Lawrence Schulman

He was born to Anna and Louis Schulman in Newark, New Jersey. He first went to the local public school, but switched to more Jewish oriented institutions, graduating from Yeshiva University in 1963. While still in college he married Claire Frangles Sherman. From Yeshiva he went to Princeton where he received the Ph.D. in physics for his thesis (under Arthur Wightman) A path integral for spin.

After completing his thesis he took a position as Assistant Professor at Indiana University (Bloomington), but in 1970 went to the Technion-Israel Institute of Technology in Haifa on a NATO postdoctoral fellowship.

At the Technion he accepted a position as Associate Professor, but only resigned from Indiana several years later as professor. In 1985, he returned to the United States as Chair of the Physics Department of Clarkson University and eventually (1988) also resigned from the Technion as a full professor. In 1991, he left the chair-ship and since then has stayed on at Clarkson as professor of physics.

In 2013, he spent part of a sabbatical at Georgia Institute of Technology and has since been adjunct professor at that institution.

Together with Phil Seiden of IBM, he began the first studies of randomized cellular automata,{{Cite journal|last1=Schulman|first1=L. S.|last2=Seiden|first2=P. E.|date=1978-09-01|title=Statistical mechanics of a dynamical system based on Conway's game of Life|journal=Journal of Statistical Physics|language=en|volume=19|issue=3|pages=293–314|doi=10.1007/BF01011727|issn=0022-4715|bibcode=1978JSP....19..293S|s2cid=37264536}} an area that morphed into a theory of star formation in galaxies, once they were joined by Humberto Gerola (an astrophysicist at IBM) who realized that star formation regions - as well as epidemic models- could be viewed as random cellular automata.{{Cite journal|last1=Seiden|first1=P. E.|last2=Schulman|first2=L. S.|last3=Gerola|first3=H.|date=September 1979|title=Stochastic star formation and the evolution of galaxies|bibcode=1979ApJ...232..702S|journal=The Astrophysical Journal|language=en|volume=232|pages=702–706|doi=10.1086/157329|issn=0004-637X}} Besides providing an explanation for spiral arms, this work ultimately solved the mystery of why dwarf galaxies can vary in their luminosity by large factors.{{Cite journal|last1=Gerola|first1=H.|last2=Seiden|first2=P. E.|last3=Schulman|first3=L. S.|date=December 1980|title=Theory of dwarf galaxies|bibcode=1980ApJ...242..517G|journal=The Astrophysical Journal|language=en|volume=242|pages=517–527|doi=10.1086/158485|issn=0004-637X|doi-access=free}}

In 1981, Schulman published Techniques and Applications of Path Integration,{{Cite web|url=http://store.doverpublications.com/0486445283.html|title=Techniques and Applications of Path Integration|website=store.doverpublications.com|access-date=2017-11-29}} from which many physicists learned about Feynman's path integral and its many applications. The book went on to become a Wiley classic and in 2005 came out in a Dover edition (with a supplement).

Once Schulman proved that there was no infinite cluster for long-range percolation in one dimension for sufficiently small but non-zero connection probability,{{Cite journal|last=Schulman|first=L. S.|date=1983|title=Long range percolation in one dimension|url=http://stacks.iop.org/0305-4470/16/i=17/a=001|journal=Journal of Physics A: Mathematical and General|language=en|volume=16|issue=17|pages=L639–L641|doi=10.1088/0305-4470/16/17/001|issn=0305-4470|bibcode=1983JPhA...16L.639S}} it became of interest whether for sufficiently large connection probability there was an infinite cluster. Together with Charles Newman, then of the University of Arizona. They used real-space renormalization methods to prove that there was.{{Cite journal|last1=Newman|first1=C. M.|last2=Schulman|first2=L. S.|date=1986-12-01|title=One dimensional 1/{{!}}j − i{{!}}S percolation models: The existence of a transition forS≦2|journal=Communications in Mathematical Physics|language=en|volume=104|issue=4|pages=547–571|doi=10.1007/BF01211064|issn=0010-3616|bibcode=1986CMaPh.104..547N|s2cid=116923610}}

Schulman lowered his Erdös number to two by collaborating with Mark Kac and others on Feynman's checkerboard path integral,{{Cite journal|last1=Gaveau|first1=B.|last2=Jacobson|first2=T.|last3=Kac|first3=M.|last4=Schulman|first4=L. S.|date=1984-07-30|title=Relativistic Extension of the Analogy between Quantum Mechanics and Brownian Motion|journal=Physical Review Letters|volume=53|issue=5|pages=419–422|doi=10.1103/PhysRevLett.53.419|bibcode=1984PhRvL..53..419G}}{{Cite journal|last1=Jacobson|first1=T.|last2=Schulman|first2=L. S.|date=1984|title=Quantum stochastics: the passage from a relativistic to a non-relativistic path integral|url=http://stacks.iop.org/0305-4470/17/i=2/a=023|journal=Journal of Physics A: Mathematical and General|language=en|volume=17|issue=2|pages=375|doi=10.1088/0305-4470/17/2/023|issn=0305-4470|bibcode=1984JPhA...17..375J}} realizing that a particle only acquires mass by scattering, reversing its speed-of-light propagation. Later the path to Erdös was reinforced by another collaboration, with his son Leonard, whose Erdös number is also one.{{Cite journal|last1=Schulman|first1=L. S.|last2=Schulman|first2=L. J.|date=January 2005|title=Wave-packet scattering without kinematic entanglement: convergence of expectation values|journal=IEEE Transactions on Nanotechnology|volume=4|issue=1|pages=8–13|doi=10.1109/TNANO.2004.840141|issn=1536-125X|bibcode=2005ITNan...4....8S|s2cid=41979767|url=http://authors.library.caltech.edu/6721/1/SCHUieeenano05.pdf}}{{Cite book|last1=Aronov|first1=Boris|last2=Erd\Hos|first2=Paul|last3=Goddard|first3=Wayne|last4=Kleitman|first4=Daniel J.|last5=Klugerman|first5=Michael|last6=Pach|first6=János|last7=Schulman|first7=Leonard J.|title=Proceedings of the seventh annual symposium on Computational geometry - SCG '91 |chapter=Crossing families |date=1991|location=New York, NY, USA|publisher=ACM|pages=351–356|doi=10.1145/109648.109687|isbn=978-0897914260|s2cid=644162}}

Quantum measurement had always seemed an oxymoron and in the 1980s Schulman conceived of a way to retain unitary time evolution while at the same time having a single "world" (in the sense of the many worlds interpretation). So measurements in quantum mechanics could yield definite results. The mechanism for achieving definite outcomes was the use of "special states" in which pure unitary evolution led to only a single outcome, when in the absence of special initial conditions many outcomes were conceivable. The need for those states at all times led to an examination of the arrow of time and of determinism (achieved here, but in a way that might have surprised Einstein, at least according to his collaborator - and Schulman's Technion colleague - Nathan Rosen).{{Cite journal|last=Schulman|first=L. S.|date=1984-06-11|title=Definite measurements and deterministic quantum evolution|journal=Physics Letters A|volume=102|issue=9|pages=396–400|doi=10.1016/0375-9601(84)91063-6|bibcode=1984PhLA..102..396S}}

These ideas have not been accepted in the mainstream of physics and Schulman himself has expressed doubts about them - his claim though is that other ideas on the quantum measurement process are even less believable.{{Cite journal|last=Schulman|first=Lawrence S.|date=2017-07-08|title=Program for the Special State Theory of Quantum Measurement|journal=Entropy|language=en|volume=19|issue=7|pages=343|doi=10.3390/e19070343|bibcode=2017Entrp..19..343S|doi-access=free}} As of 1997, the work was summarized in a book, Time's arrows and quantum measurement.{{Cite book|url=https://books.google.com/books?id=GlSWtTTBbgUC&dq=L.+S.+Schulman,+Time's+Arrows+and+Quantum+Measurement,+Cambridge+University+Press,+Cambridge,+1997&pg=PR15|title=Time's Arrows and Quantum Measurement|last=Schulman|first=Lawrence S.|date=1997-07-31|publisher=Cambridge University Press|isbn=9780521567756|language=en}} Despite the apparent finality of book publication, more than a decade later practical experimental tests of these ideas were conceived and published.{{Cite journal|last=Schulman|first=L. S.|date=2016-11-01|title=Special States Demand a Force for the Observer|journal=Foundations of Physics|language=en|volume=46|issue=11|pages=1471–1494|doi=10.1007/s10701-016-0025-8|issn=0015-9018|bibcode=2016FoPh...46.1471S|doi-access=free}}{{Cite journal|last1=Schulman|first1=L. S.|last2=Luz|first2=M. G. E. da|date=2016-11-01|title=Looking for the Source of Change|journal=Foundations of Physics|language=en|volume=46|issue=11|pages=1495–1501|doi=10.1007/s10701-016-0031-x|issn=0015-9018|bibcode=2016FoPh...46.1495S|doi-access=free}}

The arrow of time, of significance in the measurement problem, became a topic in and of itself. This goes back to Schulman's attempt to understand the Wheeler-Feynman absorber theory.{{Cite journal|last=Schulman|first=L. S.|date=1973-05-15|title=Correlating Arrows of Time|journal=Physical Review D|volume=7|issue=10|pages=2868–2874|doi=10.1103/PhysRevD.7.2868|bibcode=1973PhRvD...7.2868S}} Using similar tools he was able to demonstrate that two systems with opposite arrows of time could coexist, even with mild contact between them.{{Cite journal|last=Schulman|first=L. S.|date=1999-12-27|title=Opposite Thermodynamic Arrows of Time|journal=Physical Review Letters|volume=83|issue=26|pages=5419–5422|doi=10.1103/PhysRevLett.83.5419|arxiv=cond-mat/9911101|bibcode=1999PhRvL..83.5419S|s2cid=13302243}} There was also examination of other ideas on the arrow, including Thomas Gold's contribution (relating the thermodynamic arrow to the expansion of the universe) {{Cite journal|last=Gold|first=T.|date=1962-06-01|title=The Arrow of Time|journal=American Journal of Physics|volume=30|issue=6|pages=403–410|doi=10.1119/1.1942052|issn=0002-9505|bibcode=1962AmJPh..30..403G}} and a critique of Boltzmann's notions (now known as Boltzmann's Brain) as a form of solipsism.{{Cite book|url=https://books.google.com/books?id=AZrq7PcqhG0C&dq=Ludwig+Boltzmann,+%22Lectures+on+Gas+Theory,%22&pg=PP1|title=Lectures on Gas Theory|last=Boltzmann|first=Ludwig|date=2012-08-15|publisher=Courier Corporation|isbn=9780486152332|language=en}}{{Cite journal|last=Boltzmann|first=Ludwig|date=1965-11-01|title=Lectures on Gas Theory|journal=American Journal of Physics|volume=33|issue=11|pages=974–975|doi=10.1119/1.1971107|issn=0002-9505|bibcode=1965AmJPh..33R.974B}} See Schulman's critique on page 154 of.{{Cite journal|last=Schulman|first=L. S.|date=1973-05-15|title=Correlating Arrows of Time|journal=Physical Review D|volume=7|issue=10|pages=2868–2874|doi=10.1103/PhysRevD.7.2868|bibcode=1973PhRvD...7.2868S}}

Schulman was interested in the quantum Zeno effect, the deviation from exponential decay for short times. He predicted that the slowdown in decay that occurred in pulsed observation and the slowdown resulting from continuous measurement would differ by a factor of 4.{{Cite journal|last=Schulman|first=L. S.|date=1998-03-01|title=Continuous and pulsed observations in the quantum Zeno effect|journal=Physical Review A|volume=57|issue=3|pages=1509–1515|doi=10.1103/PhysRevA.57.1509|bibcode=1998PhRvA..57.1509S}} This was verified on Bose-Einstein condensates by a group at MIT.{{Cite journal|last1=Streed|first1=Erik W.|last2=Mun|first2=Jongchul|last3=Boyd|first3=Micah|last4=Campbell|first4=Gretchen K.|last5=Medley|first5=Patrick|last6=Ketterle|first6=Wolfgang|last7=Pritchard|first7=David E.|date=2006-12-27|title=Continuous and Pulsed Quantum Zeno Effect|journal=Physical Review Letters|volume=97|issue=26|pages=260402|doi=10.1103/PhysRevLett.97.260402|pmid=17280408|arxiv=cond-mat/0606430|bibcode=2006PhRvL..97z0402S|s2cid=2414199}}

Schulman has also contributed to practical matters through his collaboration with a group in Prague interested in luminescence and scintillators. This was first realized in a study anomalous decay caused by KAM tori in phase space (and the associated data fits) {{Cite journal|last1=Schulman|first1=L. S.|last2=Tolkunov|first2=D.|last3=Mihokova|first3=E.|date=2006-02-13|title=Stability of Quantum Breathers|journal=Physical Review Letters|volume=96|issue=6|pages=065501|doi=10.1103/PhysRevLett.96.065501|pmid=16606006|arxiv=cond-mat/0601209|bibcode=2006PhRvL..96f5501S|s2cid=12716463}} and more recently has led to studies of quantum tunneling.{{Cite journal|last1=Mihóková|first1=E.|last2=Schulman|first2=L. S.|last3=Jarý|first3=V.|last4=Dočekalová|first4=Z.|last5=Nikl|first5=M.|date=2013-07-18|title=Quantum tunneling and low temperature delayed recombination in scintillating materials|journal=Chemical Physics Letters|volume=578|issue=Supplement C|pages=66–69|doi=10.1016/j.cplett.2013.05.070|bibcode=2013CPL...578...66M}} When funds were available undergraduate students from Clarkson were sent to Prague to work in the optical materials laboratories.

Together with Bernard Gaveau (University of Paris VI) Schulman developed an embedding of a stochastic dynamical system in low dimensional Euclidean space, known as the "observable representation." This has proved useful in numerous areas from spin-glasses to ecology.{{Cite journal|last1=Gaveau|first1=B.|last2=Schulman|first2=L. S.|date=2006-03-24|title=Multiple phases in stochastic dynamics: Geometry and probabilities|journal=Physical Review E|volume=73|issue=3|pages=036124|doi=10.1103/PhysRevE.73.036124|pmid=16605615|arxiv=cond-mat/0604159|bibcode=2006PhRvE..73c6124G|s2cid=7771950}}{{Cite journal|last1=Gaveau|first1=Bernard|last2=Schulman|first2=Lawrence S.|last3=Schulman|first3=Leonard J.|date=2006|title=Imaging geometry through dynamics: the observable representation|url=http://stacks.iop.org/0305-4470/39/i=33/a=004|journal=Journal of Physics A: Mathematical and General|language=en|volume=39|issue=33|pages=10307|doi=10.1088/0305-4470/39/33/004|issn=0305-4470|arxiv=cond-mat/0607422|bibcode=2006JPhA...3910307G|citeseerx=10.1.1.560.3372|s2cid=44183518}}{{Cite journal|last=Schulman|first=L. S.|date=2007-06-20|title=Mean-Field Spin Glass in the Observable Representation|journal=Physical Review Letters|volume=98|issue=25|pages=257202|doi=10.1103/PhysRevLett.98.257202|pmid=17678051|arxiv=0705.1588|bibcode=2007PhRvL..98y7202S|s2cid=40756227}}

In 2005, he was awarded a Gutwiller fellowship from the Max Planck Institute for the Physics of Complex Systems in Dresden.{{cite web | url=http://people.clarkson.edu/~lschulma | title=L. S. Schulman }}

In 2022 he published another book, "When things grow many: Complexity, universality and emergence".{{Cite book|url=https://doi.org/10.1093/oso/9780198861881.001.0001|title=When things grow many: Complexity, universality and emergence|last=Schulman|first=Lawrence S.|date=2022-01-18|publisher=Oxford University Press|isbn= 9780198861881|language=en}} This is mainly a teaching tool.

He is the father of Leonard Schulman, Computer Science professor at the California Institute of Technology, Linda Parmet, Hebrew and Creative Design teacher at The Weber School,{{Cite web|title=Faculty/Staff Directory - The Weber School|url=https://www.weberschool.org/about-us/our-faculty/facultystaff-directory|access-date=2020-12-21|website=www.weberschool.org|language=en-US}} and David Schulman, an intellectual property attorney at Greenberg Traurig, one of the nation's largest law firms.

{{Reflist}}

• [http://people.clarkson.edu/~lschulma Home page]

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Category:1941 births

Category:Jewish American scientists

Category:Jewish agnostics

Category:Living people

Category:Date of birth missing (living people)