By K. Nakamura

Quantum and chaos, key options in modern technology, are incompatible by way of nature. This quantity offers an research into quantum delivery in mesoscopic or nanoscale structures that are classically chaotic and indicates the luck and failure of quantal, semiclassical, and random matrix theories in facing questions rising from the mesoscopic cosmos. those conventional theories are severely analysed, and this results in a brand new path. To reconcile quantum with chaos and to revive real temporal chaos in quantum platforms, a time-discrete variation of quantum dynamics is proposed. Audience:This booklet could be of curiosity to graduate scholars and researchers in physics, chemistry and arithmetic, whose paintings contains primary questions of quantum mechanics in chaotic structures.

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**Quantum versus Chaos: Questions Emerging from Mesoscopic Cosmos**

Quantum and chaos, key thoughts in modern technology, are incompatible by means of nature. This quantity offers an research into quantum delivery in mesoscopic or nanoscale structures that are classically chaotic and exhibits the luck and failure of quantal, semiclassical, and random matrix theories in facing questions rising from the mesoscopic cosmos.

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**Additional resources for Quantum versus Chaos: Questions Emerging from Mesoscopic Cosmos**

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8), and I show that for certain operators O is unnecessary because matrix elements hˆjPOPjˆi=hˆjOjˆi are independent of the projection. The four different Majorana fermions, Eq. 5), can be combined into two complex fermions, see Fig. 2 for an illustration. First, bond fermions (Baskaran et al. 2007; Yao et al. 1 Exact Solution and Projection by 27 bx χ yr b y bx c bz χ xr z fr χ r bz c bx b y χ xr−n 1 by bx χ yr−n 2 Fig. 2 The representation of spins in terms of four Majorana fermions is shown in the left.

As discussed in the introduction, fractionalization is another prominent feature of QSLs, similar to the appearance of the emergent gauge structure. All together, these features make the Kitaev model a prime example of a QSL. 3 Experimental Realization 33 exact solubility it has become the workhorse for model calculations of topologically ordered phases in 2D. The pure honeycomb model as described until now harbors gapless and gapped QSL phases, see Fig. 4, and its excitations can be shown to obey Abelian statistics (Kitaev 2006).

G. Radaelli, Y. Singh, P. R. -W. J. Baker, C. Stock, J. Taylor, Spin waves and revised crystal structure of honeycomb iridate Na2IrO3. Phys. Rev. Lett. V. Chubukov, T. Jolicoeur, Dimer stability region in a frustrated quantum Heisenberg antiferromagnet. Phys. Rev. B 44(21), 12050–12053 (1991) R. M. Hayden, G. G. D. E. -W. Cheong, Z. Fisk, Spin waves and electronic interactions in La2CuO4. Phys. Rev. Lett. 86(23), 5377–5380 (2001) L. Cooper, D. B. O. R. J. S. M. Kurn, W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms.