Bulk-edge correspondence of classical diffusion phenomena

Yoshida, Tsuneya; Hatsugai, Yasuhiro

doi:10.1038/s41598-020-80180-w

Cited by 35 publications

(20 citation statements)

References 48 publications

(54 reference statements)

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“…Recently, the importance of edge states was also pointed out in diffusion phenomena [22]. This implies that edge states would have a large effect not only on propagating wave systems but also diffusive systems such as heat conduction.…”

Section: Introductionmentioning

confidence: 97%

Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath

Makino,

Fukui,

Yoshida

et al. 2021

Preprint

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We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period a. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalising the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short time regime, which is estimated to be t < 10 −2 s for a ∼ 10 −3 m system and t < 1s for a ∼ 10 −2 m system composed of two kinds of familiar metals such as titanium, zirconium and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high energy edge states also contribute to very rapid heat conduction in a very short time regime.

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Section: Introductionmentioning

confidence: 97%

Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath

Makino,

Fukui,

Yoshida

et al. 2021

Preprint

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“…Second, PT-symmetric quantum walks and related topological properties have only been studied by the bulk–boundary corres- pondence [ 25 , 26 , 27 ], while the characterization of bulk property is thus far absent, such as diffusion property and Shannon entropy. Until very recently, the connection between diffusion property and topological property have been studied for skyrmions [ 28 ], and the relation between diffusion phenomenon and bulk–edge correspondence has been discussed [ 29 ].…”

Section: Introductionmentioning

confidence: 99%

Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks

Tian

Liu

Luo

2021

Entropy

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Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk–boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity–time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems.

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“…Dissipative couplings play a central role in superconducting circuits, ultracold atoms, and photonics, where they are used for reservoir engineering 17 , laser mode-locking 18,19 , and quantum and photonic computing [20][21][22] . Several recent studies have proposed combining dissipative and conservative couplings to enable time-reversal symmetry breaking interactions 23 and to provide novel means to induce nontrivial topological invariants 6,[24][25][26][27] . These proposals suggest that dissipative coupling, like nonlinear [28][29][30] and non-Hermitian [31][32][33][34] phenomena, may enable new topological phases and topology-inspired technologies for quantum and classical applications.…”

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confidence: 99%