To describe the interaction of the two level systems (TLSs) of an amorphous solid with arbitrary strain fields, we introduce a generalization of the standard interaction Hamiltonian. In this new model, the interaction strength depends on the orientation of the TLS with respect to the strain field through a 6×6 symmetric tensor of deformation potential parameters, [R]. Taking into account the isotropy of the amorphous solid, we deduce that [R] has only two independent parameters. We show how these two parameters can be calculated from experimental data and we prove that for any amorphous bulk material the average coupling of TLSs with longitudinal phonons is always stronger than the average coupling with transversal phonons (in standard notations, γ l > γt).PACS numbers: 63.50.+x, 61.43.Fs, 61.43.Er The thermal properties of dielectric crystals at low temperatures are well described by the Debye model. If the temperature is much smaller than the Debye temperature of the crystal, then the optical phonon modes are not excited and the only contribution to the heat capacity and heat conductivity comes from the acoustic phonons. In three dimensional (3D) systems, lowfrequency acoustic phonons have a linear dispersion relation, ω = c t,l k, where ω is the angular frequency, c t and c l are the transversal and longitudinal sound velocities, respectively, and k is the absolute value of the phonon's wavevector, k. This gives a specific heat proportional to the temperature to the power three (c V ∝ T 3 ).A good estimate for the heat conductivity, κ, is κ = 1 3 c V cl, where c is an average sound velocity and l is the phonon mean free path, which depends not only on the material, but also on the sample quality. Impurities or lattice defects, even at low concentration, reduce the phonon mean free path and in this way may decrease dramatically the heat conductivity. 1,2,3,4 As a result, the temperature dependence of the heat conductance is determined by the dependence of the phonon mean free path on its energy. Since such dependences can be very much different for different phonon scattering mechanisms, the resulting temperature dependence of κ can be in general rather complicated.In high-quality crystals of relatively small size and at sufficiently low temperature, the phonon mean free path may become comparable to or bigger than the crystal dimensions. In this case the phonons will scatter mainly at the surfaces and the mean free path is limited by the surface diffusivity and the geometrical features of the sample. 5 In this case l is independent of the phonon frequency and κ ∝ c V ∝ T 3 .Continuing to decrease the temperature and the size of the system, we get into the mesoscopic regime, where one or more dimensions of the system become comparable to the dominant phonons wavelength. Typically we find this regime in nanometer-size objects, at temperatures of a few Kelvins or less. At such scales, the phonon interaction with the surfaces becomes important, since it leads to coupling between different vibrational modes. Thi...
Nodal quasiparticles and their quantum interference effects in superconductors and magnets AIP Conf. Proc. 918, 308 (2007); 10.1063/1.2752000Quasiparticle charge imbalance, first-order phase transition and quantum criticality in ferromagnet∕superconductor∕ferromagnet double-tunnel junctions
I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. 67, 937, 1991) and I show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These inconsistencies appear when mutual exclusion statistics is manifested between different subspecies of particles in the system. In order to eliminate these inconsistencies, I introduce new mutual exclusion statistics parameters, which are proportional to the dimension of the Hilbert sub-space on which they act. These new definitions lead to properly defined particle distributions and thermodynamic properties. In another paper (arXiv:0710.0728) I show that fractional exclusion statistics manifested in general systems with interaction have these, physically consistent, statistics parameters.
Phonon modes and their dispersion relations in ultrathin homogeneous dielectric membranes are calculated using elasticity theory. The approach differs from the previous ones by a rigorous account of the effect of the film surfaces on the modes with different polarizations. We compute the heat capacity of membranes and the heat conductivity of narrow bridges cut out of such membranes, in a temperature range where the dimensions have a strong influence on the results. In the high-temperature regime we recover the three-dimensional bulk results. However, in the low-temperature limit the heat capacity C V is proportional to T (temperature), while the heat conductivity of narrow bridges is proportional to T 3/2 , leading to a thermal cutoff frequency f c = / C V ϰ T 1/2 .
We analyze heat conduction by phonons in ultrathin membranes by constructing a new theoretical framework which implies a crossover from a bulk three-dimensional phonon distribution into a quasitwo-dimensional distribution when the temperature is lowered. We calculate the corresponding changes in the relevant thermodynamic quantities. At the end we make a comparison to experimental data.[S0031-9007(98)07273-1]
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.