Mullin, William
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Professor Emeritus, Department of Physics, College of Natural Sciences
Last Name
Mullin
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William
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Physics
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Introduction
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Publication Quantum statistics: Is there an effective fermion repulsion or boson attraction?(2003-01-01) Mullin, WJ; Blaylock, GPhysicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins and validity of such exchange force ideas and the areas where they are highly misleading. We propose that explanations of quantum statistics should avoid the idea of an effective force completely, and replace it with more appropriate physical insights, some of which are suggested here.Publication Permutation cycles in the Bose-Einstein condensation of a trapped ideal gas(2000-01-01) Mullin, WJWe consider Bose–Einstein condensation for non-interacting particles trapped in a harmonic potential by considering the length of permutation cycles arising from wave function symmetry. This approach had been considered previously by Matsubara and Feynman for a homogeneous gas in a box with periodic boundary conditions. For the ideal gas in a harmonic potential, one can treat the problem nearly exactly by analytical means. One clearly sees that the noncondensate is made up of permutation loops that are of length less-than-or-equals, slantN1/3, and that the phase transition consists of the sudden growth of longer permutation cycles. The condensate is seen to consist of cycles of all possible lengths with nearly equal likelihood.Publication Theory of motional inhibition of interlayer quantum tunneling in thin 3He films(1980) Mullin, WJ; Landesmant, A.An attempt is made to interpret NMR data on 3He films for coverages just over one monolayer in terms of motion due to the quantum exchange of particles between layers. A summary of the relevant data and of various possible relaxation mechanisms is given and it is found that a portion of the data seems amenable to an interlayer exchange interpretation. The detailed theory of this process requires the use of the exchange operator concept and a Kubo-theory treatment of the effect of second-layer motion on the exchange process. It is shown that the ldquobarerdquo interlayer exchange process characterized by constant J 12 is slowed by second-layer translational motion so that the effective exchange parameter becomes \~J 12 ap J 12 2/epsiv2, where epsiv2 is a second-layer single-particle translational energy. In order to fit the NMR data it is found that epsiv2 must be evaluated in the classical limit rather than the degenerate Fermi limit, and that \~J 12 ap J 11, the exchange energy within the first-layer solid. These conditions require a helium second-layer effective mass of m * > 5m and J 12>600J 11, which are anomously large values for thesePublication Nonlinear spin dynamics of dilute He-3-He-4 at very high B/T(2000-01-01) Akimoto, H; Adams, ED; Candela, D; Mullin, WJ; Shvarts, V; Sullivan, NS; Xia, JSWe are conducting an experimental search for spin-diffusion anisotropy in dilute 3He–4He mixtures at very high B/T (17 T, 2 mK). Previous experiments have not reached sufficiently high B/T ratios to observe the effect in very dilute mixtures, for which quantitative theoretical predictions exist. The planned experiments will require NMR experiments at very high values of the dimensionless spin rotation parameter μM. We have performed numerical simulations of the nonlinear spin dynamics to assess the feasibility of spin-wave and spin-echo experiments.Publication VISCOSITY INCREASE UPON SPIN POLARIZATION OF A DILUTE FERMI GAS(1991) CANDELA, D; WEI, LJ; MCALLASTER, DR; Mullin, WJA vibrating-wire technique has been used to directly measure the viscosity increase in a dilute 3-4He solution caused by brute-force spin polarization up to 40%. The viscosity of a solution with degeneracy temperature TF=19.5 mK was measured over the temperature range 6.1–100 mK in magnetic fields of 1.00 and 7.96 T. Spin polarization caused a marked decrease in the mechanical Q of the viscometer at low temperatures. The observed viscosity is compared with calculations of the transport coefficients of dilute quantum gases for all temperatures and spin polarizations.Publication LONGITUDINAL SPIN RELAXATION IN DILUTE, POLARIZED FERMI GASES(1994) NELSON, ED; Mullin, WJWe consider the calculation of the longitudinal relaxation time T1 in a polarized Fermi system at temperatures T ranging from the degenerate statistics regime to the Boltzmann limit. We include the possibility of arbitrary polarization M of the system. While the low temperature unpolarized system behaves as T-2 as previous calculations have shown, when relaxation takes place in zero external field, polarization leads to substantially smaller values of T1 at low T, because of the opening up of the phase space between up and down Fermi spheres. For the degenerate system T1 is dependent on the value of M in contrast to results in the Boltzmann case.Publication A LEGGETT-RICE EFFECT IN SOLID HE-3-SPIN ROTATION INDUCED BY EXCHANGE(1994) COWAN, B; Mullin, WJ; TEHRANINASAB, SIn solid3He the internuclear exchange interaction may be interpreted as a molecular field, as in the Weiss theory of magnetism. In an applied magnetic field the magnetic moment precesses about the total magnetic field, to which the molecular field contributes. As Leggett showed for liquid helium in the Fermi liquid region, this leads to a modification of the time evolution of the magnetisation; it is no longer purely diffusive. In solid3He at low polarisation there is conventional spin diffusion; at high polarisations the evolution is in the form of spin waves. We show that the intermediate behaviour may be expressed in terms of a complex diffusion coefficient of constant magnitude, whose phase angle depends on the polarisation.Publication SPIN DIFFUSION IN DILUTE, POLARIZED HE-3-HE-4 SOLUTIONS(1992) Mullin, WJ; JEON, JWSpin dynamics for arbitrarily polarized and very dilute solutions of 3He in liquid 4He are described. We began at a very fundamental level by deriving a kinetic equation for arbitrarily polarized dilute quantum systems based on a method due to Boercker and Dufty. This approach allows more controlled approximations than our previous derivation based on the Kadanoff-Baym technique. Our previous work is here generalized to include T-matrix interactions rather than the Born approximation. Spin hydrodynamic equations are derived. The general equations are valid for both Fermi and Bose systems. By use of a well-known phenomenological potential to describe the 3He-3He T-matrix we calculate longitudinal and transverse spin diffusion coefficients D bottom and D ¦ and the identical-particle spin-rotation parameter Mgr. We confirm that these two diffusion constants differ at low T with D bottom approaching a constant as T rarr 0, and D¦~1/T2. Estimates of errors made by our approximations are considered in detail. Good agreement is found in comparison with data from both Cornell University and the University of Massachusetts. We find that the s-wave approximation is inadequate and that mean-field corrections are important. Comparison is also made between theory and the recent UMass viscosity measurements.Publication FLOW OF POLARIZED FERMI GASES THROUGH NARROW CHANNELS(1986) Mullin, WJThe flow of a polarized Fermi gas through channels from one cell to another can be used to study its transport properties. If the mean free path λ in the gas is smaller than the radius r of a channel, the time constant for the filling of an empty chamber can yield the viscosity of the gas in both the Boltzmann and degenerate cases. If λ>r and the gas is degenerate, a novel effect is predicted: Because the Fermi velocities of the two spin species are different, the polarization in the second cell will initially have a value greater than the equilibrium value in the first cell.Publication Viscosity of highly polarized very dilute He-3-He-4 mixtures(2002-01-01) Akimoto, H; Xia, JS; Adams, ED; Candela, D; Mullin, WJ; Sullivan, NSWe present vibrating - wire viscosity measurements on a very dilute 3He-4He mixture (X3 = 150 ppm) in fields up to 14.8 T and temperatures down to 3 mK. The 3He spin polarization is greater than 99% for the highest field and lowest temperature used. In these conditions, the s-wave scattering rate decreases due to a lack of quasiparticles with the minority spin state. This enhances all transport coefficients including the viscosity. At the lowest temperature, the hydrodynamic damping of the viscometer in a 14.8 T field was more than 10 times larger than in low fields. This indicates a many-fold increase in the mixture viscosity due to spin polarization.