Whose fault is plagiarism?

The controversy about the plagiarised Ph.D of the President of Hungary, Pal Schmitt, is making for "interesting" reading. In 1992 he received a Ph.D for a 200 page thesis that contains 17 pages directly translated from a German book. The rest seems to largely be a translation of work by a Bulgarian sports writer. A committee from the university reviewed the case and wrote a 1100+ page report (!) and concluded that he should keep his degree. The supervisors and examiners were to blame! However, following widespread criticism, the university just announced that they would revoke the degree.

Following the resignation of the German Defence minister for another plagiarised doctorate it seems that the academic backgrounds of prominent politicians are getting more scrutiny. This raises an interesting question. Which of the following is more likely to be true?

• there has been a lot of plagiarism in the social sciences and humanities but it is only being detected in the case of these politicians because of the increased scrutiny
• leading politicians are often ambitious individuals who "cut corners" and so are more prone to commit plagiarism

Unfortunately, the leadership of Australian universities is not immune from this problem. A decade ago the Vice Chancellor of Monash University, David Robinson, was forced to resign because of plagiarism.

A simple model for non-classical magnetoresistance

Previously I have posted about a diverse set of layered strongly correlated electron materials which exhibit a non-classical magnetoresistance. Specifically, the magnetoresistance can be largest (smallest) when the current and magnetic field are parallel (perpendicular).
Michael Smith has just published a nice paper Anomalous interlayer magnetoresistance in bilayer crystals which considers a simple concrete model that exhibits such behaviour. The key physics is that in alternating layers the conducting chains are perpendicular to each other. This does occur in some organic charge transfer salts, as mentioned in footnote 1 of the paper.

Should you work with a young turk or an old fart?

Picking an advisor/supervisor is one of the most important decisions that budding young science students must make at the final year undergraduate and Ph.D level. You should pick the advisor rather than the topic. A colleague once said to me, "Students are very good at picking bad supervisors."

An important aspect to the choice is whether is better to work with an energetic young faculty member (lecturer/Assistant Professor) (a "young turk") or a well established faculty member (Professor) (an "old fart").

Here are a few random thoughts on the relative merits of each. Bear in mind these are just generalisations and ultimately you will be working with (or for) an individual human being not some abstract concept or social classification. There are always exceptions.

Young turks offer you energy and enthusiasm. They have a lot riding on your success and may have significant time to invest in you. They may be working in some exciting new area or technique. Because they are closer to you in age they may be easier to build a strong personal and working relationship. On the down side they lack experience at picking research projects, particularly ones suitable to the average student, and lack experience at supervision. They may be so desperate to succeed (survive) they may want to take more credit than they deserve for your work. If they don't have tenure they may leave in the middle of your Ph.D. Will they take you with them if they move to a different institution? You want your supervisor to help you get a job or a place in a good Ph.D program. A junior scientist may not have the necessary contacts and reputation necessary for this.

In contrast, old farts may offer you wisdom, experience, and stability. Hopefully, they have learnt from the mistakes they made when they were a young turk and are now more effective at picking good research topics, particularly ones suitable for students, and will produce publishable results in a reasonable time. They may also be able to quickly see dead ends and save you a lot of time. On the other hand, they may be stuck in a rut in an old research field and be getting distant from nuts and bolts technical details. Worse, they may have lost interest in science and just be concerned about getting grants or an invited talk in some exotic locale...
They may be so busy with travel and/or administration that you will never see them. [But there are exceptions, e.g, Glenn T. Seaborg]. They don't have much riding on your success. They have already successfully graduated students. They don't need to get tenure or get promoted. If you aren't successful or bomb, it will be more likely that you will be blamed than them. But, a positive letter of reference from them may carry great weight to their extensive international network of senior colleagues and help land your next position.

On balance, I think the ideal situation is to have both a junior and senior person involved in your research. Two possible ways this might work.
i) A junior person is your main advisor, but you regularly talk informally to a senior person for feedback on what you are doing. This requires permission from your advisor.
ii) A senior person is your main advisor, but you work closely with a junior colleague in their research group, e.g., a senior postdoc.

Again, I stress these are just broad generalisations. There will always be exceptions. e.g., junior faculty who won't invest significant time in students, and old farts who won't give appropriate credit to their students. Senior people also take jobs elsewhere and may leave you behind...

I welcome comments. Who do you think might be the best option?

Quantum chemical justification for an empirical correlation

A challenge to quantum chemistry is to describe many of the empirical correlations that experimentalists have painstakingly catalogued. For example, an earlier post discusses a correlation between the rate of a photoisomerisation reaction and the electron withdrawing ability of a substitutent. An important empirical rule for organic dye molecules is the Dewar-Knott rule which relates the frequency (wavelength) of maximum light absorption [the colour of the dye] to the electron withdrawing (or donating) ability of a substituent.

Seth Olsen recently published a nice paper which gives a high level quantum chemistry justification of the Dewar-Knott rule for a family of diarylmethane dyes, including Michler's hydrol blue. The graph below shows how the excitation energy varies with a parameter characterising the composition of the ground state many-body wavefunction, and which varies with the substituent X.

Getting nervous at the biomolecular dance

Enzymes are amazing.
Today I went to an interesting chemistry seminar today by Ian Dance,
Nitrogenase reduces N2 to NH3 and CO to hydrocarbons. What chemistry is used?
It was also a David Craig lecture and was a model seminar for a general audience.

A major industrial process is the fixation of nitrogen to from ammonia.
N2 + 3H2 -> 2 NH3.
This is done via the Haber-Bosch process and requires pressures of 1000 atm and high temperatures of 450 degrees C with iron or ruthenium as catalysts.

However, nature does this at room temperature and pressure via nitrogenase enzymes. A surprising recent discovery was that vanadium nitrogenase can also reduce carbon monoxide to small hydrocarbons.

Dance used an interesting dance (!) metaphor during the talk. You need a stage [key part of the enzyme], centre stage [the active sites], dancers [the intermediate states], and a choreography [reaction mechanisms].

The stage for nitrogenase is shown below. the FeMo-co, which can be viewed as two  cubes [one is Fe4S3 and one Fe3MoS3] that have been fused together at a N vertex. Only very recently was the N atom seen in the enzyme structure.

Previously it was thought that the Mo atom on the bottom was the active site but now it is believed to be a pair of the Fe ions in the upper cube.

Something I thought were particularly interesting:
To obtain a good supply of protons to the active site one possible mean is a chain of hydrogen bonded water molecules [see the orange circles below].

A few things in the talk made me nervous.
All the calculations are based on some version of DFT. There was no mention of what functional was used, basis sets, convergence tests, or benchmarking.
Dance is using his own personal method for finding transition states.
It is not clear that he has a ground state with the correct spin, S=3/2.
There are tens of "molecular orbitals" [presumably actually Kohn-Sham orbitals] within about 1 eV of the so-called "HOMO" and "LUMO".
All the calculations are done in gas phase without implicit or explicit solvent (water + protein).
Many of the calculated activation energies are in the range 2-20 kcal/mol [0.1-1 eV for the physicists]. Is DFT really very reliable on this scale for such large molecules, particularly including 8 transition metal atoms?
Because the calculation gives too large an activation energy compared to experiment it was suggested that proton tunneling may occur below the barrier. [Apparently, it is not possible to test this hypothesis experimentally with isotope substitution.] [My experience with proton tunneling in enzymes is that this is subtle and murky issue].

Much of the material in the talk is in a summary paper

At what temperature are quasi-particles destroyed?

An interesting question [which has featured in many of my blog posts] concerns defining the coherence temperature at which quasi-particles in a Fermi liquid are "destroyed". There are several possible experimental signatures of this:

• absence of a sharp dispersing peak in the one electron spectral density (as seen in ARPES)
• collapse of the Drude peak in the optical conductivity
• collapse of the linear in T term in the specific heat capacity
• a peak in the thermopower versus temperature
• deviations of the resistivity temperature dependence from T^2
• the resistivity becoming larger than the Mott-Ioffe-Regel limit.

I tended to think that these would all occur at the approximately the same temperature.
(A Nature paper also makes a similar assumption.)
However, Jure Kokalj pointed out to me that DMFT gives quite different temperatures for the different signatures above. For example, in this PRB the thermopower and specific heat have a peak at a temperature at which there is still a Drude peak.

A PRL I recently blogged about contains the "throw away" line that got my attention:

the Fermi liquid behavior in two-particle properties is more fragile than in single-particle ones. Indeed, in the well-known Kondo problem the Kondo resonance persists at temperatures up to 2T_K while the magnetic susceptibility saturates to a Pauli form only below T=0.2T_K.

That is an order of magnitude difference in temperature scales!

This point can be seen in this nice paper by Costi, Hewson, and Zlatic. For example, compare Figures 2, 7, and 16, which show the specific heat, spectral density, and thermopower, respectively.

It would be nice to have a simple physical picture of the origin of these disparate temperature scales. Perhaps it is something as mundane as different convolutions and moments of the Fermi-Dirac distribution.

A case study in getting published

I was pleased to learn this week that my paper on hydrogen bonding has been accepted for publication in Chemical Physics Letters. I believe this may be one of the most significant papers I have written. Time will tell...

The paper has an "interesting" history. Six months ago I sent the paper with the title Unified description of hydrogen bonding and proton transfer by a two-state effective Hamiltonian to Physical Review Letters. I chose PRL because I thought the paper was significant and it approached the problem from a physicist's point of view, putting simplicity and physical insight before chemical detail. However, based on one brief referee report, an Adjunct Associate Editor rejected the paper. I wrote a rebuttal and resubmitted it. You may find the rebuttal interesting reading as it highlights what I consider to be some fundamental issues about what is good and novel science, particularly of complex chemical systems.

I was optimistic because I thought my rebuttal was persuasive [what do you think?] and I have a long track record of publishing in PRL. A few times with PRL I have received two negative reports, rebutted them, and eventually got the paper into PRL. However, the Adjunct Associate Editor would not give the paper further consideration. I found this rather disappointing.

I then gave the paper the more modest, specific, and technical title A diabatic state model for donor-hydrogen vibrational frequency shifts in hydrogen bonded complexes and sent it to Chemical Physics Letters. It received two detailed, helpful, and positive referee reports. Although one of referees still thought along the lines of "this is so simple surely someone must have done it before."

More anomalous magnetoresistance

This is the latest in a series of posts cataloguing how there are wide range of strongly correlated metals which exhibit magnetoresistance which is qualitatively different from the semi-classical orbital magnetoresistance seen in most metals due to the Lorentz force. For the latter the magnetoresistance is maximal (zero) for the current and magnetic field perpendicular (parallel) to each other.

The data above is taken from a paper reporting measurements on the quasi-one-dimensional metal Li0.9Mo6O17, which also exhibits other non-Fermi liquid properties.
The graph shows the magnetic field dependence (in Teslan) of the relative change in the interlayer resistance with the field and current parallel to one another. The different curves correspond to different temperatures, increasing from 3 K to 50 K, from top to bottom.

1000 blog posts!

I just noticed that I have now made more than 1000 posts on this blog! It is hard to believe. It all started three years ago when I heard a talk about blogging at the I2CAM annual meeting by Clifford Johnson.

The blog now gets about 3,000 page views per week. However, I still wish it generated more comments and discussion. I fear I am just not controversial enough.

Am I the students ally or adversary?

Some students see the instructor/teacher/lecturer as their ally. Someone whose role is to help them learn and understand.

Other students see the teacher as their adversary. Someone who is assessing them, critiquing them, making them feel dumb, forcing them to work, ... Someone they have to do battle with to get the marks and grade they think they deserve...

I am not sure how to get students to see me as their ally rather than their adversary. I think a lot of it boils down to my attitude and their attitude. I can change my attitude but there are some students whose attitude may not change, regardless of what I do. Also, the attitude of a class can be swayed, for better or for worse, by a few influential students. I think using a formative/summative assessment mix can help. This enables students to get feedback in a less threatening way and with lower stakes.

I welcome other ideas.

A bad metal model

There is an interesting PRB Conductivity of hard core bosons: a paradigm of a bad metal by Netanel Lindner and Assa Auerbach.
They calculate the frequency and temperature dependence of a model for hard core bosons on a square lattice at half filling. There is only a single energy scale J, the intersite boson hopping energy, in the Hamiltonian.
At low temperatures (below the Kosterlitz-Thouless transition temperature ~ J) the system is a superfluid. At T > 2J the model is in a metallic phase with a resistivity which increases approximately linearly with temperature and has values larger than the Mott-Ioffe-Regel limit (~ the quantum of resistance). There is a broad "Drude peak" with a width which is much larger than J and a spectral weight which decreases with increasing temperature.

The model also approximately obeys Homes scaling law which relates the superfluid density, the superfluid transition temperature Tc, and the conductivity at Tc, for cuprate superconductors. The authors also speculate that a peak in the optical conductivity associated with order parameter magnitude fluctuations [the Higgs mass] might be associated with the mid-infra-red peak seen in the cuprates. This does have alternative explanations in terms of fermionic excitations [see for example this PRB].

This is a nice paper because it gives very concrete results for a "simple" model Hamiltonian. How relevant it is to the cuprates remains to be seen. A definite connection would mean that the Cooper pairs persist to very high temperatures. It would be nice to see a calculation of the temperature dependence of the thermoelectric power.

Teaching tips

If you want some new (and old) ideas to improve your teaching it is worth looking at McKeachie's teaching tips: strategies, research, and theory for college and university teachers. The book is now in the 13th edition.

Desperately seeking a way to find order parameters

Much of condensed matter physics is concerned with finding the relevant order parameter for new phases of matter. Indeed this is a good way to win a Nobel Prize! This is much of what was done by Ginzburg, Neel, Leggett, de Gennes,....

A fundamental and controversial question is whether one can a priori predict new order parameters. Historically, the progression has always been:

1. Experimental discovery of a new phase of matter.
2. Proposal of an order parameter and a phenomenological (Ginzburg-Landau) theory to explain a range of experiments.
3. Proposal of an effective Hamiltonian which has a ground state with the desired spontaneous symmetry breaking and associated order parameter.
4. Justification of the effective Hamiltonian from so-called "ab initio" electronic structure calculations starting with Schrodinger's equation and the actual chemical composition of specific materials. 

The grand challenge is to invert this process, even just one step.

Laughlin and Pines seem to claim that this is essentially impossible.

There are some interesting fundamental philosophical questions as to whether the obstacles are ones of practical difficulty versus fundamental physics.

There is really interesting 2006 PRL, Systematic Derivation of Order Parameters through Reduced Density Matrices, by Shunsuke Furukawa, Grégoire Misguich, and Masaki Oshikawa.
Essentially they claim to have found a way to go from 3. to 2. above. In particular, given the results of an exact diagonalisation calculation of the low lying states of a lattice model they give a procedure to find the order parameter from looking at two nearly degenerate ground states.
They then apply the method to two concrete examples: a Heisenberg spin model on a ladder with ring exchange, and a quantum dimer model on the Kagome lattice. The method gives the correct order parameters in the first case and for the second shows there is no order parameter. I found this quite impressive and promising.

The PRL also promises future work generalising the method to more than two degenerate ground states and suggests application to frustrated two-dimensional quantum antiferromagnets. Unfortunately, I have not been able to find such work.

Being more precise about Density Functional Theory (DFT)?

It seems to me many authors (particularly non-experts) are rather sloppy when they refer to electronic structure calculations based on Density Functional Theory (DFT). They say things like "our results are in good agreement with DFT calculations" or "we calculate the excited state energies using DFT". What don't I like about this?

DFT is an exact theory,.... provided one has the exact exchange-correlation functional and one can solve the non-linear variational functional equation the density must satisfy....
Hence, DFT should always agree with experiment!

But in reality, pure DFT is practically useless. One cannot do either of the above and so much use approximate functionals such as those based on the Local Density Approximation (LDA) or Generalised Gradient Approximation (GGA). These then lead to Kohn-Sham type equations which are straight-forward to solve.

Hence, it seems to me it is preferable to say, "our experimental results are comparable to values obtained from DFT-based calculations using the LDA".
But, maybe I am just pedantic...

Polywater: lest we forget

Many readers may be unaware of an embarrassing period in the history of physical chemistry and quantum chemistry [and Science, Nature, and DARPA]. (I only know about it because I grew up hearing my father talk about it). For a few heady years around 1970, many scientists sincerely believed that there was a stable polymer form of water. This was even "supported" by quantum chemistry calculations by Allen and Kollman (Princeton University) published in Science.
Eventually, it turned out that the original experimental evidence for polywater resulted from impurities.

This sad episode is recounted in detail in the book Polywater by Felix Franks. There is a very nice review by David Eisenberg, entitled "A Scientific Gold Rush" (published in Science!) of the book. It is worth reading, including the discussion of how the fact that the existence of polywater would have violated the laws of thermodynamics did not deter many true believers...
Here is a quote from the review:

[Franks] is interested in the factors, partly nonscientific, that created the gold rush atmosphere and distorted the normal scientific process. Among the factors blamed by Franks are: 

the willingness of some scientists to submit for publication incomplete or even shoddy work in order to achieve priority; 

a breakdown in normal standards of reviewing, particularly in journals such as Nature and Science that publish short notes on matters perceived to be of wide current interest; 

a concern among administrators in defense-sponsored research agencies that in the post-Sputnik era it would be unfortunate to allow the Soviets the lead in another field; 

a fascination on the part of the public, created in part by exaggerated and inaccurate reports in the popular press, with a new form of water; 

a tendency of investigators to leak results to the press before publication;

It is fascinating and noteworthy that JACS only published one paper on polywater. Somehow some of the factors above remind me of "quantum biology" today...

Seeing the dark state in fluorescent proteins

Two years ago Seth Olsen and I published a paper, pointing out that in the Green Fluorescent Protein there should be a dark excited state [i.e. a state which does not contribute significantly to the one-photon absorption cross section] which should have a large two photon absorption (TPA) cross section. This has a natural explanation in terms of a valence bond description of the three lowest lying singlet states of the chromophore.

We were very pleased that last year there was a long article in Nature methods, Two-photon absorption properties of fluorescent proteins, by Drobizhev et al.. It contains the data below. The peak on the left (around 650 nm) is due to TPA from the dark excited state.

The authors were unaware of our work, but cite it in their latest paper on vibronic effects in two-photon absorption.

An inspirational chemist is inspired by chemistry

CNR Rao has published an auto-biography Climbing the Limitless Ladder: A Life in Chemistry. There are nice reviews in the Hindu newspaper and Chemistry World. It is impressive how he continues to be so passionate about doing science, in spite of many successes and the burden of significant administrative and advising responsibilities.

Testing universality in ultracold fermion atomic gases

Today we had a nice colloquium by Chris Vale about recent experiments from his group testing Tan's universal relations for ultracold high density (k_F a much greater than 1) atomic Fermi gases with large scattering lengths a.
This regime corresponds to the centre of the figure below, taken from a Physics Today article by Carlos Sa de Melo

There is an interesting short Physics article by Eric Braaten which puts Tan's theory in a broader historical context.

"in preparation" is not a publication

On your CV you need to clearly distinguish real publications, preprints, and works "in preparation".
When reviewing CV's I personally think the latter are just irritating, count for nothing, and should be left off your CV.

The value of course blogs

For the fourth semester I am teaching a course with a blog where students must write weekly on the blog about what they are learning. They also must write some comments on other student posts.

I think this is a very valuable experience for the students and for me. It keeps them engaged and forces them to think about what they are learning. I find it very valuable to read their posts because it gives me a good measure of their level of understanding and what topics or concepts they are struggling with. I am usually struck by how much they still need to learn and understand, and how things that seem obvious to me are not to them. It is a good reminder how about 25 years ago I struggled to master the subject too. I need to slow down my teaching and explain everything carefully. You can check out the blog here.

Onsager's semi-classical quantisation of cyclotron orbits

I have been working through a really nice paper
Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models
by J. N. Fuchs, F. Piéchon, M. O. Goerbig and G. Montambaux

The Appendix below I found particularly illuminating

Capturing the directionality of hydrogen bonding

Below is a schematic picture of hydrogen bonding between a donor D and an acceptor A.

An interesting and important question is how the potential energy of the system varies with the angle phi which measures deviations from linearity. A key property of H-bonds is that they are highly directional. This leads to the four-fold co-ordination of water in liquid and solid phases.

There is a vibrational mode associated with this co-ordinate phi.
[In water this rotation is connected to the librational mode].

Previously I posted about an empirical correlation showing how this mode hardens with the increasing strength of the H-bond (decreasing R above). This is the opposite trend to the D-H stretch frequency (associated with the r co-ordinate above) which softens with decreasing R.

I was very pleased when I discovered that the model effective Hamiltonian I proposed for H-bonding can describe this correlation (see the figure below) without introducing any new parameters.

This is discussed in more detail in the final version of my paper.

Aside: I earlier posted the graph above in a post about confirmation bias. I should say that after I did get good agreement between the theory and experiment, I did go back and check all the algebra and mathematica codes.

The beauty of the Drude model

I have been teaching the Drude model for the umpteenth time, but have a new slant I am emphasizing to the students. It only involves a single new parameter, the scattering time. Yet it is able to capture the details of a wide range of experiments on elemental metals. I think it is important for students to appreciate the importance of considering the simplest possible models, with as few free parameters as possible, and see what they can and cannot explain. Only then one should move to more advanced models which are closer to the "truth".

The age-old problem of management

Chelsea football club announced on the weekend that they are sacking their manager Andre Villas-Boas (AVB) after less than 12 months on the job.

Why is this relevant? In the midst of all the analysis one point was clear. One of the problems was that AVB was only 34 years old and was managing players who were only two years younger than him.

Sometimes this is a problem in academia. I have known of very successful young faculty members who have struggled to gain the respect needed for a good working relationship from students or postdocs who are older than them. This is a complex issue (because people are complex!). There are counter examples and every case is different but it is something to be cautious about. If you are a young faculty member think twice before you hire an older person and if you are an older student make sure you really do respect your potential advisor before you sign on.

What is wrong with this textbook?

It contains no actual experimental data. Just schematic representations of data or functional relationships.
Or, it contains "artist renditions" of data. Below is an example from Atkins' Physical Chemistry.

The best texts show actual data. Two of my favourite texts are: Biological Physics by Phil Nelson and An Introduction to Thermal Physics by Daniel Schroeder.

It is also interesting and disturbing that looking through the Australian edition of a popular introductory microeconomics text co-authored by Robert E. Frank [of Economic Naturalist fame] I could only find schematic graphs and no actual data.

Why does this matter?
After all, the figures look so much nicer and cleaner if they are just schematic. It is easier for students to understand them.

However, I think it is very important that students learn:

• Real science is messy.
• A theory is only as good as the experimental evidence for it.
• How to read, understand, and critique experimental data.

Below is a very nice figure from Kittel's Introduction to Solid State Physics. It shows the magnetic susceptibility of different elemental metals. Looking at the data gives a sense of how reliable is the prediction of the Sommerfeld (and Bloch) models that the susceptibility is independent of temperature for temperatures much less than the Fermi temperature. Unfortunately, my preferred text by Ashcroft and Mermin does not show such a graph.

Deconstructing Kondo universality

At the cake meeting this week I gave a talk on Nozieres' classic 1974 paper, A "Fermi liquid" description of the Kondo Problem at low temperatures. He gives a very elegant (but hard to follow) argument as to why the Wilson ratio should have the universal value 2, independent of the strength of the Kondo coupling J.

There is actually a clearer restatement of Nozieres' argument in a review article by Piers Coleman (see section 2.6). [I thank Ben Powell for pointing this out]. Hewson's book (Section 5.1) also has an equivalent argument but I found that even harder to follow. But, I did like the connection to Friedel's sum rule and the emphasis that the charge compressibility on the impurity site is zero.

Key assumptions (and physical insights) required in the argument seem to be:

• A Fermi liquid fixed point (J=infinity).
• An analytic dependence of the phase shift on energy.
• The Kondo singlet acts as a spinless, elastic scattering centre with phase shift pi/2 at the Fermi energy.
• The Kondo-Suhl resonance is pinned to the chemical potential.
• For quasi-particles away from the Fermi energy only interact with quasi-particles of opposite spin.

Why is the theory of strongly correlated electrons so challenging?

The field is particularly demanding due to the need to assess, integrate and synthesize large amounts of information from a diverse range of experimental, theoretical, and computational studies that use a plethora of techniques to study a multitude of properties, models, and materials. This requires significant amounts of time and experience to evaluate and make appropriate judgement calls about the relative importance and probable validity of specific pieces of information. Inadequately informed judgements can lead to wasted time due to pursuing directions that ultimately turn out to be at best irrelevant and at worst wrong.

Furthermore, an intimate knowledge of both the chemical and physical properties of solids is a necessary ingredient for the development of realistic models of different classes of complex materials. A key judgement has to be made about how much detail is necessary.

Or, is the field a mine field?