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Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

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Platinum carbide (PtC) was synthesized under extreme conditions and considered as a potential candidate for superhard materials. However, the unsettled issue concerning the structural identification has impeded the full understanding of its physical and chemical properties. Here, we examine by first-principles calculations the crystal structure under high pressure and ideal strength along several high-symmetry directions under large deformation. The current calculations reveal that the zinc blende structure is the thermodynamically stable phase, and the simulated X-ray diffraction data are in excellent agreement with the experimental pattern. Further strain-stress calculations indicate that anomalous fluctuating behaviors of ideal strength occur in PtC. These results are expected to broaden our understanding of the structural and mechanical properties for other potential superhard materials formed by heavy transition metals and light elements.

We have extensively investigated the crystal structures of N 2 CO under high pressure using the swarm structure searching technique in combination with density functional theory. Three single-bonded 3-dimensional structures with space groups of P4 3 , P4 3 2 1 2, and P2 1 2 1 2 are discovered. We show that the P4 3 phase is the most stable structure compared with N 2 and CO above 35.6 GPa. The distribution of the excess electrons on the N and O atoms does not form bonds but forms a stable lonepair state. The strong covalent bonds together with lone-pair states are the driving force for the high bulk shear modulus of N 2 CO. The P4 3 structure may be used as an advanced energetic material with an energy density of approximately 4.6 kJ g −1 , which is a little higher than the modern explosive TNT (4.2 kJ g −1 ). ■ INTRODUCTIONMetastable molecules are perceived as worthwhile synthetic goals, and their synthesis or evidence of their fleeting existence has been acclaimed. 1 In many cases, some physical and chemical properties of the metastable materials are better than those in their stable state for the same chemical composition of materials. N 2 CO, an intriguing metastable material relevant to the strongest bonded diatomic molecules N 2 and CO, has attracted special attention as a high energy density material (HEDM) and the component of planetary ices. 2 It was first detected in the form of nitrosyl cyanide (NCNO) by Horsewood and Kirby in 1971. 3 Experimentally, with the great development in synthetic chemistry, various isomers of the molecule gas N 2 CO have been observed. 4−7 Maier et al. obtained ON−CN by irradiating cyanogen di-N-oxide in solid argon at 10 K with light of wavelength 254 nm. 4 Zeng et al. found that the diazirinone (an isomer of N 2 CO) molecule could be trapped by thermal decomposition of OC(N 3 ) 2 . 7 Theoretically, the most stable isomer of the N 2 CO molecule was diazirinone on the potential energy surface. 8 The enthalpy barrier for the dissociation of diazirinone to N 2 and CO is 108 kJ mol −1 , and the exothermicity is ∼400 kJ mol −1 for the reaction. 9 The amounts of energy released per mass unit by dissociation of diazirinone and other theoretical isomers indicate these molecules as leading candidates for HEDM. Recently, Raza et al. studied HEDM for the stable structures containing carbon monoxide and nitrogen molecules. 10 High pressure is a useful way to obtain new materials, with previously unknown structure or new chemical and physical properties. 11,12 In 2004, Eremets et al. made a prominent contribution to successfully synthesize the cubic-gauche (cg) structure at high pressure (110 GPa) and high temperature (2000 K). 13,14 N 2 shows a large difference in energy between single-bond and triple-bond states. It is estimated to be one of the best HEDMs if the high pressure polymeric N 2 can be synthesized and released at ambient conditions. 15 Similarly, CO is isoelectronic and isostructural to N 2 , exhibiting similar crystal structures at low pressure. 16 However, CO has differ...

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