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Virtual Physics - issue No 10 - September 15, 1996

[Virtual Physics]

number 10, September 15, 1996

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a forum for virtual meetings of scientists and students involved in a research activity on
CONTEMPORARY PHYSICS

Editors:
Marcel Ausloos, ausloos@gw.unipc.ulg.ac.be, Institut de Physique, Université de Liège, Belgium,
Kenneth Holmlund, Kenneth.Holmlund@TP.UmU.SE, Umeå University, Sweden
Cameron L. Jones, cjones@swin.edu.au, Swinburne University of Technology, Australia
Zbigniew J.Koziol, (Editor-in-Chief) webex@ra.isisnet.com, WebExperts Inc., Canada
Michal Spalinski, Michal.Spalinski@fuw.edu.pl, Institute of Theoretical Physics, Warsaw University, Poland
Krzysztof P. Wroblewski, chris@nmr.biophys.upenn.edu, University of Pennsylvania , U.S.A.
Copyright (C) 1996 by Zbigniew Koziol.
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IN THIS ISSUE:

[0] Hall effect and geometric phases in Josephson junction arrays, by P. Ao and X.-M. Zhu
[0] Resarch and Funds
  • Comment by Ahmad Ibrahim to "Myth of Competion and NSERC Policy of Selectivity", by Berezin and Hunter Virtual Physics No 08, 1996
  • Response of Alexander Berezin
[0] PostDoc Position: NMR of optical glasses by Jonathan Stebbins

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Hall effect and geometric phases in Josephson junction arrays

P. Ao and X.-M. Zhu

Department of Theoretical Physics, Umeå University, S-901 87, Umeå, SWEDEN
Ping.Ao@TP.UmU.SE

Received August 28, 1996

Abstract

Since effectively the local contact vortex velocity dependent part of the Magnus force in a Josephson junction array is zero in the classical limit, we predict zero classical Hall effect. In the quantum limit because of the geometric phases due to the finite superfluid density at superconductor grains, rich and complex Hall effect is found in this quantum regime due to the Thouless-Kohmoto-Nightingale-den-Nijs effect.

In a Josephson junction array, because of the huge core energy, vortices cannot move into the superconducting grains. They are confined to move along the junctions and the voids (nonsuperconducting areas), an example of the guided vortex motion. Since the vortex velocity part of the Magnus force is proportional to the local superfluid density, derivable from the nonlinear Schrödinger Lagrangian formulation, this force is zero for a vortex at a void, and exponentially small at a junction. Furthermore, because of the guide motion, even the small transverse force at a junction does not produce a sideway motion. This implies that this local contact transverse force does not play a role in vortex dynamics in a Josephson junction array. Hence there is no Hall effect in the classical limit. This absence of the en route transverse force is in agreement with experimental observations.

In the quantum regime, however, vortices experience geometric phases similar to the Aharonov-Bohm effect, due to the finite superfluid density at superconductor grains. To be commensurate with the existence of the vortex inaccessible regions and the geometric phases, we consider the tight-binding limit of vortex motion. The corresponding Hamiltonian may be written as

[ Equation 1 ]

(1)

where al is the boson annihilation operator for a vortex at j-th void, and () stands for the summation over nearest neighbors. The phase Alj is defined on the links connecting the nearest neighbors, and its sum around a plaquette is equal to the geometric phase [ inline ]. A uniform geometric phase in a square lattice will be assumed, where the number of `fluxes' [phi_0 ] is the number of Cooper pairs on a superconductor grain, which may be controlled by a gate voltage. The interaction between vortices is described by Vlj, which is long range and repulsive. We will treat it as a short range repulsive interaction for a first approximation, further approximated by the hard-core conditions. The tunneling matrix element t is,

[ Equation 2 ]

(2)

where EJ is the Josephson junction energy and EC the junction charging energy.

To discuss the Hall effect of the idealized vortex problem in the quantum regime, we map the hard-core boson problem onto a fermion problem by attaching odd number of `fluxes' on each vortex. The resulting Hamiltonian for the fermion problem is

[ Equation 3 ]

(3)

where cj is the corresponding the fermion annihilation operator at the j-th void. The number of statistical fluxes [phi_s ] at the j-th void satisfies the constrain [ inline ], which means that 2m + 1 fluxes have been attached to each vortex. If this mapping gives a mean field solution with an energy gap separated from its excitations, the statistical fluxes can be adiabatically smeared over the lattice and effectively detached from vortices. In this case [phi_s ] = - (2m + 1) n , with n is the magnetic flux frustration, the number of vortices per plaquette. Then the resulting mean field problem is exactly the Harper-Azbel-Wannier-Hofstadter problem, where energy gaps do exist. The quantum Hall behaviors of such a problem have been studied in detail by Thouless, Kohmoto, Nightingale, and den Nijs. For such a system the quantum Hall conductance [sigma_fH ] is [sigma_fH ] = tr , with the integer tr the solution of the Diophantine equation r = sr q + tr p . Here the number of fluxes per plaquette [phi ] = [phi_0 ] - [phi_s ] = p/q, with p and q coprime, n = r/q, and r, sr, tr integers with |tr| < = q/2. Counting the mapping generated Chern-Simons contribution to the Hall conductance, [ inline ] the Hall conductance of the original vortex system is then [ inline ]. Converting back into the electric Hall conductance and putting back the unit, we find the electric quantum conductance of the Josephson junction array is

[ Equation 4 ]

(4)

As known in the previous study of quantum Hall effect for a given set of the `flux' [phi_0 ] and the frustration n, there may exist several values of m, that is, several mappings, with their mean-field solutions all corresponding to filled bands which are separated from excitations by energy gaps. If such a case occurs, detailed calculation is needed to find the m with the largest energy gap, which is the most stable one.

One can check that following symmetries hold for the quantum Hall conductance [ sigma_H ]: the periodicity, [ inline ] ; the odd symmetry, [ inline ], the particle-hole symmetry, [ inline ]. Because [sigma_fH ] is a non-monotonic and rapidly varying function of the `flux' (number of Cooper pairs per plaquette), [phi ] and the frustration n, so will be [sigma_H ]. We note that both positive and negative Hall conductance may be easily reached. For example, for n = 1/5 and [phi_0 ] = 1/3, we find that [ inline ]; and for n = 1/3 and [phi_0 ] = 1/5, [ inline ] with m=-1. This is in sharp contrast to the previous proposal of the quantum Hall effect in a Josephson junction array. For the special mapping 2m n = [phi_0 ] the mean-field solution is automatically within a gap, and the Hall conductance is [ inline ]. This is to the contrast with the fermion-to-fermion mapping case, where there is no energy gap which separate the mean-field solution and excitations. With these specific sets of [phi_0 ] and n and in the zero limit of their fraction parts one can take the continuous limit of the tight-binding model.

We conclude by discussing of a criterion for the classical limit, in which there is no Hall effect. The relevant energy scale is the tunneling matrix element t. When the temperature is higher than t, thermal fluctuation will destroy the quantum coherence and the vortices move classically. The quantum regime is realized for temperatures lower than t where the phase coherence is preserved. For a Josephson junction energy EJ of the order of 1 K and the junction charging energy EC comparable to EJ, t of the order of 100 mK is obtained. We point out that the Hall effect in the quantum regime may have been realized experimentally.

This work was supported by Swedish NFR.

Further References

Theoretical: X.-M. Zhu, Y. Tan, and P. Ao, Phys. Rev. Lett. 77, 562 (1996).
Experimental: C.D. Chen, P. Delsing, D.B. Haviland, and T. Claeson, in Macroscopic Quantum Phenomena and Coherence in Superconducting Networks}, Edited by C. Giovannella and M. Tinkham, World Scientific, Singapore, 1995.

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Resarch and Funds

Comment to "Myth of Competion and NSERC Policy of Selectivity" by Berezin and Hunter, Virtual Physics No 08, 1996

by Ahmad Ibrahim ahmad@cujo.icom.ca

Received: September 2, 1996
This writing was motivated by the article "Myth of Competition and NSERC Policy of Selectivity" by Berezin and Hunter in issue number 8 of Virtual Physics.

Berezin and Hunter made the statement "fund the researcher, not proposals." Unfortunately this is the present situation to a large extent; if the individual asking for grants is "known", the proposal is very much more likely to be approved. The individual becomes known in many instances because of the ability to get funds and subcontract the work to scientists. Some professors, who may not particularly care about teaching or science, are good contractors and thus become known as good scientists. I have heard on more than one occasion a speaker being introduced and the highlight of the individual's achievements being the ability to secure half million dollars in research grants per year, rather than a specific scientific or academic contribution. Appointment and promotion of faculty members in many cases are tied to securing funds more than any thing else including teaching, the primary job for which taxpayers support universities.

Thus, although it is basic that officers of NSERC(and professors) should be publicly accountable(the public here being the scientific community) and a democratic arrangement of some sort be sought, nevertheless, without changing the contemporary culture prevailing in which "contractors" are confused with "scientists", there is no hope.

Berezin and Hunter suggest that "university-based researchers should be funded at some basic level...", certainly, but by whom? This is the mandate of the university itself, administrators should be good contractors and good negotiators, their job is not just to accommodate the agenda of the government of the day. A university should establish a long term defendable strategy for learning in its widest sense, it should plan that all professors are academically productive to the fullest; this is not the job of NSERC.

In summary, there is a problem with research funding, however, I think it does not start with NSERC but rather it originates in the existing culture in universities that value contractors over scientists probably because it appears to be an easy way out of financial difficulties. It is damaging in the long run. The solution is not reached by only pointing out flaws and hope for a miracle. A long term solution involves some sacrifices and hard work to restore the respect and trust of the tax-payers, they are a force no government can trifle with. Can we start with the future tax payers: the students? Can we get contemporary professors to care to earn the trust and respect of their students?

Dr. Ahmad Ibrahim
Senior Member, IEEE
ahmad@cujo.icom.ca

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Response of Alexander Berezin berezin@mcmail.CIS.McMaster.CA

Received: September 3, 1996
Dear Dr. Koziol,

Adhering to the view that all ideas/criticism should be open, I certainly suggest you include Dr. Ibrahim's article with the next VP issue.

I believe that he is quite right in pointing out that the major source of the problem lies in the present reward system in academia. This system rewards people for (primarily) grantsmaship which is more often than not is not a researcher's own work but its successful down-contracting to a cheap(er) research labor. Dr. Ibrahim is certainly correct in presenting the most influential members of the university research elite as primarily the successful contractors.

Regarding our formula "Fund Researchers, not proposals" - here we need some clarifications. Dr. Ibrahim is right in saying that the present system (NSERC, etc) actually, formally speaking, follows this formula. This is because it largely funds (overfunds) already established researchers (old boys) regardless of quality and/or substance of their proposals, and what is even more important, REGARDLESS of the ACTUAL results of their prior work. In short, the prime criterium for the nice grant amount is to be already a member of the club, or (for the younger researcher) to be immediately supported by one (or more) of the influential memebrs of the funding club (NSERC, NIH, NSF, etc).

By the same token the system DOES NOT fund many (actually almost none, apart from some lucky exceptions) 'non-members' of the funding club and it also happens pretty much regardless of the quality and content of their proposals. NSERC's use of the peer reviewers comments is a highly peculiar one: in those cases when the applicant is deemed to be 'fundable' ('one of us'), the critical comments (or even the lack of a real research progress) are ignored and a grant is given anyway.

Conversely, in those cases when the application is from the 'outsider' (not a club member), all the positive peer review comments are ignored, while any (sometime, minor or superficial) criticism is used to 'justify' the NIL award (non-funding).

One may think than that the solution should be a 'more thorough proposal evaluation' to avoid the effects of the old-boy networking and promote the merit principle.

Unfortunately, all prior experience shows that this solution (however sensible it may appear at first glance) is unimplementable in practice. All attemps to 'improve' peer review evaluation of grant proposals invariably only worsen it because such attemps invariably ignore the INHERENT uncertainties of the peer review (ANY peer review). To ignore these uncertainties as pointless as attempting to get around the Heisenberg's uncertainty principle in position momentum measurements.

Therefore, in our (Berezin and Hunter) view the formula "Fund researchers, not proposals" should first of all be interpreted as a mechanism to alocate BASIC research grants to all (eligible in a particular context) researchers subjected only to a demonsrtation of an on-going legitimate academic activity. We have suggested using the Forsdyke's sliding scale as a basis for grant alocation mechnanism, although some other schemes are availbale as well. Of couse, the above terms also bear some weight of imprecision, but the degree of it is far, far less than the arbitrariness of the present NSERC's grant selectivity YES-NO system.

Alexander A. Berezin, PhD
Department of Engineering Physics
McMaster University, Hamilton,
Ontario, Canada, L8S 4L7
tel. (905) 525-9140 ext. 24546
e-mail: BEREZIN@MCMASTER.CA

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PostDoc Position: NMR of optical glasses

by Jonathan Stebbins, stebbins@pangea.stanford.edu

Received: September 2, 1996
As part of a large collaborative study of defects and impurities of optical glasses, we have begun a project to use NMR to characterize the short- to intermediate-range structure of rare earth element doped oxide glasses. We are seeking a postdoc to work on this project at Stanford. Planned studies are open-ended, but include the use of spin-lattice relaxation to investigate the distribution of low levels of paramagnetic dopant ions as well as a variety of high-resolution techniques to quantify the local structure of host glasses. Studies may also include in-situ, high-temperature NMR experiments. The ideal candidate for the position would have considerable experience with modern solid-state NMR techniques in inorganic materials as well as experience with inorganic glass synthesis; however, the former of these two areas is considered higher priority. Our laboratory contains a variety of facilities for glass synthesis as well as a Varian spectrometer with a wide bore 9.4 T magnet, full solids capabilities, and a range of probes including high speed MAS, DAS, MAS to 600 deg C and static to 1400 deg C.

The postdoctoral position will be for one year with a possible extension to two years, and will be available October 1, 1996. Candidates wishing a somewhat later start date may also be considered.

Contact:

Professor Jonathan Stebbins
Dept. of Geological and Environmental Sciences
Stanford University
Stanford CA 94305-2115
415-723-1140
stebbins@pangea.stanford.edu

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Virtual Physics: a forum for virtual meetings of scientists and students involved in a research activity on CONTEMPORARY PHYSICS

Editors:

Marcel Ausloos, ausloos@gw.unipc.ulg.ac.be, Institut de Physique B5,
Université de Liège, Sart Tilman, B-4000 Liège, Belgium, tel. (+32 41) 66 37 52
Kenneth Holmlund, Kenneth.Holmlund@TP.UmU.SE, Department of Theoretical Physics
Umeå University, S-907 42 Umeå, Sweden, tel. +46-(0)90-167717
Cameron L. Jones, cjones@swin.edu.au, Centre for Applied Colloid and BioColloid Science
Swinburne University of Technology, P.O. Box 218 Hawthorn, Victoria, 3122 Australia, tel. +613 9214 8935, fax +613 9819 0834
Zbigniew J. Koziol (Editor-in-Chief), WebEx@ra.isisnet.com, WebExperts Inc.,
2-6032 Compton Ave., Halifax, Nova Scotia, B3H 1E7 Canada, tel. (902) 423 2149
Michal Spalinski, Michal.Spalinski@fuw.edu.pl, Institute of Theoretical Physics,
Warsaw University, Hoza 69, 00-681 Warsaw, Poland, tel. (+48 2) 628 3031
Krzysztof P. Wroblewski, chris@nmr.biophys.upenn.edu, School of Medicine
University of Pennsylvania, Rm. C-501 Richards Bldg., Philadelphia, PA 19104-6089, U.S.A., tel. (215) 898-6396
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Copyright (C) 1996 by Zbigniew Koziol.
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