On the quantization of sectorially Hamiltonian dissipative systems
作者： M. Castagnino , M. Gadella , L.P. Lara
DOI: 10.1016/J.CHAOS.2008.10.034
关键词: Canonical quantization 、 Quantization (physics) 、 Mathematics 、 Quantum 、 Dissipative system 、 Hamiltonian (quantum mechanics) 、 Classical mechanics 、 General Mathematics
摘要: Abstract We present a theoretical discussion showing that, although some dissipative systems may have sectorial Hamiltonian description, this description does not allow for canonical quantization. However, quantum Liouville counterpart of these is possible, it unique.
harvard.edu
elsevier.com
sci-hub.se 参考文章(11)
Walter Rudin, Functional Analysis ,(1973)
I Antoniou, M Gadella, Z Suchanecki, General Properties of the Liouville Operator International Journal of Theoretical Physics. ,vol. 37, pp. 1641- 1654 ,(1998) , 10.1023/A:1026632322820
Barry Simon, Michael Reed, Fourier Analysis, Self-Adjointness ,(1975)
M. Castagnino, M. Gadella, L.P. Lara, On local Hamiltonians and dissipative systems Chaos, Solitons & Fractals. ,vol. 30, pp. 542- 551 ,(2006) , 10.1016/J.CHAOS.2006.03.094
Piero Caldirola, Forze non conservative nella meccanica quantistica Il Nuovo Cimento. ,vol. 18, pp. 393- 400 ,(1941) , 10.1007/BF02960144
I. Antoniou, S. A. Shkarin, Z. Suchanecki, The spectrum of the Liouville–von Neumann operator in the Hilbert–Schmidt space Journal of Mathematical Physics. ,vol. 40, pp. 4106- 4118 ,(1999) , 10.1063/1.532948
Mario Castagnino, Olimpia Lombardi, The classical limit of non-integrable quantum systems, a route to quantum chaos Chaos, Solitons & Fractals. ,vol. 28, pp. 879- 898 ,(2006) , 10.1016/J.CHAOS.2005.08.149
GN Ord, None, The Schrödinger and diffusion propagators coexisting on a lattice Journal of Physics A. ,vol. 29, ,(1996) , 10.1088/0305-4470/29/5/007
Eduard Prugovečki, Quantum mechanics in Hilbert space ,(1971)
Vasily E Tarasov, Quantization of non-Hamiltonian and dissipative systems Physics Letters A. ,vol. 288, pp. 173- 182 ,(2001) , 10.1016/S0375-9601(01)00548-5