Sergei Winitzki, Ph.D. (Dr. rer. nat. habil.) Research Fellow Arnold Sommerfeld Center for Theoretical Physics Department of Physics Ludwig-Maximilians University Theresienstr. 37 80333 Munich, Germany Office: 3rd floor, room 329 Tel. (+49) 89 2180 ext. 4111 Email: winitzki "at" physik.uni-m...de
Research and CV Publications Recent talks Teaching and course materials Miscellaneous lecture notes

Education

Graduate	1992-1997	Ph.D., Tufts University (Medford, Mass., USA) Adviser: Alexander Vilenkin
Undergraduate	1988-1992	equivalent of B.S., Moscow Institute of Physics and Technology (Dolgoprudny, Russia)

Employment

03.2008-present	Research Associate (C1 Wiss. Assistent)	Ludwig-Maximilians University (Munich, Germany)
10.2007-02.2008	Visiting Professor (Lehrstuhlvertretung)	University of Heidelberg (Heideberg, Germany)
09.2002-09.2007	Research Associate (C1 Wiss. Assistent)	Ludwig-Maximilians University (Munich, Germany)
2001-2002	Research Associate	Tufts University (Medford, Mass., USA)
1999-2001	Research Associate	CWRU (Cleveland, Ohio, USA)
1997-1999	Research Associate	DAMTP, University of Cambridge (Cambridge, UK)

Research interests

• Quantum cosmology, quantum gravity, eternal inflation, stochastic description of the universe
  The stochastic approach to inflationary spacetimes describes the effect of vacuum fluctuations by introducing an effective "noise field." The accumulation of large-scale fluctuations in the inflaton field generically leads to the phenomenon of "eternal inflation": the inflationary expansion of the universe does not globally terminate. During eternal inflation, the spacetime resulting from the backreaction of the amplified quantum fluctuations is highly inhomogeneous on extremely large (super-horizon) scales. I study the stochastic description of such spacetimes, in terms of probability distributions for the inflaton field and for observable quantities. The global geometry of an eternally inflating spacetime is a self-similar fractal, and the causal structure of the infinite null future is not yet clarified.
  I am also interested in studying the connection between these features of eternal inflation and the landscape of string theory as well as the holographic principle. A fundamental description of the quantum-to-classical transition in the inflationary spacetime involves quantum fluctuations of the metric, and so may yield observational constraints on quantum gravity.

• Non-Gaussian features in the CMBR, non-Gaussian statistics
  Fluctuations of the CMB temperature observable today are directly related to the origin and evolution of primordial matter. Statistical features of these fluctuations and, in particular, deviations from a Gaussian distribution allow us in principle to distinguish between currently viable alternative models of inflation and of structure formation. The possible non-Gaussian features in the CMB are a valuable source of information about the early universe, complementing the power spectrum and polarization. I study methods of extracting non-Gaussian CMBR predictions from various models of the early universe. I have developed several physically motivated analytical models of non-Gaussian fluctuations, and I am investigating the strengths and weaknesses of various methods of CMB analysis and of their power to trace the signatures of particular effects in the early universe.

• Computational and algorithmic aspects of applied mathematics
  This is a sideline of my research that concerns arbitrary-precision numerical calculations, methods of asymptotic analysis, and symbolic computation.
  

Publications

1. S. Winitzki (2009) Eternal Inflation, monograph published by World Scientific, 2009.
2. A. Linde, V. Vanchurin, and S. Winitzki (2009) "Stationary measure in the multiverse". JCAP 0901:031, 2009. Preprint arXiv:0812.0005.
3. L. A. Gergely, N. Pidokrajt, and S. Winitzki (2008) "Thermodynamics of tidal charged black holes". Preprint arXiv:0811.1548 [gr-qc].
4. S. Winitzki (2008) "Reheating-volume measure for the landscape". Phys.Rev. D 78 (2008), 123518. Preprint arXiv:0810.1517 [gr-qc].
5. S. Winitzki (2008) "Reheating-volume measure for random-walk inflation". Phys.Rev. D 78 (2008), 063517. Preprint arXiv:0805.3940 [gr-qc].
6. S. Winitzki (2008) "A volume-based measure for eternal inflation". Phys.Rev. D 78 (2008), 043501. Preprint arXiv:0803.1300.
7. S. Winitzki (2007) "Age-dependent decay in the landscape". Phys.Rev. D 77 (2008), 063508. Preprint arXiv:0712.2192.
8. J. U. Kang, V. Vanchurin, and S. Winitzki (2007) "Attractor scenarios and superluminal signals in k-essence cosmology". Phys.Rev. D 76 (2007), 083511. Preprint arxiv:0706.3994.
9. V. F. Mukhanov and S. Winitzki (2007) "Introduction to Quantum Effects in Gravity". A textbook published by Cambridge University Press, available from June 2007.
10. S. Winitzki (2006) "Predictions in eternal inflation". Invited review, Lect. Notes Phys. 738, 157-191 (2008). Preprint gr-qc/0612164.
11. F. Helmer and S. Winitzki (2006) "Self-reproduction in k-inflation." Phys.Rev. D 74 (2006), 063528. Preprint gr-qc/0608019.
12. J. Garriga, D. Schwarz-Perlov, A. Vilenkin, and S. Winitzki (2005) "Probabilities in the inflationary multiverse." JCAP01(2006)017. Preprint hep-th/0509184.
13. S. Winitzki (2005) "Cosmological particle production and the precision of the WKB approximation." Phys. Rev. D 72 (2005) 104011. Preprint gr-qc/0510001. Local copy here.
14. S. Winitzki (2005) "Time-reparametrization invariance in eternal inflation." Phys. Rev. D 71 (2005) 123507. Preprint gr-qc/0504084.
15. S. Winitzki (2005) "Conformal diagrams for a fractal landscape." Phys. Rev. D 71 (2005) 123523. Preprint gr-qc/0503061.
16. S. Winitzki (2004) "The fractal structure of inflationary spacetime." In Exploring the Universe, Proceedings XXXIX Rencontres de Moriond, La Thuile, Italy, March 26 - April 4, 2004, ed. by Y. Giraud-Héraud and J. Trân Thanh Vân. This is a shorter version of a paper in preparation. (Local copy, ps.gz)
17. J. Hong, A. Vilenkin, and S. Winitzki (2003) "Particle creation in a tunneling universe I. Massless particles." Phys. Rev. D 68 (2003) 023520. Preprint gr-qc/0210034.
18. J. Hong, A. Vilenkin, and S. Winitzki (2003) "Particle creation in a tunneling universe II. Massive particles." Phys. Rev. D 68 (2003) 023521. Preprint gr-qc/0305025.
19. S. Winitzki (2003) "Computing the incomplete Gamma function to arbitrary precision." LNCS 2667 (2003) 790 (Springer-Verlag).
20. S. Winitzki (2003) "Uniform approximations for transcendental functions." LNCS 2667 (2003) 780 (Springer-Verlag).
21. L. Pogosian, T. Vachaspati, and S. Winitzki (2002) "Signatures of primordial helicity in the CMBR." New Astron. Rev. 47 (2003) 859-862. Preprint astro-ph/0210039.
22. A. Gangui, L. Pogosian, and S. Winitzki (2002) "Cosmic string signatures in the cosmic microwave background anisotropies." New Astron. Rev. 46 (2002) 681-691. Preprint astro-ph/0112145.
23. A. Gangui, L. Pogosian, and S. Winitzki (2001) "Computation of the CMB Bispectrum from Cosmic Strings". In Physics at Extreme Energies, Proceedings of the IVth Rencontres du Vietnam, Hanoi, Vietnam, 19-25 July 2000.
24. L. Pogosian, T. Vachaspati, and S. Winitzki (2001) "Signatures of kinetic and magnetic helicity in the CMBR." Phys. Rev. D 65 (2002) 083502. Preprint astro-ph/0112536.
25. A. Z. Pinkus and S. Winitzki (2002) "YACAS: A Do-it-yourself Symbolic Algebra Environment." LNCS 2385 (2002), 332 (Springer-Verlag).
26. S. Winitzki (2001) "Violations of the null energy conditions in eternal inflation." Talk given at COSMO-2001, Rovaniemi, Finland. Preprint gr-qc/0111109.
    Published reference: S. Winitzki, in Proceedings of the International Workshop On Particle Physics And The Early Universe (COSMO-01), Rovaniemi, Finland, 2001, ed. by M. Roos, eConf C01/08/30 (2001). See also a talk by Tanmay Vachaspati at the Davis Inflation Meeting, 2003 (astro-ph/0305439).
27. S. Winitzki (2001) "The eternal fractal in the universe." Phys. Rev. D 65 (2002) 083506. Preprint gr-qc/0111048.
28. A. Gangui, L. Pogosian, and S. Winitzki (2001) "Bispectrum of cosmic microwave background from wiggly cosmic strings." Phys. Rev. D 64 (2001) 043001. Preprint astro-ph/0101453.
29. S. Winitzki and A. Vilenkin (2000), "Effective noise in stochastic description of inflation", Phys. Rev. D 61 (2000) 084008. Preprint gr-qc/9911029.
30. V. Vanchurin, A. Vilenkin, and S. Winitzki (2000) "Predictability crisis in inflationary cosmology and its resolution." Phys. Rev. D 61 (2000) 083507. Preprint gr-qc/9905097.
31. S. Winitzki and A. Kosowsky (1998) "Minkowski functional description of microwave background Gaussianity." New Astronomy 3 (1998), 75-99. Preprint astro-ph/9710164.
32. A. Vilenkin and S. Winitzki (1997) "Probability distribution for Omega in open-universe inflation." Phys. Rev. D 55 (1997) 548-559. Preprint astro-ph/9605191.
33. S. Winitzki (1997) "Conformal invariance in two-dimensional discrete field theory." Phys. Rev. D 55 (1997) 6374-6381. Preprint hep-th/9609106.
34. S. Winitzki and A. Vilenkin (1996) "Uncertainties of predictions in models of eternal inflation." Phys. Rev. D 53 (1996) 4298-4310. Preprint gr-qc/9510054.
35. A. Vilenkin and S. Winitzki (1994) "Detection of particles under potential barrier." Phys. Rev. D 50 (1994) 5409-5417. Preprint hep-th/9404163.

    Submitted or in press:

36. S. Winitzki (2003) "Arbitrary-precision computation of Chebyshev polynomials." Submitted to ICCSA 2006.
37. S. Winitzki and J.-H. P. Wu (2000) "Inter-Scale correlations as measures of CMB Gaussianity." Preprint astro-ph/0007213. Submitted to APJ.
38. S. Winitzki (1998) "Non-Gaussian signature of weak gravitational lensing in the CMB." Preprint astro-ph/9806105. Submitted to PRD.

Recent talks

• New measure for the cosmological landscape, incorporating the new results
• Cosmological particle production and the precision of the WKB approximation - slides from a talk at QFEXT 2005, Barcelona, Spain
• Conformal diagrams for a fractal landscape - slides from a talk at LMU Munich, Germany, 2005
• Fractal structure of inflationary spacetime - talk at Moriond 2004, La Thuile, Italy; see also the proceedings and numerical simulations

Teaching and course materials

Miscellaneous lecture notes

• Classical mechanics
  • Perturbation theory for anharmonic oscillations (2006). Explanation of the Lindstedt-Poincaré method.
  • Advanced canonical methods (2006). Hamilton-Jacobi equation, action-angle variables, adiabatic invariants.
  • Classical mechanics (2006). Partial set of introductory notes incorporating the material distributed for the mechanics course in 2006.

• Electrodynamics
  • Separation of variables (2005). Explanations and example problems in both English and German.
  • Introduction to Green's functions (2005). Explanations in English (also separately), example problems in German.

• Quantum mechanics
  • Hilbert spaces, Hermitian operators, generalized vectors (2004)
  • Algebraic calculations with operators, commutation relations (2004).
  • Canonical quantization, measurement postulate, harmonic oscillator, coherent states, holomorphic representation (2004).
  • Density operators, mixed states, entropy (2004).
  • Introduction to quantum scattering (2003). Two lectures I prepared for the course Quantum Mechanics II.
  • Randomness and reality (2004). An almost non-technical essay about the interpretation of quantum mechanics.
  • Jordan's theorem, or Why there is no phase operator (2004).

• WKB approximation
  • The Miller-Good improvement of the WKB approximation (2002). Material from Quantum Mechanics by Galindo and Pascual, vol. 2.
  • A simple derivation of the WKB approximation (2005). An elementary introduction and numerical examples. No quantum mechanics required.
  • Perturbative improvement of the WKB approximation (2004). I also explained the perturbative improvement procedure in a paper on a related topic.

• Gravitation
  • Topics in advanced general relativity (2005). Lecture notes in progress.
  • Degrees of freedom of classical fields (2005). A definition of the number of degrees of freedom and a method to compute it.
  • Why the vierbein is a "square root" of the metric (2004).
  • The Frenet-Serret construction and the Fermi-Walker transport (2008).

• Mathematical aspects of physics
  • The Vandermonde determinant (2008). Three derivations and a generalization.
  • Hessians of inverse functions (2008). An elementary derivation of a theorem used in thermodynamics.
  • Introduction to asymptotic series (2006). Examples of asymptotic expansions and Borel summation.
  • Computation of some functional determinants through Riemann's zeta function (2006). Some examples and tricks.
  • Why the Dirac delta function cannot be applied to complex arguments (2004).
  • Renormalization group made clearer (2004). In progress.
  • Circle-valued random fields (2004). I study some properties of such "phase fields"; in particular, I define a Gaussian phase field.
  • Asymptotics of some thermodynamical integrals (2004). An approach using a systematic perturbation theory expansion.
  • An easy approximation to the error function and its inverse (2005).
  • Average number of collisions in a perfect hash (2001). Updated version (2008). A combinatorial problem solved through unusual generating functions.
  • Basic linear algebra with exterior products (1992 -- 2009). A free textbook on finite-dimensional linear algebra with an emphasis on exterior products and coordinate-free approach. This book is currently sold through LULU.COM at a very low price. You can also download for free the electronic version and a version for book printing. (GNU Free Documentation License). See also the official page of this book.

• Why physics is hard to learn no matter how much you already know (2004). A semi-popular essay on learning and teaching theoretical physics.
• Teach yourself touch typing in two hours (2009).