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tion they u was initially propod for the analysis of a model describing interacting rel-ativistic particles in two-dimensional space-time (10). The theory now operates in a differ-ent world of particles: Phonons, which are normal modes of th e entire system, are replaced by weakly interacting soliton-like particles that are fermions traveling through th e system. Th e new th eory cannot be re-normalized, which should be expected given that it is the old one in disgui. However, if residual weak interactions
between the new soliton-like particles are neglected, the theory can be treated exactly, and th e inter-actions between the prototype particles—the日语n2
ph onons—remain practically unch anged.The interactions are encoded in the nonlin-ear transformation rules from one theory to the other and allow any hydrodynamic ob-rvable to be calculated explicitly.
The beauty of Imambekov and Glazman’s work is that it provides an example of a mean-ingful quantum field theory for a problem lacking a consistent perturbative formulation.The mathematics of this theory is not only interesting—it describes real systems with rich phenomenology, and should allow for further explorations. For example, it should be possible to develop a theory of quantum wave breaking and quantum shock waves.
References
1. A. Imambekov, L. I. Glazman, Science 323, 228 (2009);published online 27 November 2008 (10.1126/science.1165403).
2.R. P. Feynman, QED: The Strange Theory of Light and Matter (Princeton Univ. Press, Princeton, NJ, 1985).
3. D. Kleppner, R. Jackiw, Science 289, 893 (2000).教师节演讲稿
4.G. Volovik, JETP Lett . 82, 319 (2005).
5.S. J. Tans et al., Nature 386, 474 (1997).
6.H. Moritz, T. Stferle, M. Köhl, T. Esslinger, Phys. Rev. Lett.91, 250402 (2003).
7.T. Giamarchi, Quantum Physics in One Dimension (Oxford Univ. Press, Oxford, UK, 2003).
8.M. Pustilnik, M. Khodas, A. Kamenev, L. I. Glazman, Phys.Rev. Lett.96, 196405 (2006).
9. D. N. Aristov, Phys. Rev. B 76, 085327 (2007).10. D. Mattis, E. Lieb, J. Math. Phys.6, 304 (1965).
10.1126/science.1168389
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hen a glass is heated, it melts and begins to flow. This tran-sition from an elastic solid to
a flowing fluid is a distinguishing feature of the glass transition, one of the most widely studied, yet in
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completely under-stood, pha transitions (1). The applica-tion of stress can also make a glass flow;softer glass, including many polymers,
yield wh en subjected to sufficiently large stress (2). The equivalence of
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the two routes to flow is a basic tenet of jam-ming, a conceptual means of unifying glassy behavior with that of granular materials such as sand (3). The shear-induced flow of sand, or other granular materials, is well studied. On page 231 of this issue, Lee et al . (4) show that the nature of shear-induced flow in molecular glass can now be probed. By measuring the motion of small probe molecules in a polymer glass, they find fluidlike properties when the glass is sheared; however, the route to melting the glass is different from that followed when it is heated. Lee et al.u an optical method to measure the rate of rotation of small dye molecules embedded within thin slabs of lightly cross-linked poly(methyl methcrylate) (PMMA).The probe molecules provide a direct, local measure of the fluidity of the polymer. As the temperature is incread and th e polymer glass starts to flow, the structural relaxation rate of th e polymer, as determined by th e motion of th e probe molecules, becomes measurable and begins to increa with tem-perature, adopting the characteristic stretched exponential form of a fluid very clo to the glass transition (5). Moreover, the structural relaxation exhibits the strong spatial hetero-geneity commonly obrved in a fluid very
clo to the glass transition (5, 6). The new experiments investigate the behavior of the probe molecules when the polymer is sub-jected to an external uniaxial tension; the sam-ple is pulled apart by its two ends. Initially,when the strain is small, the structural relax-ation rate increas sligh tly, and can be described by a theory that incorporates the effects of the induced strain energy, which lowers the activation barriers for the relax-ation of th e probe molecules due to th eir shear-induced rotation (7). The shape of the decay retains th e ch aracteristic stretch ed exponential form. However, as both the strain and strain rate increa, the relaxation rate of th e probe molecules increas by veral orders of magnitude, and the shape of the relaxation becomes nearly exponential. At this point, the sample undergoes plastic flow, and at the molecular scale, the glass melts due to the induced strain.This shear-induced melting is exactly what is expected within the jamming picture. The basic concepts of jamming can be understood from the perspective of a granular material,such as a bucket of sand. Normally, the sand in the bucket is a solid; it does not flow and it supports a stress, as easily proven by stepping on it—th e sand supports your weigh t.However, if you tip the bucket, the sand flows,much like a fluid. Here, gravity provides the shear stress that caus the sand to change from a solid to a fluid. To make the analogy between granular sand and a glass requires a cond route to fluidizing th e sand—by increasing its effective temperature. This can be accomplished by gently shaking it, or by blowing air slowly up through the sand, to slightly suspend a
ll the grains in the flow of air (8). In this ca, the grains are rapidly moving,but are trapped in place by all their neighbors.
This rapid random motion of the grains is akin to an incread effective temperature. To com-plete the jamming picture, there is a third means of fluidizing a solid, and th at is to Small probes reveal that glass can melt in different ways.
Unjamming a Polymer Glass
David A. Weitz
MATERIALS SCIENCE
Shear flow. Schematics comparing shear-induced flow in a granular material (left ) and a glassy polymer (right ).Published by AAAS
decrea the volume fraction. This may be dif-ficult to comprehend for sand in air, so imag-ine instead immersing the sand in a fluid to provide buoyancy. Then, if you decrea the number of grains per unit volume, you will eventually have so few grains that they will no longer be lf-supporting, and thus the solid will be fluidized. Any of the three routes can take the system throug
h the solid-to-f luid transition, and much work has been devoted to explore the generality of this concept for gran-ular systems. By contrast, there have been fewer attempts to explore the same concept of jamming for molecular glass.
television缩写The importance of the experiments by Lee et al.is that they establish that shear does induce melting of the glass, and that the result-ant flowing material has many features of a liquid, particularly as evidenced by the relax-ation of the probe molecules. However, the experiments also establish that the nature of the solid-to-fluid transition is different when it is shear-induced as compared with thermally
induced melting. The sheared sample lacks the large spatial heterogeneities that charac-terize a melting sample.
Moreover, in a sheared sample, there is a narrower distribution of barriers to relaxation than in a sample that has melted. Instead, it is tempting to think that the impod shear rate ts the scale for all the relaxations, resulting in a much narrower range of rates. Moreover,flow occurs in localized regions, in agreement with the picture of shear transformation zones (9), and the volume of the regions is consis-tent with that found in computer simulations (9) and in measurements of a colloidal glass (10), a material that straddles a granular sys-tem and a molecular glass.
The comparison between a granular sys-tem and a molecular glass, as originally postu-lated by the jamming concept, remains an intriguing and appealing hypothesis. The experiments provide strong evidence for the merit of this perspective, suggesting that com-puter simulations of jammed granular systems
under shear may also provide new insight into the behavior of sheared molecular glass.However, a detailed understanding of the true extent of the analogy must await confirmation by further studies. The approach of Lee et al.should help make this possible.
References and Notes
1. C. A. Angell, Science 267, 1924 (1995).
2.H. E. H. Meijer, L. E. Govaert, Prog. Polym. Sci. 30, 915(2005).
3. A. J. Liu, S. R. Nagel, Nature 396, 21 (1998).
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4.H.-N. Lee, K. Paeng, S. F. Swallen, M. D. Ediger, Science 323, 231 (2009).
5.M. D. Ediger, Annu. Rev. Phys. Chem. 51, 99 (2000).
6. E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, D. A.Weitz, Science 287, 627 (2000).
7.H. Eyring, J. Chem. Phys. 4, 283 (1936).
8.N. Menon, D.J. Durian, Phys. Rev. Lett. 79, 3407 (1997).9.M. L. Falk, J. S. Langer, Phys Rev E. 57, 7192 (1998).10.P. Schall, D. A. Weitz, F. Spaepen, Science 318, 1895
(2007).
11.This work was supported by the NSF (grant DMR-0602684) and the Harvard Materials Science Rearch and Engineering Center (grant DMR-0820484).
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magine that you are a white student wait-ing with two other students, one black and one white, for a psychology experiment to begin. The black student steps out of the room for a moment, lightly bumping against the white student on his way out. While he is out of earshot, the white student comments,“T ypical, I hate it when black people do that.”How would you feel? And if you later had the choice, with which of the other students would you prefer to work? If you anticipate being upt and avoiding the fellow who made the racist remark, you are like most “forecaster”participants in a study by Kawakami et al.(1)on page 276 in this issue. The were students,lf-identified as members of racial groups other than black, who predicted how they would react after reading about or viewing a videotaped enactment of the events.
Other participants in the study, from the same student population as the forecasters,actually experienced this event, with actors portraying the white and black students in the scenario. Surprisingly, when asked during the
experiment how they felt, the “experiencers”did not report feeling any more upt when the racist
comment was made than when the same event occurred without any comment being made at all. Nor did the experiencers tend to avoid the originator of the racist comment. The f indings are an example of what social psychologists call a failure of affective forecasting: People often mispredict how they would feel (and therefore act) in imagined or future situations (2, 3). In other words, our emotional reactions (or lack of them) often
surpri us. Indeed, if our emotions never sur-prid us, they would fail to perform one of their most important functions: to call our attention to important aspects of a situation that we otherwi might not have consciously noted. For example, one reason for poor emo-tion forecasting is that experiencers react to a much wider range of cues in a situation,whereas forecasters focus more narrowly on its most salient features (such as the racist remark in the study by Kawakami et al.) (4).One thing emotions can inform us about,sometimes to our surpri, is who we are in a given situation. This happens becau emotions can ari from our identification with social groups and not only from our individual lf (5,6). For example, imagine you are a woman in an organization, learning that a female col-league has won promotion to upper manage-ment. Y ou may feel disappointment and envy if you are taking an individual perspective. But if you are thinking of yourlf instead primarily as a woman, you may feel pride and happiness at this blow to the “glass c
eiling” (7). Thus, f eel-ing happy rather than envious may tell you, per-haps to your surpri, what group membership defines you in the specific situation.
What identities and corresponding emo-tional and behavioral reactions are possible in
Why are our predictions of how we’ll feel or act sometimes wrong?
Surprising Emotions
Eliot R. Smith 1and Diane M. Mackie 2
pivot
BEHAVIOR
Who would be in this situation?Depending on the identity (such as egalitarian or racist) that is acti-vated in a given situation, people can experience different emotions and behave in different ways.But people often fail to predict accurately their iden-tity and emotions in a future or imagined situation.
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Published by AAAS
