*Armando Francesco Borghesani*

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199213603
- eISBN:
- 9780191707421
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213603.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

In liquid helium, an electron is surrounded by a cavity called an electron bubble of 20 Ångstroms in diameter. A positive helium ion is solvated by an electrostriction induced solid helium-ice shell ...
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In liquid helium, an electron is surrounded by a cavity called an electron bubble of 20 Ångstroms in diameter. A positive helium ion is solvated by an electrostriction induced solid helium-ice shell called a snowball of 7 Ångstroms in diameter. By studying their transport properties, these objects are well suited for the testing of the microscopic properties of superfluidity. At low temperatures and with small electric fields, the drift velocity of the charges depends on their interaction with the elementary excitations of the superfluid: phonons, rotons, and 3He atomic impurities. At higher fields, ions produce quantized vortex rings and vortex lines and studying these sheds light on quantum hydrodynamics. In the fermionic liquid, the 3He isotope ion transport properties display important pieces of information on the coupling of a charge to a Fermi liquid and on the richer topological structure of the superfluid phases appearing at ultralow temperatures. In the normal liquid phases of both isotopes, ions and electrons are used to probe classical hydrodynamics at the λ-transition and at the liquid-vapor transition at which long-range critical fluctuations of the appropriate order parameter occur. Several experiments have investigated the structure of electron bubbles. Electron drift velocity measurements in dense helium gas have elucidated the dynamics of electron bubble formation. This book provides a review of the more than forty-year-long experimental and theoretical research on the transport properties of electrons and ions in liquid and gaseous helium.Less

In liquid helium, an electron is surrounded by a cavity called an electron bubble of 20 Ångstroms in diameter. A positive helium ion is solvated by an electrostriction induced solid helium-ice shell called a snowball of 7 Ångstroms in diameter. By studying their transport properties, these objects are well suited for the testing of the microscopic properties of superfluidity. At low temperatures and with small electric fields, the drift velocity of the charges depends on their interaction with the elementary excitations of the superfluid: phonons, rotons, and ^{3}He atomic impurities. At higher fields, ions produce quantized vortex rings and vortex lines and studying these sheds light on quantum hydrodynamics. In the fermionic liquid, the ^{3}He isotope ion transport properties display important pieces of information on the coupling of a charge to a Fermi liquid and on the richer topological structure of the superfluid phases appearing at ultralow temperatures. In the normal liquid phases of both isotopes, ions and electrons are used to probe classical hydrodynamics at the λ-transition and at the liquid-vapor transition at which long-range critical fluctuations of the appropriate order parameter occur. Several experiments have investigated the structure of electron bubbles. Electron drift velocity measurements in dense helium gas have elucidated the dynamics of electron bubble formation. This book provides a review of the more than forty-year-long experimental and theoretical research on the transport properties of electrons and ions in liquid and gaseous helium.

*A.F. Borghesani*

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199213603
- eISBN:
- 9780191707421
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213603.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter describes the main experimental techniques used to measure the drift velocity in superfluid 4He at low temperature. The experimental results are then presented by showing the ...
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This chapter describes the main experimental techniques used to measure the drift velocity in superfluid 4He at low temperature. The experimental results are then presented by showing the contributions to the ion drag due to the different elementary excitations of the superfluid. The theoretical description of the processes of ion scattering off phonons, rotons, and 3He atomic impurities is also presented, and the theoretical predictions are compared with experimental results. The use of the formalism of the Boltzmann transport equation to predict how the drag force on an ion in the superfluid is determined by the different scattering mechanisms is discussed.Less

This chapter describes the main experimental techniques used to measure the drift velocity in superfluid ^{4}He at low temperature. The experimental results are then presented by showing the contributions to the ion drag due to the different elementary excitations of the superfluid. The theoretical description of the processes of ion scattering off phonons, rotons, and ^{3}He atomic impurities is also presented, and the theoretical predictions are compared with experimental results. The use of the formalism of the Boltzmann transport equation to predict how the drag force on an ion in the superfluid is determined by the different scattering mechanisms is discussed.

*A.F. Borghesani*

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199213603
- eISBN:
- 9780191707421
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213603.003.0023
- Subject:
- Physics, Condensed Matter Physics / Materials

The realization that ions of different size are produced in liquid 3He with different concentrations of 4He isotopic impurities has allowed researchers to select the ion to be studied just by ...
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The realization that ions of different size are produced in liquid 3He with different concentrations of 4He isotopic impurities has allowed researchers to select the ion to be studied just by changing the purity of the liquid. At about 70 mK, the positive ion mobility has a discontinuity related to the impossibility of further increase of an 4He-rich halo around the ion. Below the discontinuity, the temperature dependence of the mobility in the zero-field limit is well described by theory. At the discontinuity, it has been possible to determine the growth dynamics of the halo. The field dependence of the mobility also follows fairly accurately the theoretical description that takes into account ion recoil. The drift velocity non-linearities have put into evidence the equivalence of temperature and drift velocity in determining the ion mean energy.Less

The realization that ions of different size are produced in liquid ^{3}He with different concentrations of ^{4}He isotopic impurities has allowed researchers to select the ion to be studied just by changing the purity of the liquid. At about 70 mK, the positive ion mobility has a discontinuity related to the impossibility of further increase of an ^{4}He-rich halo around the ion. Below the discontinuity, the temperature dependence of the mobility in the zero-field limit is well described by theory. At the discontinuity, it has been possible to determine the growth dynamics of the halo. The field dependence of the mobility also follows fairly accurately the theoretical description that takes into account ion recoil. The drift velocity non-linearities have put into evidence the equivalence of temperature and drift velocity in determining the ion mean energy.

*Melvin Lax, Wei Cai, and Min Xu*

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780198567769
- eISBN:
- 9780191718359
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567769.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the Langevin treatment of the Fokker–Planck process and diffusion. The form of Langevin equation used is different from the stochastic differential equation using Ito's ...
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This chapter discusses the Langevin treatment of the Fokker–Planck process and diffusion. The form of Langevin equation used is different from the stochastic differential equation using Ito's calculus lemma. The transform of the Langevin equation obeys the ordinary calculus rule, hence can be easily performed and some misleadings can be avoided. The origin of the difference between this approach and that using Ito's lemma comes from the different definitions of the stochastic integral. This chapter also discusses drift velocity, an example with an exact solution, use of Langevin equation for a general random variable, extension of this equation to the multiple dimensional case, and means of products of random variables and noise source.Less

This chapter discusses the Langevin treatment of the Fokker–Planck process and diffusion. The form of Langevin equation used is different from the stochastic differential equation using Ito's calculus lemma. The transform of the Langevin equation obeys the ordinary calculus rule, hence can be easily performed and some misleadings can be avoided. The origin of the difference between this approach and that using Ito's lemma comes from the different definitions of the stochastic integral. This chapter also discusses drift velocity, an example with an exact solution, use of Langevin equation for a general random variable, extension of this equation to the multiple dimensional case, and means of products of random variables and noise source.