Electron counting statistics and coherent states of electric current
Open accessAbstract
A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Within such an approach, counting charge without breaking the circuit is possible. As an application, we derive the counting statistics in a single channel conductor at finite temperature and bias. For a perfectly transmitting channel the counting distribution is Gaussian, both for zero-point fluctuations and at finite temperature. At constant bias and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics. Another application considered is the noise due to short current pulses that involve few electrons. We find the time-dependence of the driving potential that produces coherent noise-minimizing current pulses, and display analogies of such current states with quantum-mechanical coherent states.
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In higher-dimensional lattices, states obeying the Area law may still be amenable to classical simulation using tensor networks, density functional theories, or quantum Monte Carlo.
“In higher-dimensional lattices, states which obey the socalled 'Area law' [97], where quantum correlations are smaller than in generic states, may still be amenable to a classical simulation using state-of-the-art techniques such as tensor networks [77, 81, 82, 198, 199], Density Functional Theories [86], or Quantum Monte Carlo [75].”
From Can one trust quantum simulators? (2012) · cites this paper as [199]
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Can one trust quantum simulators?
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- Authors
- Levitov, L. S., Lee, H., & Lesovik, G. B.
- Affiliations
- Massachusetts Institute of Technology (US)
- Osipyan Institute of Solid State Physics RAS (RU)
- ORCID
- Levitov, Leonid S.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1996-10-01
- Volume
- 37
- Issue
- 10
- Pages
- 4845-4866
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W1965870922
- Cited by
- 949
- References
- 21
- Citations by year
- 2026: 18 · 2025: 35 · 2024: 36 · 2023: 39 · 2022: 31 · 2021: 43 · 2020: 54 · 2019: 57 · 2018: 43 · 2017: 32 · 2016: 42 · 2015: 47 · 2014: 47 · 2013: 46 · 2012: 38
- FWCI
- 1.92
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum transport, current measurement, spin precession, finite temperature, normal distribution, binomial distribution, vacuum fluctuations, current fluctuations, short current pulses, noise minimization, driving potential
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