Topological Quantum Order: Stability Under Local Perturbations
Spiros Michalakis, Los Alamos National Laboratory
We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. We focus on 2D models of TQO for which the unperturbed Hamiltonian H_0 can be written as a sum of local pairwise commuting projectors. A perturbed Hamiltonian H=H_0+ epsilon V involves a generic perturbation V that can be written as a sum of short-range bounded-norm interactions. Let lambda_1, ldots, lambda_g be the set of g lowest eigenvalues of H, where g is the ground state egeneracy of H_0. We prove that if epsilon is below a constant threshold value then all eigenvalues lambda_1, ldots, lambda_g coincide up to exponentially small corrections and separated from the rest of the spectrum of H by a constant gap. This result implies that H and H_0 can be connected by an adiabatic path without closing the gap. Our proof goes by setting up Hamiltonian flow equations transforming a generic perturbation to a special "block-diagonal" perturbation that preserves the ground subspace of H_0. These flow equations are analyzed using Lieb-Robinson bounds and the theory of relatively bounded operators. Our technical tools might be useful for analyzing other stability problems for quantum spin systems.
http://www.cs.caltech.edu/seminars/abstracts/09-10/michalakis-s.html
http://www.bogotobogo.com, http://www.epicmath.com
Friday, January 8, 2010
Computer Science and Economics:
Computer Science and Economics: The faculty of the Division of Engineering and Applied Science and the Division of the Humanities and Social Sciences of the California Institute of Technology invite applications for a tenure-track position in computer science and economics. Examples of research areas of interest include multi-agent systems, game theory, mechanism design, and distributed systems, although the quality of the work is more important than the area. We are seeking highly qualified candidates who are committed to a career in research and teaching.
The term of initial appointment is normally four years, if untenured, and is contingent upon completion of the Ph.D.
Application InstructionsApplicants should submit an electronic application, including (in pdf format) a letter of application describing your current research, a curriculum vita, three letters of recommendation, and samples of your work. Please use our on-line application system. Questions about the application process may be directed to search@cs.caltech.edu
The California Institute of Technology is an Equal Opportunity/Affirmative Action Employer. Women, minorities, veterans, and disabled persons are encouraged to apply.
http://www.eas.caltech.edu/positions/cs-econ/index.html
http://www.bogotobogo.com, http://www.epicmath.com
The term of initial appointment is normally four years, if untenured, and is contingent upon completion of the Ph.D.
Application InstructionsApplicants should submit an electronic application, including (in pdf format) a letter of application describing your current research, a curriculum vita, three letters of recommendation, and samples of your work. Please use our on-line application system. Questions about the application process may be directed to search@cs.caltech.edu
The California Institute of Technology is an Equal Opportunity/Affirmative Action Employer. Women, minorities, veterans, and disabled persons are encouraged to apply.
http://www.eas.caltech.edu/positions/cs-econ/index.html
http://www.bogotobogo.com, http://www.epicmath.com
News
News
Hareem T. Maune, a graduate student studying carbon nanotube physics, and Si-ping Han, a graduate student investigating the interactions between carbon nanotubes and DNA, have developed DNA origami nanoscale breadboards for carbon nanotube circuits. "This collaborative research project is evidence of how we at Caltech select the top students in science and engineering and place them in an environment where their creativity and imagination can thrive," says Ares Rosakis, chair of the Division of Engineering and Applied Science at Caltech and Theodore von Kármán Professor of Aeronautics and Professor of Mechanical Engineering. The work of these students was supervised by: Erik Winfree, Associate Professor of Computer Science, Computation and Neural Systems, and Bioengineering; William A. Goddard III, Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics; Paul W.K. Rothemund, Senior Research Associate, and Marc Bockrath, Associate Professor of Physics at University of California Riverside. Read More... 11.10.09
Congratulations to Tracey Ho, Assistant Professor of Electrical Engineering and Computer Science, and Andrew D. Straw, Postdoctoral Scholar in Bioengineering for being awarded 2010 Young Investigator Research Program grants by the Air Force Office of Scientific Research. They are among only 38 scientists and engineers who will be awarded a total of $14.6 million in grants. Read more... 10.29.09
Event Processing: Designing IT Systems for Agile Companies is the title of a new book by K. Mani Chandy, Simon Ramo Professor and Professor of Computer Science. 10.08.09
The Walter and Leonore Annenberg Center for Information Science and Technology and the GALCIT Guggenheim project have both won top honors from the American Institute of Architects -Pasadena/Foothill Chapter. This is the second time Guggenheim has won this honor! 10.01.09
Dr. Paul Rothemund, Senior Research Associate in Bioengineering, Computer Science, and Computation and Neural Systems, and colleagues have developed a new technique to orient and position self-assembled DNA shapes and patterns--or "DNA origami"--on surfaces that are compatible with today's semiconductor manufacturing equipment. They "have removed a key barrier to the improvement and advancement of computer chips. They accomplished this through the revolutionary approach of combining the building blocks for life with the building blocks for computing," said Professor Ares Rosakis, Chair of Division of Engineering and Applied Science and Theodore von Kármán Professor of Aeronautics and Mechanical Engineering. Read More... 08.18.09
The molecular computational research of Erik Winfree, Associate Professor of Computer Science, Computation and Neural Systems, and Bioengineering, focuses on understanding how chemical systems can perform information processing and how to program a set of molecules to carry out instructions. This exciting research was recently featured in Discover. Read more... 08.18.09
The Walter and Leonore Annenberg Center for Information Science and Technology (IST), designed by the architectural firm Frederick Fisher and Partners, is near completion. The building which is nicknamed "the green building" will be home to some participants of the IST initiative, an interdisciplinary research and instruction program addressing the growth and impact of information as it relates to all science and engineering practices. The building dedication ceremony is scheduled for October 30, 2009 please visit the EAS division website for more information on the event. Read more...
Jehoshua "Shuki" Bruck, Caltech's Gordon and Betty Moore Professor of Computation and Neural Systems and Electrical Engineering, has won the Richard P. Feynman Prize for Excellence in Teaching. Caltech's most prestigious teaching honor, the prize was established in 1993 "to honor annually a professor who demonstrates, in the broadest sense, unusual ability, creativity, and innovation in undergraduate and graduate classroom or laboratory teaching." A member of the Caltech faculty since 1994, Bruck was the founding director of Information Science and Technology (IST) at Caltech. His research combines work on the design of distributed information systems and the theoretical study of biological circuits and systems. Kudos!
Andreas Krause will be joining the Computer Science department in January as Assistant Professor. His focus is on machine learning algorithms and probabilistic reasoning both in theory and in complex real world systems, with applications including environmental monitoring, building automation, traffic prediction, and activity recognition. Welcome Professor Krause!
http://www.cs.caltech.edu/news.html
http://www.bogotobogo.com, http://www.epicmath.com
Hareem T. Maune, a graduate student studying carbon nanotube physics, and Si-ping Han, a graduate student investigating the interactions between carbon nanotubes and DNA, have developed DNA origami nanoscale breadboards for carbon nanotube circuits. "This collaborative research project is evidence of how we at Caltech select the top students in science and engineering and place them in an environment where their creativity and imagination can thrive," says Ares Rosakis, chair of the Division of Engineering and Applied Science at Caltech and Theodore von Kármán Professor of Aeronautics and Professor of Mechanical Engineering. The work of these students was supervised by: Erik Winfree, Associate Professor of Computer Science, Computation and Neural Systems, and Bioengineering; William A. Goddard III, Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics; Paul W.K. Rothemund, Senior Research Associate, and Marc Bockrath, Associate Professor of Physics at University of California Riverside. Read More... 11.10.09
Congratulations to Tracey Ho, Assistant Professor of Electrical Engineering and Computer Science, and Andrew D. Straw, Postdoctoral Scholar in Bioengineering for being awarded 2010 Young Investigator Research Program grants by the Air Force Office of Scientific Research. They are among only 38 scientists and engineers who will be awarded a total of $14.6 million in grants. Read more... 10.29.09
Event Processing: Designing IT Systems for Agile Companies is the title of a new book by K. Mani Chandy, Simon Ramo Professor and Professor of Computer Science. 10.08.09
The Walter and Leonore Annenberg Center for Information Science and Technology and the GALCIT Guggenheim project have both won top honors from the American Institute of Architects -Pasadena/Foothill Chapter. This is the second time Guggenheim has won this honor! 10.01.09
Dr. Paul Rothemund, Senior Research Associate in Bioengineering, Computer Science, and Computation and Neural Systems, and colleagues have developed a new technique to orient and position self-assembled DNA shapes and patterns--or "DNA origami"--on surfaces that are compatible with today's semiconductor manufacturing equipment. They "have removed a key barrier to the improvement and advancement of computer chips. They accomplished this through the revolutionary approach of combining the building blocks for life with the building blocks for computing," said Professor Ares Rosakis, Chair of Division of Engineering and Applied Science and Theodore von Kármán Professor of Aeronautics and Mechanical Engineering. Read More... 08.18.09
The molecular computational research of Erik Winfree, Associate Professor of Computer Science, Computation and Neural Systems, and Bioengineering, focuses on understanding how chemical systems can perform information processing and how to program a set of molecules to carry out instructions. This exciting research was recently featured in Discover. Read more... 08.18.09
The Walter and Leonore Annenberg Center for Information Science and Technology (IST), designed by the architectural firm Frederick Fisher and Partners, is near completion. The building which is nicknamed "the green building" will be home to some participants of the IST initiative, an interdisciplinary research and instruction program addressing the growth and impact of information as it relates to all science and engineering practices. The building dedication ceremony is scheduled for October 30, 2009 please visit the EAS division website for more information on the event. Read more...
Jehoshua "Shuki" Bruck, Caltech's Gordon and Betty Moore Professor of Computation and Neural Systems and Electrical Engineering, has won the Richard P. Feynman Prize for Excellence in Teaching. Caltech's most prestigious teaching honor, the prize was established in 1993 "to honor annually a professor who demonstrates, in the broadest sense, unusual ability, creativity, and innovation in undergraduate and graduate classroom or laboratory teaching." A member of the Caltech faculty since 1994, Bruck was the founding director of Information Science and Technology (IST) at Caltech. His research combines work on the design of distributed information systems and the theoretical study of biological circuits and systems. Kudos!
Andreas Krause will be joining the Computer Science department in January as Assistant Professor. His focus is on machine learning algorithms and probabilistic reasoning both in theory and in complex real world systems, with applications including environmental monitoring, building automation, traffic prediction, and activity recognition. Welcome Professor Krause!
http://www.cs.caltech.edu/news.html
http://www.bogotobogo.com, http://www.epicmath.com
Nobel Laureate Ahmed Zewail Named United States Science Envoy
Nobel Laureate Ahmed Zewail Named United States Science Envoy
Caltech scientist will promote science and technology partnerships among nationsPASADENA, CALIF. - Nobel Laureate Ahmed Zewail, the Linus Pauling Professor of Chemistry and professor of physics at the California Institute of Technology (Caltech), has been named an envoy in the new U.S. Science Envoy Program, created to foster science and technology collaborations between the United States and nations throughout the Middle East, North Africa, and South and Southeast Asia. Zewail, who was also appointed to President Obama's Council of Advisors on Science and Technology earlier this year, is one of three eminent Americans who will serve as the first scientist-diplomats in the new program.
Secretary of State Hillary Clinton announced the appointment of "three of America's leading scientists" in a major address on November 3 in Marrakesh, Morocco. She described the program as one of several partnerships in the key areas of economic opportunity, science and technology, and education that are being launched in the wake of President Obama's speech last June at Cairo University, in which he promised a "new beginning" in America's relationship with Muslim communities around the world.
"It is a great honor and humbling responsibility to take on such a challenge in a tumultuous and changing world," said Zewail, who received the 1999 Nobel Prize in Chemistry for groundbreaking research into how atoms join together to form molecules. "After years of research on the dynamics of chemical bonds, I look forward to helping to forge new bonds among nations."
The Egyptian-born Zewail will serve as science envoy to 10 nations of the Middle East, where, according to the State Department, he will "engage counterparts, deepen and develop partnerships in all areas of science and technology, and foster meaningful collaboration to meet the greatest challenges facing the world today in health, energy, the environment, as well as in water and resource management."
"Ahmed Zewail is an ideal choice for science envoy," said Caltech president Jean-Lou Chameau. "He brings to the post superb scientific credentials and an abiding commitment to promoting science and technology for both its own sake and the betterment of society, and he is held in high esteem throughout the world. I am delighted that he will have the opportunity to serve both our nation and the international community in this capacity."
Zewail is internationally known for his work in femtosecond chemistry, in which he pioneered the use of ultrafast laser techniques to record atoms in the act of making and breaking molecular bonds-the basis of all chemical reactions-on the timescale at which such reactions actually occur, about one millionth of a billionth of a second. He currently directs the Physical Biology Center for Ultrafast Science and Technology at Caltech, with a focus on the development of four-dimensional microscopy, a new field established to visualize the behavior in space and time of matter at the nanoscale.
Zewail has a long-standing interest in global affairs, particularly as they relate to science, technology, and higher education, and his commentaries have appeared in Britain's Independent and the Wall Street Journal, among other publications. In a piece published earlier this fall in the Boston Globe and the International Herald Tribune, he called on Muslim nations to join with the West in new science and technology partnerships, an agenda that he will now be in a unique position to advance as U.S. science envoy.
The Caltech professor's numerous honors include the Albert Einstein World Award of Science, the Benjamin Franklin Medal, the Robert A. Welch Award, the Leonardo da Vinci Award, the Wolf Prize, and the King Faisal Prize. He has been awarded the Order of the Grand Collar of the Nile, Egypt's highest state honor, and has been featured on postage stamps issued to honor his contributions to science and humanity. He holds honorary degrees from 35 universities around the world, and is an elected member of many professional academies and societies, including the National Academy of Sciences, the Royal Society of London, and the Swedish, Russian, and French academies.
Zewail's fellow envoys are Bruce Alberts, president of the National Academy of Sciences from 1993 to 2005, and Elias Zerhouni, director of the U.S. National Institutes of Health from 2002 to 2008. Alberts, professor emeritus of biochemistry at the University of California, San Francisco, and editor in chief of Science magazine, will serve as the envoy to South and Southeast Asia. Zerhouni, a native of Algeria and professor of radiology and biomedical engineering at Johns Hopkins University, will be the envoy to North Africa.
http://media.caltech.edu/press_releases/13303
http://www.bogotobogo.com, http://www.epicmath.com
Caltech scientist will promote science and technology partnerships among nationsPASADENA, CALIF. - Nobel Laureate Ahmed Zewail, the Linus Pauling Professor of Chemistry and professor of physics at the California Institute of Technology (Caltech), has been named an envoy in the new U.S. Science Envoy Program, created to foster science and technology collaborations between the United States and nations throughout the Middle East, North Africa, and South and Southeast Asia. Zewail, who was also appointed to President Obama's Council of Advisors on Science and Technology earlier this year, is one of three eminent Americans who will serve as the first scientist-diplomats in the new program.
Secretary of State Hillary Clinton announced the appointment of "three of America's leading scientists" in a major address on November 3 in Marrakesh, Morocco. She described the program as one of several partnerships in the key areas of economic opportunity, science and technology, and education that are being launched in the wake of President Obama's speech last June at Cairo University, in which he promised a "new beginning" in America's relationship with Muslim communities around the world.
"It is a great honor and humbling responsibility to take on such a challenge in a tumultuous and changing world," said Zewail, who received the 1999 Nobel Prize in Chemistry for groundbreaking research into how atoms join together to form molecules. "After years of research on the dynamics of chemical bonds, I look forward to helping to forge new bonds among nations."
The Egyptian-born Zewail will serve as science envoy to 10 nations of the Middle East, where, according to the State Department, he will "engage counterparts, deepen and develop partnerships in all areas of science and technology, and foster meaningful collaboration to meet the greatest challenges facing the world today in health, energy, the environment, as well as in water and resource management."
"Ahmed Zewail is an ideal choice for science envoy," said Caltech president Jean-Lou Chameau. "He brings to the post superb scientific credentials and an abiding commitment to promoting science and technology for both its own sake and the betterment of society, and he is held in high esteem throughout the world. I am delighted that he will have the opportunity to serve both our nation and the international community in this capacity."
Zewail is internationally known for his work in femtosecond chemistry, in which he pioneered the use of ultrafast laser techniques to record atoms in the act of making and breaking molecular bonds-the basis of all chemical reactions-on the timescale at which such reactions actually occur, about one millionth of a billionth of a second. He currently directs the Physical Biology Center for Ultrafast Science and Technology at Caltech, with a focus on the development of four-dimensional microscopy, a new field established to visualize the behavior in space and time of matter at the nanoscale.
Zewail has a long-standing interest in global affairs, particularly as they relate to science, technology, and higher education, and his commentaries have appeared in Britain's Independent and the Wall Street Journal, among other publications. In a piece published earlier this fall in the Boston Globe and the International Herald Tribune, he called on Muslim nations to join with the West in new science and technology partnerships, an agenda that he will now be in a unique position to advance as U.S. science envoy.
The Caltech professor's numerous honors include the Albert Einstein World Award of Science, the Benjamin Franklin Medal, the Robert A. Welch Award, the Leonardo da Vinci Award, the Wolf Prize, and the King Faisal Prize. He has been awarded the Order of the Grand Collar of the Nile, Egypt's highest state honor, and has been featured on postage stamps issued to honor his contributions to science and humanity. He holds honorary degrees from 35 universities around the world, and is an elected member of many professional academies and societies, including the National Academy of Sciences, the Royal Society of London, and the Swedish, Russian, and French academies.
Zewail's fellow envoys are Bruce Alberts, president of the National Academy of Sciences from 1993 to 2005, and Elias Zerhouni, director of the U.S. National Institutes of Health from 2002 to 2008. Alberts, professor emeritus of biochemistry at the University of California, San Francisco, and editor in chief of Science magazine, will serve as the envoy to South and Southeast Asia. Zerhouni, a native of Algeria and professor of radiology and biomedical engineering at Johns Hopkins University, will be the envoy to North Africa.
http://media.caltech.edu/press_releases/13303
http://www.bogotobogo.com, http://www.epicmath.com
The math undergraduate ...
The physics program offers instruction in the fundamentals of modern physics and provides a foundation for graduate study as well as providing an excellent basis for future work in a wide variety of allied fields. The graduate program is meant to prepare students for a career in original scientific research or research combined with teaching. A full spectrum of courses is offered with the aim of providing a firm foundation in basic physics in areas of contemporary investigation.
The math undergraduate program gives students an understanding of the broad outlines of modern mathematics, to stimulate an interest in research, and to prepare them for later work, either in pure mathematics or allied sciences. The principal aim of the graduate program is to develop the student's ability to do original research in mathematics in universities, industry or government. Independent and critical thinking is fostered by direct contact with faculty members.
The astrophysics program prepares students for creative and productive careers in astrophysical research. With the goal of understanding the physical processes that govern the universe, its constituents, and their evolution, astronomy uses the apparatus and methodology of physics to gather and interpret data. The opportunity exists for students to take advantage of the many observational facilities owned and operated by Caltech.
http://www.pma.caltech.edu/GSR/divfacinfo.html
http://www.bogotobogo.com, http://www.epicmath.com
The math undergraduate program gives students an understanding of the broad outlines of modern mathematics, to stimulate an interest in research, and to prepare them for later work, either in pure mathematics or allied sciences. The principal aim of the graduate program is to develop the student's ability to do original research in mathematics in universities, industry or government. Independent and critical thinking is fostered by direct contact with faculty members.
The astrophysics program prepares students for creative and productive careers in astrophysical research. With the goal of understanding the physical processes that govern the universe, its constituents, and their evolution, astronomy uses the apparatus and methodology of physics to gather and interpret data. The opportunity exists for students to take advantage of the many observational facilities owned and operated by Caltech.
http://www.pma.caltech.edu/GSR/divfacinfo.html
http://www.bogotobogo.com, http://www.epicmath.com
Computer Science at Caltech
The computer science department at Caltech consists of a small group of students, faculty and staff. The small size and collegial atmosphere at Caltech facilitates close working relationships among faculty and students, and encourages novel interdisciplinary research. Students are encouraged to tailor their programs of courses and research to fit their specific needs. Students often collaborate on large projects, but each student is treated as an important individual, with unique goals, drives and needs.
Research emphases are in algorithms; communication protocols, concurrent computation, and networks; graphics and human-computer interaction; novel computational substrates, including quantum mechanical computers and molecular computers; VLSI, with a specific emphasis on asynchronous and analog VLSI; high-confidence systems, including fault tolerance, program verification, and security; information theory; learning theory; computer vision; and large-scale scientific computing. Projects frequently involve connections with other disciplines such as Physics, Biology, Mathematics, Mechanics, Control and Dynamical Systems, and Electrical Engineering.
Undergraduates are encouraged to do research. Many have papers in conferences or journals. The opportunity for close collaboration with faculty and graduate students on research, the flexibility of developing your own research and course structure, and outstanding facilities, makes Caltech an ideal environment for motivated undergraduates.
Graduate study in Computer Science is a full-time program. Students are admitted only with the Ph.D. as the degree objective, although an M.S. degree is a required step in the program. Students join a research group and participate in research from the very beginning, so it is important that applicants have a defined area of interest before applying. The first year emphasizes course work and master's thesis research. Students in their second year complete their master's thesis preliminary to the candidacy examination. After passing the candidacy exam, students devote their time to research on the doctoral dissertation. The program requires a minimum of three academic years of residence.
Applications are accepted once per year, no later than January 1st, and reviewed at that time for admission and financial aid for admission the following September. In order for all candidates to receive equal consideration, unofficial evaluations of likelihood admission will not be made. Applications are reviewed after all credentials, including recommendation letters and official copies of test scores, have been received. GRE scores are required, with a subject test of the student's choice strongly recommended. It is strongly recommended that applicants take the GRE in October to allow enough time for Caltech to receive the scores by January. Early submissions are encouraged as application reviews are already in progress in December.
Applications are encouraged from fields other than computer science, but applicants should be aware that the program is mathematically and scientifically oriented. Students who hold a Ph.D. degree from another institution are not normally admitted to graduate standing at Caltech to pursue a second Ph.D. degree.
- from http://www.cs.caltech.edu
http://www.bogotobogo.com, http://www.epicmath.com
Research emphases are in algorithms; communication protocols, concurrent computation, and networks; graphics and human-computer interaction; novel computational substrates, including quantum mechanical computers and molecular computers; VLSI, with a specific emphasis on asynchronous and analog VLSI; high-confidence systems, including fault tolerance, program verification, and security; information theory; learning theory; computer vision; and large-scale scientific computing. Projects frequently involve connections with other disciplines such as Physics, Biology, Mathematics, Mechanics, Control and Dynamical Systems, and Electrical Engineering.
Undergraduates are encouraged to do research. Many have papers in conferences or journals. The opportunity for close collaboration with faculty and graduate students on research, the flexibility of developing your own research and course structure, and outstanding facilities, makes Caltech an ideal environment for motivated undergraduates.
Graduate study in Computer Science is a full-time program. Students are admitted only with the Ph.D. as the degree objective, although an M.S. degree is a required step in the program. Students join a research group and participate in research from the very beginning, so it is important that applicants have a defined area of interest before applying. The first year emphasizes course work and master's thesis research. Students in their second year complete their master's thesis preliminary to the candidacy examination. After passing the candidacy exam, students devote their time to research on the doctoral dissertation. The program requires a minimum of three academic years of residence.
Applications are accepted once per year, no later than January 1st, and reviewed at that time for admission and financial aid for admission the following September. In order for all candidates to receive equal consideration, unofficial evaluations of likelihood admission will not be made. Applications are reviewed after all credentials, including recommendation letters and official copies of test scores, have been received. GRE scores are required, with a subject test of the student's choice strongly recommended. It is strongly recommended that applicants take the GRE in October to allow enough time for Caltech to receive the scores by January. Early submissions are encouraged as application reviews are already in progress in December.
Applications are encouraged from fields other than computer science, but applicants should be aware that the program is mathematically and scientifically oriented. Students who hold a Ph.D. degree from another institution are not normally admitted to graduate standing at Caltech to pursue a second Ph.D. degree.
- from http://www.cs.caltech.edu
http://www.bogotobogo.com, http://www.epicmath.com
Subscribe to:
Posts (Atom)