Tim Halpin-Healy 
Ann Whitney Olin Professor   Barnard/Columbia Physics  
healy@phys.columbia.edu 
Telephone: (212)854-5102 
Ph.D. 1987 
Harvard University  
Mentors: Bert Halperin,
Mehran Kardar, Edouard Brézin   
A.B. 1981 
Princeton University  
Thesis Advisor: David Gross
 
The Dynamics of Conformity & Dissent,
Arne Soulier & THH, Phys. Rev. Lett. 90, 258103 (2003). 
Directed Polymers vs. Directed Percolation, THH, Phys. Rev. E58, 4096RC (1998). 
Chemical Wave Refraction Phenomena, Sin-Chun Hwang BC'96, & THH, Phys. Rev. E54, 3009 (1996).
Kinetic Roughening, Stochastic Growth, Directed Polymers & all that,THH & Y-C Zhang, Phys. Rep. 254, 215-415 (1995).  
Disturbing the Random Energy Landscape,  THH & D. Herbert BC'92, Phys. Rev. E48, 1617RC (1993). 
Depinning by Quenched Randomness, M. Zapotocky & THH, Phys. Rev. Lett. 67, 3463C (1991).  
Diverse Manifolds in Random Media, THH, Phys. Rev. Lett. 62, 442 (1989).  
My primary interests include phase transitions, critical phenomena, & the renormalization group; secondary concerns: kinetic roughening, reaction-diffusion systems, nonlinear dynamics, Nature's pattern formation. In recent years, I have concentrated my efforts on understanding the statistical mechanics of directed polymers in random media (DPRM), a baby version of the spin-glass and one of the few tractable problems in ill-condensed matter. Because of a mapping via the stochastic Burgers equation, the DPRM pays off handsomely, with important implications for vortex-line wandering in disordered superconductors, the propagation of flame fronts, domain-wall roughening in impurity-stricken magnets, as well as the dynamic scaling properties of Eden clusters. Tools of the trade are tied to the renormalization group in modern form, including both numerical and analytical approaches. Listed at left are a number of papers that I take particular pride in. They give a good sense of the statistical mechanical problems I like to work on.
Columbia Graduate Students:
Martin Z CU*91,  Yi-Kuo Yu CU*94,  N.-N. Pang CU*95,  Arne Soulier CU*02,  Aylin Cimenser CU*04   
Barnard Researchers- >17 total; selection:
B. Tamminga BC'93,  Yick Chan BC'93,  Sheila David BC'95,  Hasmik Diratzouian BC'96,  Rocio Patino BC'96,  Michelle Baird BC'96,  Rocky Novoseller BC'98, 
Mary Pratt BC'01,  Natalie Arkus BC'03,  W.-K. Wong BC'06,  Whitney Becker BC'07   
CU Summer HS Program: Class of 2005, '6, '7, '8   Expt'l & Theoretical Physics Course

Also:
Co-Director, Barnard College Centennial Scholars Program 
Director, BC Science & Public Policy Program; co-teach Science & The State

Miscellany:
CV  
NSF Grant 
South Africa Trip 
KPZ Review w/Zhang 
Recent Talk: The Dynamics of Conformity & Dissent  
Senior Thesis (1981)- Are Glueballs Found? Answer: Maybe (1995), though they're a slippery lot... (2005) ;-> 
Troisième Cycle Lectures (EPFL- Lausanne, Switzerland)- I. Interfacial Critical Phenomena, II. 3d Critical Wetting, III. Diverse Manifolds, IV. Realm of KPZ 
E=mc^2 

SECEDER applet, trial version here!  

Some Older, Research-Related, Stuff:

Click here for a picture of BZ Chemical Wave Refraction & Snell's Law

In this figure, we show a snapshot of a circular trigger wave which, having been initiated earlier in a double-layer membrane of thickness 304 microns, has propagated across the interface into a single layer 152 microns thick, where it travels more slowly, the refracted wave front being noticeably flattened. The geometry of the refracted front (definitely non-circular!! Check out next image....) is consistent with that dictated by Snell's Law, assuming a relative index of refraction n=1.45+/- 0.05. Independent measurements of chemical wave speeds in the two different media, obtained simply by tracking the radius of the expanding circle as a function of time, indicate a velocity ratio, 1.44+/-0.06, in fine agreement with this value. At the moment captured, incident trigger wave radius is 21 mm. This gives you a sense of the scale. The small depression in the center of the field of view was created by the 1mm diameter silver wire used to instigate the BZ trigger wave. Silver locally depletes the bromide concentration in the carefully prepared metastable BZ reagent mixture, thereby by kicking off a single cycle of this nonlinear oscillatory chemical reaction. For another manifestation of Snell's Law, see BZ Critical Angles. By initiating a trigger wave at the diameter end point of the membrane sandwich, being sure to touch the silver wire on the double layer side of the interface, we generate a wave front effectively incident at 90 degrees. The refracted wave front in the single layer is observed canted at the maximal angle, arcsin(1/n), predicted by Snell's Law. Our measured value, 43+/-1 degrees, yields a velocity ratio n=v2/v1=1.47+/-0.02, in good agreement with the previous, alternative determination. For more details regarding our work on BZ chemical wave refraction phenomena, have a look at the paper above written with Sin-Chun Hwang BC'96, a Barnard College chemical physics major.

Here, for a glimpse of something completely different: DPRM River Basin Delta

This relates to my work on the statistical mechanics of extremal trajectories in a random energy landscape. The immediate goal is to explain how the geometric complexity of optimal patterns differs from those generated by random processes. We'd like to understand to what degree various directed patterns found in nature, whether they be geomorphological (e.g., the Nile Delta) or biological (e.g., capillary blood vessel networks in the human eye) in character, represent globally optimal solutions within their given context. Plenty of info to be found in section 5.8 of the KPZ review paper that I wrote with Y.-C. Zhang @Universite Fribourg, Switzerland. See paper #5, as well, coauthored by Devorah Herbert BC'92, physics, shown here on graduation day with Bonnie Tamminga BC'93, another Barnard physics major who spent a summer working on KPZ statistical mechanics. Devorah's now a playwright; Bonnie went on for a PhD in experimental particle physics, a distinguished Leon Ledermann Post-Doctoral Fellowship at FermiLab, and is now an Assistant Professor in the Physics Department, Yale University.

Finally, an abstract regarding a separate DPRM issue: Tuning the Trip to KPZ Asymptopia

This paper followed from work with Rocky Novoseller BC'98, a graduate of the BC/CU 3-2 Engineering Program, concerning optimal access to the asymptotic scaling properties of the 2+1 dimensional DPRM. It is a natural postlude to the first reference listed above, which relates the blood connection between the DPRM & directed percolation. If the DPRM random bond energies are drawn from a full gaussian distribution, we obtain a reasonable estimate, ~0.216, of the energy fluctuation exponent, known to be slightly less than 1/4. Interestingly, if we bisect the gaussian, using just its right half, so that individual low energy bonds now appear with a relatively high probability, our scaling analysis suffers tremendously, yielding a very poor estimate, ~0.116, for the 2+1 DPRM energy exponent. This is a shock, of sorts, b/c a demi-gaussian biased low produces an abundance of cheap bonds, presumably a boon to the DPRM, which at zero temperature seeks a globally minimal path thru the random energy landscape. By contrast, using just the left half (i.e., a demi-gaussian biased high....), which leaves the polymer with a vanishingly small opportunity for the lowest energy bonds, we achieve the quickest route to asymptopia, our effective energy exponent reaching the value 0.245 after just 100 steps! For a view of the raw transfer matrix data, click here: Scaling Plot. Note the graph is double log, plotting energy fluctuation as ordinate, path length as abscissa. Asymptotically, the data sets are linear, with energy exponent read off as slope of the line.