Heat flow in liquid helium in the transition region

1970 ◽  
Vol 315 (1521) ◽  
pp. 239-247 ◽  
Keyword(s):  
Heat Flow ◽  
Liquid Helium ◽  
Free Path ◽  
Transition Region ◽  
Cross Section ◽  
Low Temperatures ◽  
Circular Cross Section ◽  
Mean Free Path ◽  
Theoretical Treatment ◽  
Tube Radius

A theoretical treatment is given of heat flow at low temperatures in liquid helium, contained in a tube of circular cross-section. Results are obtained for arbitrary ratio of phonon–phonon collision mean free path to tube radius, and agree with experiment to within a few parts per cent.

Poiseuille gas flow in the transition regime I. Formulation of the general theory

1967 ◽  
Vol 301 (1467) ◽  
pp. 387-400 ◽  
Keyword(s):  
Cross Section ◽  
Gas Flow ◽  
Circular Cross Section ◽  
Collision Operator ◽  
Mean Free Path ◽  
Theoretical Treatment ◽  
Transition Regime ◽  
Velocity Dependence ◽  
Tube Radius ◽  
Intermolecular Collision

A theoretical treatment is given of gas flow along a tube of circular cross-section for arbitrary ratio of intermolecular collision mean free path to tube radius. A general solution is obtained of the Boltzmann equation which is valid for any intermolecular collision operator. The spatial variation of this solution is exhibited explicitly and its velocity dependence is given in terms of the solution of certain integral equations.

Experiments on the flow of heat in liquid helium below 0.7 °K

1958 ◽  
Vol 246 (1246) ◽  
pp. 390-405 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Liquid Helium ◽  
Free Path ◽  
Empirical Relation ◽  
Mean Free Path ◽  
Series Of Experiments ◽  
The Mean ◽  
Set Up ◽  
Low Pressures ◽  
Measured Thermal Conductivity

A series of experiments has been performed to study the steady flow of heat in liquid helium in tubes of diameter 0.05 to 1.0 cm at temperatures between 0.25 and 0.7 °K. The results are interpreted in terms of the flow of a gas of phonons, in which the mean free path λ varies with temperature, and may be either greater or less than the diameter of the tube d . When λ ≫ d the flow is limited by the scattering of the phonons at the walls, and the effect of the surface has been studied, but when λ ≪ d viscous flow is set up in which the measured thermal conductivity is increased above that for wall scattering. This behaviour is very similar to that observed in the flow of gases at low pressures, and by applying kinetic theory to the problem it can be shown that the mean free path of the phonons characterizing viscosity can be expressed by the empirical relation λ = 3.8 x 10 -3 T -4.3 cm. This result is inconsistent with the temperature dependence of λ as T -9 predicted theoretically by Landau & Khalatnikov (1949).

Light scattering by phonons in the presence of a heat flow

1968 ◽  
Vol 46 (24) ◽  
pp. 2843-2845 ◽  
Author(s):  
Allan Griffin
Keyword(s):  
Light Scattering ◽  
Heat Flow ◽  
Temperature Gradient ◽  
Free Path ◽  
Mean Free Path ◽  
Photon Scattering ◽  
The Mean ◽  
Anti Stokes

If the temperature in an insulating crystal decreases in the z-direction, there are more phonons with momentum qz > 0 than with qz < 0. The resulting difference between the Stokes and anti-Stokes Brillouin intensities is proportional to the mean free path of the phonon involved and to the temperature gradient. The effect should be observable by either neutron or photon scattering.

scholarly journals Metallicity and Superconductivity in Doped Strontium Titanate

2019 ◽  
Vol 10 (1) ◽  
pp. 25-44 ◽  
Author(s):  
Clément Collignon ◽  
Xiao Lin ◽  
Carl Willem Rischau ◽  
Benoît Fauqué ◽  
Kamran Behnia
Keyword(s):  
Liquid Helium ◽  
Free Path ◽  
Coulomb Interaction ◽  
Strontium Titanate ◽  
Room Temperature ◽  
Mean Free Path ◽  
Helium Temperature ◽  
Ongoing Research ◽  
Low Concentrations ◽  
Wide Gap

Strontium titanate is a wide-gap semiconductor avoiding a ferroelectric instability thanks to quantum fluctuations. This proximity leads to strong screening of static Coulomb interaction and paves the way for the emergence of a very dilute metal with extremely mobile carriers at liquid-helium temperature. Upon warming, mobility decreases by several orders of magnitude. Yet, metallicity persists above room temperature even when the apparent mean free path falls below the electron wavelength. The superconducting instability survives at exceptionally low concentrations and beyond the boundaries of Migdal–Eliashberg approximation. An intimate connection between dilute superconductivity and aborted ferroelectricity is widely suspected. In this review, we give a brief account of ongoing research on bulk strontium titanate as an insulator, a metal, and a superconductor.

The anomalous skin effect

1952 ◽  
Vol 215 (1123) ◽  
pp. 481-497 ◽  
Keyword(s):  
Free Path ◽  
Low Temperatures ◽  
Skin Effect ◽  
Mean Free Path ◽  
Skin Depth ◽  
Surface Conductance ◽  
High Frequencies ◽  
Surface Imperfections ◽  
Anomalous Skin Effect ◽  
Cadmium Lead

The anomalous skin effect arises in good conductors at low temperatures and high frequencies when the electronic mean free path becomes comparable with or greater than the classically calculated skin depth. Measurements have been made on a number of metals at frequencies of 1200 and 3600 Mc/s, and the form of variation of r. f. surface conductance with d. c. conductivity agrees well with that predicted theoretically by Reuter & Sondheimer, assuming that the electrons are scattered diffusely when they hit the surface of the metal. From the results, estimates are made of the effective value of σ/ l , the ratio of d. c. conductivity to mean free path, and hence of the free surface area of the occupied region of k -space. The estimate for copper agrees well with that expected theoretically; those for silver and gold are rather lower than the theoretical values. For the other metals investigated, tin, cadmium, lead and aluminium, no theoretical estimates are available. The results are very sensitive to the presence of surface imperfections; the effect of these is discussed.

Quantum Theory of Stokes Parameters for Thomson Scattering in a Magnetised Plasma

1991 ◽  
Vol 9 (2) ◽  
pp. 325-325
Author(s):  
Chih-Kang Chou ◽  
Hui-Hwa Chen
Keyword(s):  
Magnetic Field ◽  
Angular Distribution ◽  
Quantum Theory ◽  
Free Path ◽  
Strong Magnetic Field ◽  
Cross Section ◽  
Mean Free Path ◽  
Thomson Scattering ◽  
Stokes Parameters ◽  
Scattering Process

Extended abstractThomson scattering in pulsar magnetospheres has previously been studied by several authors. The most distinguishing feature is the fact that the super-strong magnetic field (B ~ 1012 G) greatly affects the Thomson scattering process, resulting in resonances in the scattering cross-section (Canuto et al. 1971; Herold 1979; Chou 1986; Daugherty and Harding 1986). The important consequences of these cyclotron resonances are the increase in the photon mean free path in the scattering regions, and strongly affecting the angular distribution, and polarisation properties of the scattered photons (Chou 1986; Chou et al. 1989).

Thermal Conductivity of Single-Crystal and Sintered RBa2Cu3O7 at low Temperatures

1987 ◽  
Vol 99 ◽  
Author(s):  
J. E. Graebner ◽  
L. F. Schneemeyer ◽  
R. J. Cava ◽  
J. V. Waszczak ◽  
E. A. Rietman
Keyword(s):  
Thermal Conductivity ◽  
Particle Size ◽  
Single Crystals ◽  
Free Path ◽  
Low Temperatures ◽  
Rayleigh Scattering ◽  
Resonant Scattering ◽  
Sintered Sample ◽  
Mean Free Path ◽  
Strong Scattering

ABSTRACTThe thermal conductivity k of micro-twinned single crystals of YBa2Cu3O7 and HoBa2Cu3O7 and a sintered sample of YBa2Cu3O7 has been measured for temperatures 0.03<T<5K. For the single crystals, k is small and varies as T1.8-1.9 This behavior resembles k for glassy insulators except for the lack of a plateau above IK. It is concluded that the thermal carriers are phonons with their mean free path limited by resonant scattering from tunneling entities, as in glasses. Suggestions for the location of tunneling systems are given. For the sinter, k is still smaller but does not follow a power law T-dependence. It is similar to other sintered ceramics with the same particle size, where the phonon mean free path is dominated by Rayleigh scattering from the particles. This strong scattering from the microstructure presumably masks the scattering from TS within each particle.

Effective phonon mean-free path and slip heat flow in rarefied phonon hydrodynamics

2015 ◽  
Vol 379 (40-41) ◽  
pp. 2652-2656 ◽  
Author(s):  
I. Carlomagno ◽  
A. Sellitto ◽  
D. Jou
Keyword(s):  
Heat Flow ◽  
Free Path ◽  
Mean Free Path

scholarly journals The mean free path of electrons in polar crystals

1939 ◽  
Vol 171 (947) ◽  
pp. 496-504 ◽  
Keyword(s):  
Free Path ◽  
Conduction Band ◽  
Thermal Energy ◽  
Low Temperatures ◽  
Energy Levels ◽  
Stoichiometric Composition ◽  
Mean Free Path ◽  
Polar Crystals ◽  
Absorption Of Light ◽  
The Mean

Polar crystals of stoichiometric composition at low temperatures are insulators of electricity. If, however, electrons are raised into the normally empty conduction band of energy levels, either through the absorption of light or the thermal energy of surrounding atoms, the crystal can conduct. The purpose of this note is to calculate the mean free path of such electrons, and hence their mobility (velocity of drift in unit field). The results obtained will be compared with experimental material obtained from semi-conductors and from substances which show photoconductivity.

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