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- Keyword
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- Bose-Einstein condensation (4)
- Ideal Bose gas (2)
- Permutation cycles (2)
- Boltzmann equation - transport equation - Snider equation - BBGKY hierarchy - virial corrections - molecular fields (1)
- Bose-Einstein condensates - Fock state - Interferometers - NOON state (1)
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- Dilute solutions (1)
- Fermi fluids (1)
- He-3 normal liquid polarized (1)
- He-3-He-4 mixture liquid (1)
- NMR (1)
- Nanotubes (1)
- Path-integral Monte Carlo (1)
- Path-integral Monte Carlo simulations (1)
- Quantum fluid (1)
- Quantum fluids (1)
- Quantum theory (1)
- Refrigeration (1)
- Spin polarized He-3 (1)
- Spin-polarized He-3-He-4 mixtures (1)
- Spontaneous symmetry breaking (1)
- Two-dimensional Bose systems (1)
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Articles 31 - 60 of 64
Full-Text Articles in Physical Sciences and Mathematics
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.
Quantum-Monte-Carlo Calculations For Bosons In A Two-Dimensional Harmonic Trap, S Heinrichs, Wj Mullin
Quantum-Monte-Carlo Calculations For Bosons In A Two-Dimensional Harmonic Trap, S Heinrichs, Wj Mullin
William J. Mullin
Path-Integral-Monte-Carlo simulation has been used to calculate the properties of a two-dimensional (2D) interacting Bose system. The bosons interact with hard-core potentials and are confined to a harmonic trap. Results for the density profiles, the condensate fraction, and the superfluid density are presented. By comparing with the ideal gas we easily observe the effects of finite size and the depletion of the condensate because of interactions. The system is known to have no phase transition to a Bose-Einstein condensation in 2D, but the finite system shows that a significant fraction of the particles are in the lowest state at low …
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 …
Nonlinear Leggett-Rice Effect In Spin Polarised Solid He-3, S Kingsley, B Cowan, Wj Mullin, S Tehraninasab
Nonlinear Leggett-Rice Effect In Spin Polarised Solid He-3, S Kingsley, B Cowan, Wj Mullin, S Tehraninasab
William J. Mullin
Spin diffusion involves the transport of the vector magnetisation, characterised by a diffusiontensor. A magnetic field destroys the system’s isotropy so that while longitudinal diffusion is real, transverse diffusion becomes complex. The imaginary part leads to spin rotation since the spin current may no longer be parallel to the spin density. In spin polarised solid3He the molecular field of the exchange interaction leads to such an effect. We have evaluated the elements of the diffusion tensor to show this. A nonlinearity arises since the diffusion tensor so-calculated depends on the magnetisation. We show that this behaviour is described by the …
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 …
Spin Transport In Very Dilute He-3-He-4 At Very High B/T, H Akimoto, Js Xia, Ed Adams, D Candela, Wj Mullin, Ns Sullivan
Spin Transport In Very Dilute He-3-He-4 At Very High B/T, H Akimoto, Js Xia, Ed Adams, D Candela, Wj Mullin, Ns Sullivan
William J. Mullin
We report preliminary results for pulsed-NMR measurements on a very dilute 3 He- 4 He mixture (x 3 =900 ppm) in a 14.74 T field at temperatures down to 3 mK. The aim of the project is to investigate low temperature transverse spin relaxation and possible spin diffusion anisotropy. Spin-echo and T1-type measurements were employed to measure the transverse and longitudinal spin diffusion coefficients. At high temperatures both spin diffusion coefficients are well explained assuming a quasiparticle interaction consistent with previous experiments. Conversely, at low temperatures the measured value of |lambdaohgrtaubottom| is apparently limited to about ten by a poorly-understood …
Spin Diffusion In 2d And 3d Quantum Solids, B Cowan, Wj Mullin, E Nelson
Spin Diffusion In 2d And 3d Quantum Solids, B Cowan, Wj Mullin, E Nelson
William J. Mullin
A moment method is used to compute the anisotropic spin diffusion constant in two-dimensional (2D) adsorbed and bulk (3D) quantum solids in which the spin motion is induced by an exchange Hamiltonian. Computations are carried out in 2D for the square and triangular lattices and in 3D for the hcp lattice. It is assumed that there are pair and three-particle exchange processes only. Since, in hcp3He, exchange processes out of the basal planeJprime may occur at a different rate from processes in the planeJ, comparison with experimental results on single crystals should allow the determination ofJ andJprime. Our results are …
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 …
Giant Viscosity Enhancement In A Spin-Polarized Fermi Liquid, H Akimoto, Js Xia, D Candela, Wj Mullin, Ed Adams, Ns Sullivan
Giant Viscosity Enhancement In A Spin-Polarized Fermi Liquid, H Akimoto, Js Xia, D Candela, Wj Mullin, Ed Adams, Ns Sullivan
William J. Mullin
The viscosity is measured for a Fermi liquid, a dilute 3He-4He mixture, under extremely high magnetic field/temperature conditions (B≤14.8 T, T≥1.5 mK). The spin-splitting energy μB is substantially greater than the Fermi energy kBTF; as a consequence the polarization tends to unity and s-wave quasiparticle scattering is suppressed for T≪TF. Using a novel composite vibrating-wire viscometer an enhancement of the viscosity is observed by a factor of more than 500 over its low-field value. Good agreement is found between the measured viscosity and theoretical predictions based upon a t-matrix formalism.
Spin Diffusion In Trapped Gases: Anisotropy In Dipole And Quadrupole Modes, Wj Mullin, Rj Ragan
Spin Diffusion In Trapped Gases: Anisotropy In Dipole And Quadrupole Modes, Wj Mullin, Rj Ragan
William J. Mullin
Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows unusual diffusion anisotropy in both dipole and quadrupole modes. Moreover, the lack of spin …
Interferometry With Independent Bose-Einstein Condensates: Parity As An Epr/Bell Quantum Variable, F Laloe, Wj Mullin
Interferometry With Independent Bose-Einstein Condensates: Parity As An Epr/Bell Quantum Variable, F Laloe, Wj Mullin
William J. Mullin
When independent Bose-Einstein condensates (BEC), described quantum mechanically by Fock (number) states, are sent into interferometers, the measurement of the output port at which the particles are detected provides a binary measurement, with two possible results ±1. With two interferometers and two BEC’s, the parity (product of all results obtained at each interferometer) has all the features of an Einstein-Podolsky-Rosen quantity, with perfect correlations predicted by quantum mechanics when the settings (phase shifts of the interferometers) are the same. When they are different, significant violations of Bell inequalities are obtained. These violations do not tend to zero when the number …
Quantum-Limited Mass Flow Of Liquid He-3, G Lambert, G Gervais, Wj Mullin
Quantum-Limited Mass Flow Of Liquid He-3, G Lambert, G Gervais, Wj Mullin
William J. Mullin
We consider theoretically the possibility of observing unusual quantum fluid behavior in liquid 3He and solutions of 3He in 4He systems confined to nanochannels. In the case of pure ballistic flow at very low temperature the conductance will be quantized in units of 2m2/h. We show that these steps should be sensitive to increases in temperature. We also use a random scattering matrix simulation to study flow with diffusive wall scattering. Universal conductance fluctuations analogous to those seen in electron systems should then be observable. Finally we consider the possibility of crossover to a one-dimensional system at sufficiently low temperature, …
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 …
Landau Damping Of Spin Waves In Trapped Boltzmann Gases, Rj Ragan, Wj Mullin, Eb Wiita
Landau Damping Of Spin Waves In Trapped Boltzmann Gases, Rj Ragan, Wj Mullin, Eb Wiita
William J. Mullin
A semiclassical method is used to study Landau damping of transverse pseudo-spin waves in harmonically trapped ultracold gases in the collisionless Boltzmann limit. In this approach, the time evolution of a spin is calculated numerically as it travels in a classical orbit through a spatially dependent mean field. This method reproduces the Landau damping results for spin-waves in unbounded systems obtained with a dielectric formalism. In trapped systems, the simulations indicate that Landan damping occurs for a given spin-wave mode because of resonant phase space trajectories in which spins are "kicked out" of the mode (in spin space). A perturbative …
Bose-Einstein Condensation, Fluctuations, And Recurrence Relations In Statistical Mechanics, Wj Mullin, Jp Fernandez
Bose-Einstein Condensation, Fluctuations, And Recurrence Relations In Statistical Mechanics, Wj Mullin, Jp Fernandez
William J. Mullin
We calculate certain features of Bose–Einstein condensation in the ideal gas by using recurrence relations for the partition function. The grand canonical ensemble gives inaccurate results for certain properties of the condensate that are accurately provided by the canonical ensemble. Calculations in the latter can be made tractable for finite systems by means of the recurrence relations. The ideal one-dimensional harmonic Bose gas provides a particularly simple and pedagogically useful model for which detailed results are easily derived. An analysis of the Bose system via permutation cycles yields insight into the physical meaning of the recurrence relations.
Ursell Operators In Statistical Physics .3. Thermodynamic Properties Of Degenerate Gases, P Gruter, F Laloe, Ae Meyerovich, W Mullin
Ursell Operators In Statistical Physics .3. Thermodynamic Properties Of Degenerate Gases, P Gruter, F Laloe, Ae Meyerovich, W Mullin
William J. Mullin
We study in more details the properties of the generalized Beth Uhlenbeck formula obtained in a preceding article. This formula leads to a simple integral expression of the grand potential of any dilute system, where the interaction potential appears only through the matrix elements of the second order Ursell operator U2. Our results remain valid for significant degree of degeneracy of the gas, but not when Bose Einstein (or BCS) condensation is reached, or even too close to this transition point. We apply them to the study of the thermodynamic properties of degenerate quantum gases: equation of state, magnetic susceptibility, …
Interference Of Bose-Einstein Condensates: Quantum Nonlocal Effects, Wj Mullin, F Laloe
Interference Of Bose-Einstein Condensates: Quantum Nonlocal Effects, Wj Mullin, F Laloe
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 …
Anisotropic Spin Diffusion In Trapped Boltzmann Gases, Wj Mullin, Rj Ragan
Anisotropic Spin Diffusion In Trapped Boltzmann Gases, Wj Mullin, Rj Ragan
William J. Mullin
Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions leads to 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 …
Absence Of Fragmentation In Two-Dimensional Bose-Einstein Condensation, Jp Fernandez, Wj Mullin
Absence Of Fragmentation In Two-Dimensional Bose-Einstein Condensation, Jp Fernandez, Wj Mullin
William J. Mullin
We investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional isotropically trapped Bose gas at finite temperature. For the ideal gas, the procedure reproduces the exact harmonic-oscillator eigenfunctions and the Bose distribution. We use a new collocation-minimization method to study the interacting gas in the Hartree-Fock approximation and obtain a ground-state wavefunction and condensate fraction consistent with those obtained by other methods. The populations of the next few eigenstates increase at the expense of the ground state but continue to …
Longitudinal Spin Relaxation In A Dilute, Degenerate Fermi Gas At Arbitrary Polarization, Ed Nelson, Wj Mullin
Longitudinal Spin Relaxation In A Dilute, Degenerate Fermi Gas At Arbitrary Polarization, Ed Nelson, Wj Mullin
William J. Mullin
We calculate the longitudinal magnetic relaxation timeT 1 –1 for a dilute, polarized Fermi gas with short range interactions at low temperatures. In the limit of small polarizationsT 1 –1 is proportional toT –2 in agreement with earlier predictions, while in the opposite caseT 1 –1 is strongly affected by polarization, and in the limit of large polarizations becomes proportional to the square of the energy separation between the Fermi surfaces for up and down spins. The possibility of measuringT 1 in dilute solutions of 3 He in superfluid 4 He is investigated.
Answer To Question #28 Bernoulli Equation, Wj Mullin
Answer To Question #28 Bernoulli Equation, Wj Mullin
William J. Mullin
Abstract unavailable
Proposed Nmr Determination Of The Exchange Parameters In Hexagonal-Close-Packed He-3, Wj Mullin, Ed Nelson
Proposed Nmr Determination Of The Exchange Parameters In Hexagonal-Close-Packed He-3, Wj Mullin, Ed Nelson
William J. Mullin
We calculate the relaxation times for an oriented single crystal of hexagonal-close-packed solid 3He, which, according to the theory of Roger and co-workers, is dominated by triple exchange. The anisotropy of the relaxation times is a function of the ratio of exchange rates in the basal plane to those out of the plane and may be used to determine this ratio. Results are presented for T1 and T2 as a function of frequency as well as of crystal orientation.
Theory Of Cooling By Flow Through Narrow Pores, Wj Mullin, N Kalechofsky
Theory Of Cooling By Flow Through Narrow Pores, Wj Mullin, N Kalechofsky
William J. Mullin
We consider the possibility of adding a stage to a dilution refrigerator to provide additional cooling by “filtering out” hot atoms. Three methods are considered: (1) effusion, where holes having diameters larger than a mean-free path allow atoms to pass through easily; (2) particle waveguidelike motion using very narrow channels that greatly restrict the quantum states of the atoms in a channel; (3) wall-limited diffusion through channels, in which the wall scattering is disordered so that local density equilibrium is established in a channel. We assume that channel dimensions are smaller than the mean-free path for atom-atom interactions. The particle …