Quantum physics and number theory

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Quantum physics and number theory
Wolfgang Schleich Abteilung für
Quantenphysik Universität Ulm
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Overview

• Factorization with Gauss sums
• Scaling laws
• Implementation in atoms
• NMR experiment
• Wave packets and Riemann Zeta function
• Autocorrelation function
• Logarithmic spectrum
• Schrödinger cats

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• I. Sh. Averbukh Rehovot
• M. Bienert Ulm
• O. Crasser
• M. Freyberger
• B. Girard Toulouse
• D. Haase
• F. Haug
• E. Lutz
• H. Mack
• H. Maier
• M. Mehring Stuttgart
• W. Merkel
• G. G. Paulus Texas
• W. P. Schleich

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Cornu spiral
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Factorization with Gauss sums
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Scaling law
Rescaling
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Chirped pulse
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Floquet ladder
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Pulse train
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Gauss as a schoolboy
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Factorization N15757313172331
M10
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Contrast
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NMR Implementation
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Echo
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NMR Experiment N15757313172331
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Decoherence N15757313172331
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Probing the limits...
M200
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Autocorrelation function
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Special unharmonic oscillator
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Inverse problem
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Potential
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Riemann-Siegel formula
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Schrödinger cat
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Analytic Continuation and Entanglement
coherent state
Riemann zeta function
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• www.physik.uni-ulm.de/ quan/book/Zahlenverschl.pdf
  
• password numbers

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Summary

• Factorization with Gauss sums
• Scaling laws
• Implementation in atoms
• NMR experiment
• Wave packets and Riemann Zeta function
• Autocorrelation function
• Logarithmic spectrum
• Schrödinger cats

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