Energy Density and Current in Quantum Theory

Mathews, W. N.

doi:10.1119/1.1987650

Cited by 10 publications

(11 citation statements)

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“…( 28) and there is a priori no physical but only technical grounds to favor one choice over the others, as noticed in Ref. 83 .…”

Section: Energy Density Local Energy Current and Power Densitymentioning

confidence: 99%

“…Our definition (29) corresponds to the discretized version on a lattice of the energy density of the second kind put forward in Ref. 83 , which leads to a symmetrized energy current density (I E ji below). The same definition has been used in e.g.…”

Section: Energy Density Local Energy Current and Power Densitymentioning

confidence: 99%

“…To be fully precise, Refs. 38,63,83,84 dealt with the inherent ambiguity in the definition of the Hamiltonian density operator Ĥi (so as Ĥ = i Ĥi ) but the same discussion holds for εi .…”

Section: Energy Density Local Energy Current and Power Densitymentioning

confidence: 99%

“…The proof goes in two steps. We start from the one-body problem in the continuum 83 and discretize on a lattice the probablity density ρ N (r, t) = ψ * ψ, the probability current density j N (r, t) = Re[ψ * vψ], the energy density ρ E (r, t) = Re[ψ * εψ], and the (symmetrized) energy current density j E (r, t) = 1 2 Re[(εψ) * (vψ) + ψ * vεψ], where ψ(r, t) is the particle wave-function, v = (−i ∇ − eA)/m the velocity operator and ε(r, v, t) the energy operator of the one-body continuous problem. Those quantities satisfy the continuity equations dρ N /dt + ∇ • j N = 0 and dρ E /dt + ∇ • j E = e j N • E. Thereby we obtain the onebody contributions of ρ N i , I N ij , ρ E i , and…”

Section: Appendix D: Resonant Level Model Within the Non Equilibrium ...mentioning

confidence: 99%

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Simulating time-dependent thermoelectric transport in quantum systems

Slimane,

Reck,

Fleury

2019

Preprint

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We put forward a gauge-invariant theoretical framework for studying time-resolved thermoelectric transport in an arbitrary multiterminal electronic quantum system described by a non-interacting tight-binding model. The system is driven out of equilibrium by an external time-dependent electromagnetic field (switched on at time t0) and possibly by static temperature or electrochemical potential biases applied (from the remote past) between the electronic reservoirs. Numerical simulations are conducted by extending to energy transport the wave-function approach developed by Gaury et al. and implemented in the t-Kwant library. We provide a module that allows us to compute the time-resolved heat currents and powers in addition to the (already implemented) charge currents, and thus to simulate dynamical thermoelectric transport through realistic devices, when electron-electron and electron-phonon interactions can be neglected. We apply our method to the non-interacting Resonant Level Model and verify that we recover the results reported in the literature for the time-resolved heat currents in the expected limits. Finally, we showcase the versatility of the library by simulating dynamical thermal transport in a Quantum Point Contact subjected to voltage pulses.

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“…( 28) and there is a priori no physical but only technical grounds to favor one choice over the others, as noticed in Ref. 83 .…”

Section: Energy Density Local Energy Current and Power Densitymentioning

confidence: 99%

Section: Energy Density Local Energy Current and Power Densitymentioning

confidence: 99%

Section: Energy Density Local Energy Current and Power Densitymentioning

confidence: 99%

Section: Appendix D: Resonant Level Model Within the Non Equilibrium ...mentioning

confidence: 99%

See 2 more Smart Citations

Simulating time-dependent thermoelectric transport in quantum systems

Slimane,

Reck,

Fleury

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…To show explicitly that this quantity is real, one needs to make a set of transformations on the right hand side of this equation: Integrating by parts over both times and using Eq. (25). Then, we arrive at an equation which is the complex conjugate of Eq.…”

Section: E Heat Noise In Terms Of the Excess-correlation Matrixmentioning

confidence: 99%

Heat and charge transport measurements to access single‐electron quantum characteristics

Moskalets

Haack

2016

Physica Status Solidi (b)

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In the framework of the Floquet scattering‐matrix theory, we discuss how electrical and heat currents accessible in mesoscopics are related to the state of excitations injected by a single‐electron source into an electron waveguide. We put forward an interpretation of a single‐particle heat current, which differs essentially from that of an electrical current. We show that the knowledge of both a time‐dependent electrical current and a time‐dependent heat current allows the full reconstruction of a single‐electron wave function. In addition, we compare electrical and heat shot noise caused by splitting of a regular stream of single‐electron excitations. If only one stream impinges on a wave splitter, the heat shot noise is proportional to the well‐known expression of the charge shot noise, reflecting the partitioning of the incoming single particles. The situation differs when two electronic streams collide at the wave splitter. The shot noise suppression, due to the Pauli exclusion principle, is governed by different overlap integrals in the case of charge and of heat.

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Quasiparticle, charge, and energy conservation in weak‐coupling superconductors

Mathews

1978

Physica Status Solidi (b)

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The conservation of quasiparticles, electric charge, and energy in weak-couplihg superconductors is discussed and correlated with the interpretation of the quasiparticles as particle and hole excitations. The formulation employed is that of the Bogolyubov-de Gennes equations. In the absence of spin-dependent interactions these equations are written in the form of a time-dependent Schrodinger equation with a two-component wave function and a two-by-two matrix Hamiltonian. Accordingly, the desired conservation laws are discussed on much the same basis as in ordinary quantum theory. The generalization to permit nonlocal quasiparticle and pair potentials and spin-dependent interactions is briefly presented.Die Konservierung von Quasipartikeln, elektrischer Ladung und Energie in schwach-gekoppelten Supraleitern wird besprochen und mit der Auslegung von Quasipartikeln als Partikel-und Lijcheranregungen in ffbereinstimmung gebracht. Die angewandten Formulierungen sind diejenigen der Bogolyubov-de Gennes-Gleichungen. Ohne spimbhiingige Wechselwirkungen werden diese Gleichungen als eine zeitabhiingige Schrodinger-Gleichung betrachtet, die als Wellenfunktion mit zwei Komponenten und einer Hamilton-Matrix vom Rang awei behandelt werden. Entsprechend werden die Gesetze der Konservierung auf der gleichen Basis wie in der iiblichen Quantentheorie besprochen. Die Verallgemeinerung auf nichtlokale Quasipartikelpotentiale und Paarpotentiale und auf spinabhiingige Wechselwirkungen wird kura besprochen.

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Energy Density and Current in Quantum Theory

Cited by 10 publications

References 0 publications

Simulating time-dependent thermoelectric transport in quantum systems

Simulating time-dependent thermoelectric transport in quantum systems

Heat and charge transport measurements to access single‐electron quantum characteristics

Quasiparticle, charge, and energy conservation in weak‐coupling superconductors

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