantum many-body systems with certain static random impurities. We present exact analytical results that elucidate how purely ballistic heat waves in standard CFT can acquire normal and anomalous diffusive contributions due to our impurities. Our results include impurity-averaged Green's functions describing the time evolution of the energy density and the heat current, and an explicit formula for the thermal conductivity that, in addition to a universal Drude peak, has a nontrivial real regular contribution that depends on details of the impurities.

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“…In reality the bodies are in contact with the exterior that can be thought as a thermal reservoir at some given temperature. This is, of course, an extremely important 6 Note that here we abuse notation and use P 0 , E 0 to designate, respectively, the measure and expectation in path space determined by the initial measure (that we also called P 0 , hence the abuse). Of course, in the deterministic case all is determined by the initial condition, but in the random case the measure in path space describes also the randomness of the dynamics.…”

Section: The Models: Microscopic Dynamicsmentioning

confidence: 99%