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Observation Of Spin Rotation Effects In Polarized He-3-He-4 Mixtures, Wj Gully, Wj Mullin
Observation Of Spin Rotation Effects In Polarized He-3-He-4 Mixtures, Wj Gully, Wj Mullin
William J. Mullin
Quantum exchange effects, predicted to occur in the spin diffusion of polarized nondegenerate gases, have been observed in a 3He-4He mixture by spin-echo techniques. Measurements of the spin rotation parameter (μM0)2 and diffusion constant D are in reasonable agreement with theoretical predictions until the degeneracy temperature is approached.
Nonlocal Quantum Effects With Bose-Einstein Condensates, F Laloe, Wj Mullin
Nonlocal Quantum Effects With Bose-Einstein Condensates, F Laloe, Wj Mullin
William J. Mullin
Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed to all condensates and treated as unknown classical quantities. However, this image is not always sufficient: when all particles are measured, quantum mechanics predicts probabilities that are sometimes in contradiction with it, as illustrated by quantum violations of local realism. In this Rapid communication, we show that interferometers can be used to demonstrate a large variety …
Nonlinear Spin Dynamics Of Dilute He-3-He-4 At Very High B/T, H Akimoto, Ed Adams, D Candela, Wj Mullin, V Shvarts, Ns Sullivan, Js Xia
Nonlinear Spin Dynamics Of Dilute He-3-He-4 At Very High B/T, H Akimoto, Ed Adams, D Candela, Wj Mullin, V Shvarts, Ns Sullivan, Js Xia
William J. Mullin
We 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.
Viscosity Of Highly Polarized Very Dilute He-3-He-4 Mixtures, H Akimoto, Js Xia, Ed Adams, D Candela, Wj Mullin, Ns Sullivan
Viscosity Of Highly Polarized Very Dilute He-3-He-4 Mixtures, H Akimoto, Js Xia, Ed Adams, D Candela, Wj Mullin, Ns Sullivan
William J. Mullin
We 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 …
Longitudinal And Transverse Spin Diffusion In Polarized He-3-He-4 Solutions, Jw Jeon, Wj Mullin
Longitudinal And Transverse Spin Diffusion In Polarized He-3-He-4 Solutions, Jw Jeon, Wj Mullin
William J. Mullin
Spin dynamics for arbitrarily polarized and very dilute 3He-4He solutions are described. We generalize previous work to include 3He-4He phenomenological interactions, and we calculate longitudinal and transverse spin diffusion coefficients and the identical-particle spin-rotation parameter. Good agreement is found in comparison with recent data. The s-wave approximation is found to be inadequate and mean-field corrections are important.
A Study Of Bose-Einstein Condensation In A Two-Dimensional Trapped Gas, Wj Mullin
A Study Of Bose-Einstein Condensation In A Two-Dimensional Trapped Gas, Wj Mullin
William J. Mullin
We examine the possibility of Bose-Einstein condensation (BEC) in two-dimensional (2D) system of interacting particles in a trap. We use a self-consistent mean-field theory of Bose particles interacting by a contact interaction in the Popov and WKB approximations. The equations show that the normal state has a phase transition at some critical temperature T c but below T c the Bose-Einstein condensed state is not a consistent solution of the equations in the thermodynamic limit. This result agrees with a theorem recently discussed by the author that shows that a BEC state is impossible for an interacting gas in a …
Derivation Of Transverse Spin-Wave Dynamics From A Kinetic Equation In A Rotating Reference, Wj Mullin, Rj Ragan
Derivation Of Transverse Spin-Wave Dynamics From A Kinetic Equation In A Rotating Reference, Wj Mullin, Rj Ragan
William J. Mullin
In 1997 Fomin challenged the results of several theoretical groups who had predicted that there could be finite damping of spin-waves in the limit T -> 0. His method involved deriving a Lagrangian in a reference frame tied to the oscillating magnetization. He claimed to show that there was no diffusive damping (that is, of second order in wave vector q). We reopen this question by examining, under similar conditions, how a kinetic equation behaves in an equivalent reference frame. We arrive at Fomin's equations modified by inclusion of q2 damping of the spin-wave modes. Our result sharpens and perhaps …
Quantum Statistics: Is There An Effective Fermion Repulsion Or Boson Attraction?, Wj Mullin, G Blaylock
Quantum Statistics: Is There An Effective Fermion Repulsion Or Boson Attraction?, Wj Mullin, G Blaylock
William J. Mullin
Physicists 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.
Analysis Of Certain Binary Collision Approximation Closures Of The Bbgky Hierarchy, Rf Snider, Wj Mullin, F Laloe
Analysis Of Certain Binary Collision Approximation Closures Of The Bbgky Hierarchy, Rf Snider, Wj Mullin, F Laloe
William J. Mullin
The closure of the BBGKY hierarchy to obtain the Boltzmann equation requires, in particular, restricting particle interactions to include only isolated binary collisions. Boercker and Dufty accomplish this by approximating the three-particle reduced density operator in a particular manner that favours correlation between two of the particles, while ignoring the correlation with the third. The tradition of most other closures has more closely followed Boltzmann's original thinking to completely neglect any reference to three-particle effects while assuming a generalized form of molecular chaos for the pair density operator. The two closures are compared in two ways: (a) by finding iterated …
Longitudinal Relaxation-Time For Dilute Quantum Gases, Wj Mullin, F Laloe, Mg Richards
Longitudinal Relaxation-Time For Dilute Quantum Gases, Wj Mullin, F Laloe, Mg Richards
William J. Mullin
We calculate the longitudinal relaxation timeT 1 for a polarized spin-1/2 Fermi gas, in zero magnetic field, for conditions of temperatureT and densityn such that Boltzmann statistics are valid. Our results show generally thatT 1 is independent of polarization of the gas. At highT, where the thermal wavelength lambda is small compared to the scattering lengtha, T 1 is proportionalT 1/2, while at lowT, such that lambda is greater thana, T 1 is proportional toT –1/2.T 1 thus has a minimum at some intermediate temperature confirming the numerical results of Shizgal. Physical arguments show that the existence of the minimum …
Kinetic-Equation For Dilute, Spin-Polarized Quantum-Systems, Jw Jeon, Wj Mullin
Kinetic-Equation For Dilute, Spin-Polarized Quantum-Systems, Jw Jeon, Wj Mullin
William J. Mullin
A kinetic equation, which includes the effects of degeneracy, is derived for dilute, polarized systems by the Green's function method of Kadanoff and Baym. When the Born approximation is used for the self-energy, the equation reduces to a result due to Silin. In the Boltzmann limit our result is equivalent to the equation of Lhuillier and Laloë, with the addition of a mean-field drift term analogous to that appearing in the Landau-Silin equation. Our kinetic equation is used to derive an expression for the transverse spin-diffusion relaxation time, τ>, for a Fermi system. In the Boltzmann and low-polarization limits …
Some Equilibrium Properties Of Polarized, Dilute-Solutions Of H-3 In Superfluid He-4, P Hessling, Wj Mullin
Some Equilibrium Properties Of Polarized, Dilute-Solutions Of H-3 In Superfluid He-4, P Hessling, Wj Mullin
William J. Mullin
Formulas for of osmotic pressure and second sound velocity of a polarized system are derived and applied to polarized dilute solutions of3He in superfluid4He. Results are compared to experiment. Agreement is reasonable, but inferior to that obtained for transport properties reinforcing the claim of Meyerovich that the theory may have some conceptual difficulties.
Bose Condensation Of Idealized Spin-Polarized Atomic-Hydrogen In Equilibrium, Wj Mullin
Bose Condensation Of Idealized Spin-Polarized Atomic-Hydrogen In Equilibrium, Wj Mullin
William J. Mullin
A model of spin-polarized hydrogen (H↑) is treated in which interactions between atoms are neglected while the single-atom Zeeman and hyperfine interactions are treated exactly. These magnetic terms in the Hamiltonian are found to affect substantially the Bose-Einstein condensation and the various thermodynamic variables. Computations are discussed of the condensation temperature, condensate density, and specific heat in order to indicate how changes in magnetic field strength might be expected to affect future measurements on this quantum system.
Symmetry Constraints On The Spin Dynamics Of Polarised He-3, B Cowan, Wj Mullin, S Tehrani-Nasab
Symmetry Constraints On The Spin Dynamics Of Polarised He-3, B Cowan, Wj Mullin, S Tehrani-Nasab
William J. Mullin
The Leggett–Rice effect in liquid 3He was proposed on the basis of Fermi liquid interactions of the 3He quasiparticles. Consideration of the interparticle interactions in polarised gaseous 3He led, similarly, to spin rotation effects describable by a Leggett–Rice equation. In spin polarised solid 3He an analogous effect has been proposed from a consideration of the inter-nuclear exchange interaction. We show, in this paper, that spin rotation behaviour of the Leggett–Rice type in all these systems may be understood as a consequence of symmetry constraints.
Solution Of The Kinetic-Equation For Polarized Fermi Systems At All Temperatures, Jw Jeon, Wj Mullin
Solution Of The Kinetic-Equation For Polarized Fermi Systems At All Temperatures, Jw Jeon, Wj Mullin
William J. Mullin
We have solved the kinetic equation for a dilute, polarized Fermi system for a range of temperatures from the degenerate limit to the Boltzmann case. The solution is possible because we have been able to reduce the collision integral to two-fold form. We calculate the spin diffusion constant and find the expected results for the degenerate and Boltzmann limits, improved results for the high polarization regime in which one spin species is degenerate and one Boltzmann, and values for all intermediate temperatures as well. Because of a relation between the collision time and the “spin rotation quality parameter”, µ, we …
Exact Transport-Properties Of Degenerate, Weakly Interacting, And Spin-Polarized Fermions, Wj Mullin, K Miyake
Exact Transport-Properties Of Degenerate, Weakly Interacting, And Spin-Polarized Fermions, Wj Mullin, K Miyake
William J. Mullin
Exact results for the transport coefficients of a highly degenerate spin-polarized Fermi system are presented. The case of weakly interacting particles, such as dilute3He in4He or D darr, is treated. The results are compared to the variational treatment and corrections as large as 8% are found. Detailed behavior of the polarization of an ideal Fermi gas as a function of temperature and magnetic field is discussed as a model for dilute3He in4He. Limits of applicability of the formulas are given. We find that at appropriate fields and temperatures, the two spin species may be considered to be a mixture of …
Flow Of Polarized Fermi Gases Through Narrow Channels, Wj Mullin
Flow Of Polarized Fermi Gases Through Narrow Channels, Wj Mullin
William J. Mullin
The 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 …
A Leggett-Rice Effect In Solid He-3-Spin Rotation Induced By Exchange, B Cowan, Wj Mullin, S Tehraninasab
A Leggett-Rice Effect In Solid He-3-Spin Rotation Induced By Exchange, B Cowan, Wj Mullin, S Tehraninasab
William J. Mullin
In 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 …
The Condensate Number In Pimc Treatments Of Trapped Bosons, Wj Mullin, Sd Heinrichs, Jp Fernandez
The Condensate Number In Pimc Treatments Of Trapped Bosons, Wj Mullin, Sd Heinrichs, Jp Fernandez
William J. Mullin
In path integral Monte Carlo (PIMC) treatments of harmonically trapped bosons, one cannot use the usual long-range constant limit of the one-body reduced density matrix ρ1 to determine the condensate number n0 because ρ1 always approaches zero in a trap. W. Krauth found that the longest permutation cycle arising in the simulation gives a consistent value of n0. Our analytical studies of the ideal gas suggest other ways of using permutation cycles to determine n0. We test these approaches on simulations involving finite-size ideal and interacting gases and find that the methods are consistent.
Creation Of Noon States By Double Fock-State/Bose-Einstein Condensates, Wj Mullin, F. Laloe
Creation Of Noon States By Double Fock-State/Bose-Einstein Condensates, Wj Mullin, F. Laloe
William J. Mullin
NOON states (states of the form |N〉 a |0〉 b +|0〉 a |N〉 b where a and b are single particle states) have been used for predicting violations of hidden-variable theories (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state/Bose-Einstein condensates as sources in a modified Mach Zender interferometer can lead to the creation of the NOON state in which a and b refer to arms of the interferometer and N is the total number of particles in the two condensates. The modification …
Transverse Spin Diffusion In Polarized Fermi Gases, Jw Jeon, Wj Mullin
Transverse Spin Diffusion In Polarized Fermi Gases, Jw Jeon, Wj Mullin
William J. Mullin
We solve a recently derived kinetic equation for a dilute quantum system at arbitrary degeneracy and polarization, M. From this equation we develop a spin hydrodynamic equation that allows the generalization of the treatment of spin waves and the Leggett-Rice effect to polarized degenerate Fermi gases. We find a transverse spin-diffusion collision time τ⊥ that is often shorter than the corresponding longitudinal collision time τ∥ that is often shorter than the corresponding longitudinal collision time t⊥. As T→0, τ∥ approaches T-independent value, in constrast to τ⊥∼1/T2. Spin waves would thus continue to be damped even to T=0 K.
Transport In The Highly Polarized Fermi System - A Mixture Of Degenerate And Classical Fluids, Wj Mullin, K Miyake
Transport In The Highly Polarized Fermi System - A Mixture Of Degenerate And Classical Fluids, Wj Mullin, K Miyake
William J. Mullin
It is shown that, at low temperature and high polarization, a spin-1/2 Fermi system becomes a mixture of a degenerate fluid (up spins) and a fluid described by Boltzmann statistics (down spins). The down spins become classical when the polarization is so high that their Fermi energy becomes much less thankT. For weakly interacting systems the coefficients of thermal conductivity, viscosity, and spin diffusion are computed by kinetic theory arguments and from the Boltzmann equation. Comparisons are made with coefficients of the fully degenerate systems at zero and high polarization; altered temperature and magnetic field dependences result.
Longitudinal Spin Relaxation In Dilute, Polarized Fermi Gases, Ed Nelson, Wj Mullin
Longitudinal Spin Relaxation In Dilute, Polarized Fermi Gases, Ed Nelson, Wj Mullin
William J. Mullin
We 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 …
Anisotropic Spin Diffusion And Multiple Spin Echoes In He-3-He-4 Solutions, Rj Ragan, Wj Mullin
Anisotropic Spin Diffusion And Multiple Spin Echoes In He-3-He-4 Solutions, Rj Ragan, Wj Mullin
William J. Mullin
We propose a theta1-t1-theta2 pulse-NMR experiment to detect the spin-diffusion anisotropy, Delta=Dpar-Dbottom, in degenerate spin-polarized3He-4He mixtures, where Dbottom and dparare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the 3He concentration x3 ap 4% the spinrotation parameter vanishes (mgrM rarr0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of DeltaD. For slight anisotropy, i.e. DeltaD/Dpar lap0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in …
Theory Of Spin Diffusion Of Dilute, Polarized Fermions For All Temperatures, Jw Jeon, Wj Mullin
Theory Of Spin Diffusion Of Dilute, Polarized Fermions For All Temperatures, Jw Jeon, Wj Mullin
William J. Mullin
We describe the solution of the transport equation over the entire range of temperature from the Boltzmann to fully degenerate regimes for dilute, polarized Fermi systems. Since spin-polarized systems can show unusual quantum effects involving spin rotation in both Boltzmann and degenerate regimes, a solution of the kinetic equation over the whole temperature range is expected to be useful. Our results for the longitudinal spin diffusion coefficient reduce to the known limits in the Boltzmann and degenerate regimes and also to the expected form in the peculiar high-polarization regime in which one spin species is degenerate and the other described …
Theory Of A Polarized Fermi-Liquid In 2 Dimensions - Spin Diffusion, K Miyake, Wj Mullin
Theory Of A Polarized Fermi-Liquid In 2 Dimensions - Spin Diffusion, K Miyake, Wj Mullin
William J. Mullin
The spin diffusion coefficientD of a polarized two-dimensional degenerate Fermi fluid is evaluated as a model of submonolayer3He adsorbed on a flat substrate. The problem is formulated to account fully for Fermi liquid and spin polarization effects. Because in two dimensions, for zero or weak polarization, the only allowed scattering angles are zero and pgr, the transport coefficients become expressible in terms of Landau parameters without approximation. The dependence ofD on polarizationP is given for arbitraryP. For unpolarized and weakly polarized systems, in particular, it is shown thatD –1 simT 2lnT andT 2lnP, respectively. The two-dimensional kinetic equation is found …
The Origin Of The Phase In The Interference Of Bose-Einstein Condensates, Wj Mullin, R Krotkov, F Laloe
The Origin Of The Phase In The Interference Of Bose-Einstein Condensates, Wj Mullin, R Krotkov, F Laloe
William J. Mullin
We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a condensate wave function with a definite phase. We investigate the origin of this phase and the theoretical basis of treating interference. It is possible to construct a phase state for which the particle number is uncertain, but the phase is known. How such a state would be prepared before an experiment is not obvious. We show that a phase can also arise from experiments using condensates with known particle numbers. The analysis of measurements in such states also gives …
Nmr Relaxation-Times For A Dilute Polarized Fermi Gas, Wj Mullin, F Laloe, Mg Richards
Nmr Relaxation-Times For A Dilute Polarized Fermi Gas, Wj Mullin, F Laloe, Mg Richards
William J. Mullin
We calculate the longitudinal relaxation time T1 for a polarized Boltzmann Image Fermi gas. We show that T1 is independent of polarization of the gas. At high T, where the thermal wavelength a is small compared to the scattering length a, T1 is proportional Image , while at low T, such that λ is greater than a, T1 is proportional to Image . T1 thus has a minimum at some intermediate temperature confirming the numerical results of Shizgal. The existence of the minimum does not depend on the presence of an attractive part of the potential. As an example of …
On The Snider Equation, F Laloe, Wj Mullin
On The Snider Equation, F Laloe, Wj Mullin
William J. Mullin
We study the physical content of the Snider quantum transport equation and the origin of a puzzling feature of this equation, which implies contradictory values for the one-particle density operator. We discuss in detail why the two values are in fact not very different provided that the studied particles have sufficiently large wave packets and only a small interaction probability, a condition which puts a limit on the validity of the Snider equation. In order to improve its range of application, we propose a reinterpretation of the equation as a ldquomixedrdquo equation relating the real one-particle distribution function (on the …
Spin Diffusion In Dilute, Polarized He-3-He-4 Solutions, Wj Mullin, Jw Jeon
Spin Diffusion In Dilute, Polarized He-3-He-4 Solutions, Wj Mullin, Jw Jeon
William J. Mullin
Spin 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 …