The Resonance Phenomena Associated with the Time Asymmetry in Non-Hermitian Quantum Mechanics

Resonances are defined as the poles of the scattering matrix. The poles are associated with the complex eigenvalues of the Hamiltonian which are embedded in the lower half of the complex plane. The asymptotes of the corresponding eigenfunctions are exponentially diverged. Therefore, the resonance eigenfunctions are not embedded in the Hermitian domain of the Hamiltonian. The time asymmetric problem is discussed for these types of non-Hermitian Hamiltonians and several solutions of this problem are proposed.     

Algebraic Formulation of Quantum Decoherence

An algebraic formalism for quantum decoherence in systems with continuous evolution spectrum is introduced. A certain subalgebra, dense in the characteristic algebra of the system, is defined in such a way that Riemann–Lebesgue theorem can be used to explain decoherence in a well defined final pointer basis.     

Quantum Lax Operators and Discrete 2+1-Dimensional Integrable Models

A specific quantum Lax operator, forming a quantum U _q (sl n) chain, is suggested. The intertwining R L L relation is proved. The invariant local 2+1-dimensional reformulation of the auxiliary linear problem for the L-operator is discussed.     

Altering the Remote Past

An abstract treatment of Bell inequalities in proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that a property of a system can be changed by the timing of a distant measurement, which could take place in the future.     

Fock Theories and Quantum Logics

The notion of Fock theory is introduced in the framework of quantum logics, which are here orthomodular atomic lattices satisfying the covering property. It is shown that there are some fundamental facts concerning particles, which may be successfully discussed in this general context. One of these facts is to establish the theoretical conditions for considering particles as sharply defined entities. The other refers to the theoretical circumstances, which almost impose to consider that some particles have a structure, meaning they are composed from other particles. This last problem is strongly related with the conservative time evolutions.     

非等同双原子与双模腔场拉曼相互作用模型的腔场谱

研究了非等同双原子与双模腔场拉曼相互作用模型的腔场谱,分析了谱结构随原子与腔场相对耦合常数R=g2/g1的变化规律,发现R对真空场、弱场、强场谱结构都有不同程度的影响.当R=1或R=0时,一般呈现简并的谱结构,而当R介于0与1之间时,腔场谱一般呈现复杂的非对称多峰结构.同时还发现,当R固定不变时,低频腔场初始场强对高频真空场谱结构也有较明显的影响. 关键词： 量子光学 腔场谱 拉曼相互作用 双模腔场     

A Generalization of a Two-Parameter Quantization for the Group GL 2(k)

We generalize a well-known two-parameter quantization for the group GL ₂(k) (over an arbitrary field k). Specifically, a certain class of Hopf algebras is constructed containing that quantization. The algebras are constructed given an arbitrary coalgebra and an arbitrary pair of its commuting anti-isomorphisms, and are defined by quadratic relations. They are densely linked to the compact quantum groups introduced by Woronowicz. We give examples of Hopf algebras that can be rowed up to the two-parameter quantization for GL ₂(k).     

A method and program for mass quantum chemical calculations of protein—ligand docking complexes

A new fast computational method for mass calculations of docking complexes by the AM1/PM3 semiempirical methods is proposed. The computation time is shortened by at least an order of magnitude compared to alternative schemes of quantum chemical calculations. The root-mean-square deviation of the AM1 calculated energies of formation of complexes from the results obtained by conventional diagonalization procedure is at most 0.4 kcal mol⁻¹. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 418–420, February, 2008.