Crossover from diffusive to ballistic transport in periodic quantum maps

Wójcik, Daniel K.; Dorfman, J. R.

doi:10.1016/j.physd.2003.09.012

Cited by 15 publications

(12 citation statements)

References 50 publications

(116 reference statements)

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“…As pointed out in Ref. [35], this scaling reflects universal fluctuations of the quasi-energy spectra and eigenfunctions of the system. To the best of our knowledge, this effect has not been discussed in connection with the QKR.…”

Section: Frequencies ω < ∼ ∆supporting

confidence: 54%

Theory of localization and resonance phenomena in the quantum kicked rotor

Tian

Altland²

2010

New J. Phys.

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Abstract. We present an analytic theory of quantum interference and Anderson localization in the quantum kicked rotor (QKR). The behavior of the system is known to depend sensitively on the value of its effective Planck's constant,h. We show here that for rational values ofh/(4π) = p/q, it bears a similarity to a disordered metallic ring of circumference q and threaded by an Aharonov-Bohm flux. Building on this correspondence, we obtain quantitative results for the timedependent behavior of the QKR kinetic energy, E(t) (this is an observable that sensitively probes the system's localization properties). For values of q smaller than the localization length ξ , we obtain scaling E(t) ∼ t 2 , where = 2π/q is the quasi-energy level spacing on the ring. This scaling is indicative of a long time dynamics that is neither localized nor diffusive. For larger values q ξ , the functions E(t) → ξ 2 saturate (up to exponentially small corrections ∼ exp(−q/ξ )), thus reflecting essentially localized behavior.

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Section: Frequencies ω < ∼ ∆supporting

confidence: 54%

Theory of localization and resonance phenomena in the quantum kicked rotor

Tian

Altland²

2010

New J. Phys.

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“…This has been remarkably demonstrated for the quantum multibaker map in Ref. [14]. In order for diffusion to persist up to arbitrarily long times, the quantum system must contain infinitely many degrees of freedom, for instance, by the coupling with some environment in the subsystem-plusreservoir approach we adopt in the present paper.…”

Section: Introductionmentioning

confidence: 72%

Exactly Solvable Model of Quantum Diffusion

Esposito

Gaspard

2005

J Stat Phys

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We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wavenumber contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. On the other hand, an analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling.

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“…This consequence opportunely reflects the equivalent mobility contributed by the drift and diffusion effects similarly to a leverage. However, the drift effect at the smallest channel-length device is unapparent, and the diffusion effect is dominant, similarly to ballistic carrier behavior [28,29]. This phenomenon at L mask = 33 nm is similar to the depletion effect coming from the channel punch-through, not the enhancement effect [1].…”

Section: Discussionmentioning

confidence: 99%

Channel Mobility Model of Nano-Node MOSFETs Incorporating Drain-and-Gate Electric Fields

Chao

Huang

et al. 2022

Crystals

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A novel channel mobility model with two-dimensional (2D) aspect is presented covering the effects of source/drain voltage (VDS) and gate voltage (VGS), and incorporating the drift and diffusion current on the surface channel at the nano-node level, at the 28-nm node. The effect of the diffusion current is satisfactory to describe the behavior of the drive current in nano-node MOSFETs under the operations of two-dimensional electrical fields. This breakthrough in the model’s establishment opens up the integrity of long-and-short channel devices. By introducing the variables VDS and VGS, the mixed drift and diffusion current model effectively and meaningfully demonstrates the drive current of MOSFETs under the operation of horizontal, vertical, or 2D electrical fields. When comparing the simulated and experimental consequences, the electrical performance is impressive. The error between the simulation and experiment is less than 0.3%, better than the empirical adjustment required to issue a set of drive current models.

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Crossover from diffusive to ballistic transport in periodic quantum maps

Cited by 15 publications

References 50 publications

Theory of localization and resonance phenomena in the quantum kicked rotor

Theory of localization and resonance phenomena in the quantum kicked rotor

Exactly Solvable Model of Quantum Diffusion

Channel Mobility Model of Nano-Node MOSFETs Incorporating Drain-and-Gate Electric Fields

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