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Course# PHYS-436: Statistical physics IV

Summary

This first part of the course covers non-equilibrium statistical processes and the treatment of fluctuation dissipation relations by Einstein, Boltzmann and Kubo. Moreover, the fundamentals of Markov processes, stochastic differential and Fokker Planck equations, mesoscopic master equation, noise s

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Tobias Kippenberg

Tobias J. Kippenberg is Full Professor of Physics at EPFL and leads the Laboratory of Photonics and Quantum Measurement. He obtained his BA at the RWTH Aachen, and MA and PhD at the California Institute of Technology (Caltech in Pasadena, USA). From 2005- 2009 he lead an Independent Research Group at the MPI of Quantum Optics, and is at EPFL since. His research interest are the Science and Applications of ultra high Q microcavities; in particular with his research group he discovered chip-scale Kerr frequency comb generation (Nature 2007, Science 2011) and observed radiation pressure backaction effects in microresonators that now developed into the field of cavity optomechanics (Science 2008). Tobias Kippenberg is alumni of the “Studienstiftung des Deutschen Volkes”. For his invention of “chip-scale frequency combs” he received he Helmholtz Price for Metrology (2009) and the EFTF Young Investigator Award (2010). For his research on cavity optomechanics, he received the EPS Fresnel Prize (2009). In addition he is recipient of the ICO Prize in Optics (2014), the Swiss National Latsis award (2015), the German Wilhelm Klung Award (2015) and ZEISS Research Award (2018). He is fellow of the APS and OSA, and listed since 2014 in the Thomas Reuters highlycited.com in the domain of Physics. EDUCATION 2009: Habilitation (Venia Legendi) in Physics, Ludwig-Maximilians-Universität München 2004: PhD, California Institute of Technology (Advisor Professor Kerry Vahala) 2000: Master of Science (Applied Physics), California Institute of Technology 1998: BA in Physics, Technical University of Aachen (RWTH), Germany 1998: BA in Electrical Engineering, Technical University of Aachen (RWTH), Germany ACADEMIC POSITIONS 2013 - present: Full Professor EPFL 2010 - 2012: Associate Professor EPFL 2008 - 2010: Tenure Track Assistant Professor, Ecole Polytechnique Federale de Lausanne 2007 - present: Marie Curie Excellent Grant Team Leader, Max Planck Institute of Quantum Optics (Division of Prof.T.W. Hänsch) 2005 - present: Leader of an Independent Junior Research Group, Max Planck Institute 2005- present: Habilitant (Prof. Hänsch) Ludwig-Maximilians-Universität (LMU) 2005-2006: Postdoctoral Scholar, Center for the Physics of Information, California Institute of Technology 2000-2004: Graduate Research Assistant, California Institute of Technology PRIZES AND HONORS: ZEISS Research Award 2018 Fellow of the APS 2016 Klung-Wilhelmy Prize 2015 Swiss Latsis Prize 2014 Selected Thomson Reuters Highly Cited Researcher in Physics, 2014/2015 ICO Prize, 2013 EFTF Young Scientist Award (for "invention of microresonator based frequency combs") 2010 Fresnel Prize of the European Physical Society (for contributions to Optomechanics) 2009 Helmholtz Prize for Metrology (for invention of the monolithic frequency comb) 2009 1st Prize winner of the EU Contest for Young Scientists, Helsinki, Finland. Sept. 1996 Jugend forscht 1st Physics Prize at the German National Science Contest May 1996 FELLOWSHIPS Fellow of the German National Merit Foundation ("Studienstiftung des Deutschen Volkes") 1998-2002 Member of the Daimler-Chysler-Fellowship-Organization 1998-2002 Dr. Ulderup Fellowship 1999-2000 RESEARCH INTERESTS Experimental and theoretical research in photonics, notably high Q optical microcavities and their use in cavity quantum optomechanics and frequency metrology PUBLICATIONS AND OFTEN CITED METRICS*: >70 Publications in peer reviewed journals Researcher Google Profile: http://scholar.google.ch/citations?user=PRCbG2kAAAAJ&hl=en h-Index 54 (Google scholar H: 64, >25,000 citations) Thomson Reuters/Claravite List of Highly Cited Researchers (2014,2015,2016,2017) *careful in its use: https://www.aps.org/publications/apsnews/201411/backpage.cfm* KEY PUBLICATIONS AND REVIEWS: A. Ghadimi, et al. Elastic strain engineering for ultra high Q nanomechanical oscillators Science, (2018) Trocha, et al. Ultrafast distance measurements using soliton microresonator frequency combs Science, Vol. 359 (2018) [joint work with C. Koos] Pablo-Marin et al. Microresonator-based solitons for massively parallel coherent optical communications Nature (2017) [joint work with C. Koos] V. Brasch, et al. Photonic chip-based optical frequency comb using soliton Cherenkov radiation. Science, vol. 351, num. 6271 (2015) Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Reviews of Modern Physics 86, 1391-1452, (2014) Wilson, D. J. et al. Measurement and control of a mechanical oscillator at its thermal decoherence rate. Nature (2014). Verhagen, E., Deleglise, S., Weis, S., Schliesser, A. & Kippenberg, T. J. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482, 63-67 (2012). Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Microresonator-based optical frequency combs. Science 332, 555-559, (2011). Weis, S. et al. Optomechanically induced transparency. Science 330, 1520-1523 (2010). Kippenberg, T. J. & Vahala, K. J. Cavity optomechanics: back-action at the mesoscale. Science 321, 1172-1176, (2008). Del'Haye, P. et al. Optical frequency comb generation from a monolithic microresonator. Nature (2007) Schliesser, A., DelHaye, P., Nooshi, N., Vahala, K. & Kippenberg, T. Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction. Physical Review Letters 97, (2006).

PHYS-101(g): General physics : mechanics

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Boltzmann equation

The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872. The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random but biased transport of the particles making up that fluid.

Quantum master equation

A quantum master equation is a generalization of the idea of a master equation. Rather than just a system of differential equations for a set of probabilities (which only constitutes the diagonal elements of a density matrix), quantum master equations are differential equations for the entire density matrix, including off-diagonal elements. A density matrix with only diagonal elements can be modeled as a classical random process, therefore such an "ordinary" master equation is considered classical.

Dissipation

In thermodynamics, dissipation is the result of an irreversible process that affects a thermodynamic system. In a dissipative process, energy (internal, bulk flow kinetic, or system potential) transforms from an initial form to a final form, where the capacity of the final form to do thermodynamic work is less than that of the initial form. For example, transfer of energy as heat is dissipative because it is a transfer of energy other than by thermodynamic work or by transfer of matter, and spreads previously concentrated energy.

Fokker–Planck equation

In statistical mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces and random forces, as in Brownian motion. The equation can be generalized to other observables as well. The Fokker-Planck equation has multiple applications in information theory, graph theory, data science, finance, economics etc.

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MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.

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