The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

Büttiker, Μ.

doi:10.1007/978-3-540-73473-4_9

Cited by 5 publications

(10 citation statements)

References 55 publications

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“…For a mesoscopic sample coupled to leads, this scattering region is by definition the sample [27]. So, partial density of states (PDOS) of a mesoscopic sample is defined as [27] ρ(α,…”

Section: Injectance and Friedel Sum Rulementioning

confidence: 99%

“…PDOS are quite physical and manifests in a variety of experimental situations in mesoscopic systems [25,26,27]. For example, decoherence in the scattering region is proportional to the time electrons spend in the scattering region.…”

Section: Injectance and Friedel Sum Rulementioning

confidence: 99%

“…As another example, consider a sinusoidal voltage of frequency ω, V β (ω) applied at incident lead β. The current measured at lead α will be [27],…”

Section: Injectance and Friedel Sum Rulementioning

confidence: 99%

“…Ref. [40] did conclude that ρ(α, β) or τ (α, β) are physical and later on found to be so [27]. But regimes where they become negative has not received any theoretical attention beyond 1D.…”

Section: Injectance and Friedel Sum Rulementioning

confidence: 99%

“…However, in all these studies there is no reference to well established theorems and results on discontinuous phase changes and lapses known for a long time in the community that studies classical wave trains [21,22]. Such phase changes are still very important in mesoscopic physics as they are related to breakdown of parity effect [8], interpretation of Friedel sum rule (FSR) [10,13,15,23], relation to partial density of states (PDOS) [20,24,25,26,27,28], etc. that determine the thermodynamic properties of a mesoscopic system which is absent in case of classical waves.…”

Section: Introductionmentioning

confidence: 99%

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Negative partial density of states in mesoscopic systems

Satpathi

Deo

2016

Annals of Physics

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Since the experimental observation of quantum mechanical scattering phase shift in mesoscopic systems, several aspects of it has not yet been understood. The experimental observations has also accentuated many theoretical problems related to Friedel sum rule and negativity of partial density of states. We address these problems using the concepts of Argand diagram and Burgers circuit. We can prove the possibility of negative partial density of states in mesoscopic systems. Such a conclusive and general evidence cannot be given in one, two or three dimensions. We can show a general connection between phase drops and exactness of semi classical Friedel sum rule. We also show Argand diagram for a scattering matrix element can be of few classes based on their topology and all observations can be classified accordingly.

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“…For a mesoscopic sample coupled to leads, this scattering region is by definition the sample [27]. So, partial density of states (PDOS) of a mesoscopic sample is defined as [27] ρ(α,…”

Section: Injectance and Friedel Sum Rulementioning

confidence: 99%

Section: Injectance and Friedel Sum Rulementioning

confidence: 99%

“…As another example, consider a sinusoidal voltage of frequency ω, V β (ω) applied at incident lead β. The current measured at lead α will be [27],…”

Section: Injectance and Friedel Sum Rulementioning

confidence: 99%

Section: Injectance and Friedel Sum Rulementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Negative partial density of states in mesoscopic systems

Satpathi

Deo

2016

Annals of Physics

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Wigner time delay and related concepts: Application to transport in coherent conductors

Texier

2016

Physica E: Low-dimensional Systems and Nanostructures

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The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems ; the case of disorder in 1D with a chiral symmetry is discussed and the relation with exponential functionals of the Brownian motion underlined. Another approach for the analysis of time delay statistics is the random matrix approach, from which we review few results. As a pratical illustration, we briefly outline a theory of non-linear transport and AC transport developed by Büttiker and coworkers, where the concept of Wigner-Smith time delay matrix is a central piece allowing to describe screening properties in out-of-equilibrium coherent conductors.The published version has been updated.

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Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

Grabsch¹,

Savin²,

Texier³

2018

J. Phys. A: Math. Theor.

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We consider wave propagation in a complex structure coupled to a finite number N of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the concept of time delays, related to the energy (or frequency) derivative of the scattering matrix S. We develop a random matrix approach to study the statistical properties of the symmetrised Wigner-Smith time-delay matrix Q s = −i S −1/2 ∂ ε S S −1/2 , and obtain the joint distribution of S and Q s for the system with non-ideal contacts, characterised by a finite transmission probability (per channel) 0 < T 1. We derive two representations of the distribution of Q s in terms of matrix integrals specified by the Dyson symmetry index β = 1, 2, 4 (the general case of unequally coupled channels is also discussed). We apply this to the Wigner time delay τ W = (1/N ) tr Q s , which is an important quantity providing the density of states of the open system. Using the obtained results, we determine the distribution P N,β (τ ) of the Wigner time delay in the weak coupling limit N T 1 and identify the following three regimes. (i) The large deviations at small times (measured in units of the Heisenberg time) are characterised by the limiting behaviour P N,β (τ ) ∼ τ −βN 2 /2−3/2 exp − βN T /(8τ ) for τ T .(ii) The distribution shows the universal τ −3/2 behaviour in some intermediate range T τ 1/(T N 2 ). (iii) It has a power law decay P N,β (τ ) ∼ T 2 N 3 (T N 2 τ ) −2−βN/2 for large τ 1/(T N 2 ).

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The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

Cited by 5 publications

References 55 publications

Negative partial density of states in mesoscopic systems

Negative partial density of states in mesoscopic systems

Wigner time delay and related concepts: Application to transport in coherent conductors

Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

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