Deformation Quantization of a Certain Type of Open Systems

被引:0
作者
Florian Becher
Nikolai Neumaier
Stefan Waldmann
机构
[1] Physikalisches Institut,Fakultät für Mathematik und Physik
[2] Albert-Ludwigs-Universität Freiburg,undefined
来源
Letters in Mathematical Physics | 2010年 / 92卷
关键词
53D55; 81S22; deformation quantization; open systems; completely positive maps;
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中图分类号
学科分类号
摘要
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of the open time evolution. The usual example of linearly coupled harmonic oscillators is discussed.
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页码:155 / 180
页数:25
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  • [11] Sternheimer D.(2007)Stochastic Moyal product on the Wiener space J. Math. Phys. 48 023509-316
  • [12] Bordemann M.(2006)The damped harmonic oscillator in deformation quantization Phys. Lett. A352 309-878
  • [13] Römer H.(1986)Quantization and the Index Sov. Phys. Dokl. 31 877-700
  • [14] Waldmann S.(2007)Canonical quantization of so-called non-Lagrangian systems Eur. Phys. J. C 50 691-375
  • [15] Brittin W.E.(2009)Complete positivity of Rieffel’s deformation quantization J. Noncommut. Geom. 3 361-216
  • [16] Bursztyn H.(2003)Deformation quantization of Poisson manifolds Lett. Math. Phys. 66 157-8051
  • [17] Waldmann S.(2005)Deformation quantization of linear dissipative systems J. Phys. A 38 8039-255
  • [18] Bursztyn H.(1991)Weyl manifolds and deformation quantization Adv. Math. 85 224-206
  • [19] Waldmann S.(1977)On the quantization of dissipative systems Zeitschrift für Physik B 26 201-182
  • [20] Bursztyn H.(2001)Quantization of non-Hamiltonian and dissipative systems Phys. Lett. A 288 173-75