Anharmonic effects in librational motion of N2-type crystals

Antsygina, T. N.; Slusarev, V. A.; Freǐman, Yu. A.; Эренбург, А. И.

doi:10.1007/bf00681448

Cited by 23 publications

(14 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It therefore captures all the statistical properties of τ (k) once the distribution of ξ(x) is known. Denoting by x c the correlation length of V (x) and assuming that x c and k −1 are the smallest length scales of the system, then it was proven in [1] that the variable ξ(x) is a Brownian motion of the form:…”

mentioning

confidence: 99%

Universality of the Wigner Time Delay Distribution for One-Dimensional Random Potentials

1999

View full text Add to dashboard Cite

We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out on samples whose sizes are large compared to the localisation length (localised regime). The case of small samples is also discussed (ballistic regime). We provide a physical argument which explains in a quantitative way the origin of the exponential divergence of the moments. The occurence of a log-normal tail for finite size systems is analysed. Finally, we present exact results in the low energy limit which clearly show a departure from the universal behaviour.The problem of quantum scattering by chaotic or disordered systems is encountered in many fields ranging from atomic or molecular physics as well as in the scattering of electromagnetic microwaves. Some properties of the scattering process are well captured through the concept of time delay. This quantity, which goes back to Eisenbud and Wigner [7], is related to the time spent in the interaction region by a wave packet of energy peaked at E. It can be expressed in terms of the derivative of the S matrix with respect to the energy. In the context of chaotic scattering the approach based on random matrix theory (RMT) provides a statistical description of the time delays. This problem was first studied by a supersymmetric approach [11] and in [13] by using a statistical analysis. This latter work provides a derivation for the one channel case for the different universality classes. Recently it served as a starting point for [3] where the N channel distribution is shown to be given by the Laguerre ensemble of RMT. In spite of its success, such a description by RMT is not entirely satisfactory, in particular it does not apply to strictly one-dimensional systems [10] for which strong localisation effects occur. Furthermore it does not shed much light on the physical mechanisms which are responsible for the universal distribution. In this work we explore another approach by considering the scattering by a one-dimensional random potential. In this case the existence of universal distributions was first conjectured in [6] on the basis of a comparative study of two different models. This was further supported by [16] where the random potential is still of a different kind.The purpose of this letter is to present a new derivation that accounts for the universality and also to provide a physical picture that explains the origin of the algebraic tail of the distribution in terms of resonances. Further details will be given elsewhere [22]. To begin with, let us briefly recall the model. We consider the Schrödinger equation on the half line x 0:

show abstract

mentioning

confidence: 99%

Universality of the Wigner Time Delay Distribution for One-Dimensional Random Potentials

1999

View full text Add to dashboard Cite

show abstract

“…19) were obtained for relaxation times, which took into account the phonon polarization in different processes of phonon decay/production (l«l+t, l«t+t, etc.) as a function of temperature and frequency.…”

Section: Resultsmentioning

confidence: 99%

“…Usually, the polarization-averaged relaxation rate for N-processes is obtained from the analysis of thermal conductivity experimental results for cryocrystals. The inverse relaxation time t w N T -1 ( , ) is therefore found using expressions with fitting parameters [11,14,[18][19][20][21]. However, comparison with low-temperature experiment is most often made using Eq.…”

Section: Resultsmentioning

confidence: 99%

“…To analyze our experimental results, we used Eq. (7) and other expressions [11,19,20] as trial functions.…”

Section: Resultsmentioning

confidence: 99%

“…(10) The intensity of N-processes can be expressed in terms of the characteristics of the crystal [21]. To estimate the intensity of normal phonon scattering, we used for t N -1 the expression [19][20][21] …”

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

The peculiarities of heat transfer in CO2 and N2O solids at low temperatures

Sumarokov

Stachowiak

Jeżowski

2007

Low Temperature Physics

View full text Add to dashboard Cite

The thermal conductivities of CO 2 and N 2 O solids have been investigated in the low-temperature range 1-40 K. The thermal conductivities of CO 2 and N 2 O are large compared with those of simple molecular crystals such as N 2 , CO, or O 2 in the whole investigated temperature range. Analysis of the experimental data by the Callaway method shows that relatively large size of crystalline grains, low density of dislocations and weak phonon-phonon interaction might be the reasons for the good thermal conduction in these crystals at temperatures near the maxima. A comparison between calculated values of the intensity of normal phonon scattering processes and experiment gives evidence that in N 2 O there is an additional (in comparison with CO 2 ) giant scattering of phonons. This scattering is described in the frameworks of soft potential model by the resonance phonon scattering on tunnel states and low-energy vibratons.PACS: 63.20.-e Phonons in crystal lattices; 66.70.+f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves; 44.10.+i Heat conduction.

show abstract

Coherent transport and nonlocality in mesoscopic SNS junctions: anomalous magnetic interference patterns

Barzykin

Zagoskin

1999

Superlattices and Microstructures

View full text Add to dashboard Cite

We show that in ballistic mesoscopic SNS junctions the period of critical current versus magnetic flux dependence (magnetic interference pattern), I c ( ), changes continuously and nonmonotonically from 0 to 2 0 as the length-to-width ratio of the junction grows, or temperature drops. In diffusive mesoscopic junctions the change is even more drastic, with the first zero of I c ( ) appearing at 3 0 .The effect is a manifestation of nonlocal relation between the supercurrent density and superfluid velocity in the normal part of the system, with the characteristic scale, the normal metal coherence length, and arises due to restriction of the quasiparticle phase space near the lateral boundaries of the junction. It explains the 2 0 -periodicity recently observed by Heida et al. [Phys. Rev. B57, R5618 (1998)]. We obtained explicit analytical expressions for the magnetic interference pattern for a junction with an arbitrary length-to-width ratio. Experiments are proposed to directly observe the 0 → 2 0 -and 0 → 3 0 -transitions. c 1999 Academic Press Key words: nonlocality, mesoscopic, Josephson.It is well established that the electrodynamics of the superconductors is nonlocal on the scale of ξ 0 [1, 2], and so is the current-phase relation (since vector potential and superconducting phase both enter through one gauge-invariant, combination superfluid velocity). In the normal layer of an SNS system, the place of ξ 0 is taken by the normal metal coherence length, ξ T = v F /2πk B T (in the ballistic limit, L l i , where l i is the impurity scattering length),is the diffusion constant of electrons in the dirty metal [3,4]. This length can obviously greatly exceed ξ 0 at low enough temperatures, and is limited only by the inelastic scattering length in the system, l φ , which also diverges as T → 0. (The latter gives the scale of classical nonlocality in mesoscopic systems, related to †

show abstract

Anharmonic effects in librational motion of N2-type crystals

Cited by 23 publications

References 47 publications

Universality of the Wigner Time Delay Distribution for One-Dimensional Random Potentials

Universality of the Wigner Time Delay Distribution for One-Dimensional Random Potentials

The peculiarities of heat transfer in CO2 and N2O solids at low temperatures

Coherent transport and nonlocality in mesoscopic SNS junctions: anomalous magnetic interference patterns

Contact Info

Product

Resources

About