Complex Structures and Quantization

J. M. Isidro

The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space [Formula: see text], but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a complex structure on [Formula: see text]. When the latter is a complex-analytic manifold admitting just one complex structure, there is a unique quantization whose classical limit is [Formula: see text]. Then the notion of coherence is the same for all observers. However, when [Formula: see text] admits two or more nonbiholomorphic complex structures, there is one different quantization per different complex structure on [Formula: see text]. The lack of analyticity in transforming between nonbiholomorphic complex structures can be interpreted as the loss of quantum-mechanical coherence under the corresponding transformation. Observers using one complex structure perceive as coherent the states that other observers, using a different complex structure, do not perceive as such. This is the notion of a quantum-mechanical duality transformation: the relativity of the notion of a quantum.

Valery Vasil'evich Kozlov, Oleg Georgievich Smolyanov

Structures and objects used in Hamiltonian secondary quantization are discussed. By the secondary quantization of a Hamiltonian system ℋ, we mean the Schrödinger quantization of another Hamiltonian system ℋ 1 for which the Hamiltonian equation is the Schrödinger one obtained by the quantization of the original Hamiltonian system ℋ. The phase space of ℋ 1 is the realification ℍ R of the complex Hilbert space ℍ of the quantum analogue of ℋ equipped with the natural symplectic structure. The role of a configuration space is played by the maximal real subspace of ℍ.

Gerald V. Dunne

Heimo G. Latal, W. Schweiger

Takashi Yokokawa, Osamu Shinya, Yuji Shinohara +1 more

We have developed a high performance and programmable LDPC decoder VLSI for decoding structured LDPC codes. In this paper, the architecture of the decoder and the structured parity check matrices are described along with the quantization method. We adopt floating point (FP) quantization method in check node processors so as to shrink down the complexity of look up tables (LUTs) of the Gallager function, and avoid performance degradation. Finally, simulation results show that the FP quantization method achieves high performance for wide range of code rates