Unitarity of Generalized Fourier–Gauss Transforms

Abstract

A generalized Fourier–Gauss transform is an operator acting in a Boson Fock space and is formulated as a continuous linear operator acting on the space of test white noise functions. It does not admit, in general, a unitary extension with respect to the norm of the Boson Fock space induced from the Gaussian measure with variance 1 but is extended to a unitary isomorphism if the Gaussian measure is replaced with the ones with different covariance operators. As an application, unitarity of a generalized dilation is discussed.     

Generation of nonclassical states in a large detuning cavity

By using the theory of cavity QED, we study the system in which a two-level atom interacts with a cavity in the case of large detuning. Through the selective detecting of atomic state, Schrodinger cat states and entangled coherent states are easily generated. When the atom is driven by a weak classical field and the cavity field is in the Schrodinger cat state, we study the conditions of generating the Fock states and the maximal success probability. The maximal success probability in our scheme is larger than the previous one.     

A Categorical Framework for the Quantum Harmonic Oscillator

This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely general one in which Hilbert spaces play no special role. Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates of the lowering operators. Generalised exponentials also emerge naturally in this setting, and we demonstrate that coherent states are produced by the exponential of a raising morphism acting on the zero-particle state. Finally, we examine all of these constructions in a suitable category of Hilbert spaces, and find that they reproduce the conventional mathematical structures.     

两粒子相容可观察量共同本征矢的推导

利用有序算符正规乘积内的积分技术(IWOP)和待定系数法,推导出了两粒子相对坐标算符x^1-x^2与总动量算符p^1 p^2的共同本征矢|η〉在Fock空间中的展开式,为解决这类问题提供了一种行之有效的方法,这对提高学生的学习素质和加深学生对理论知识的理解会有一定的帮助.     

Levy Constrained Search in Fock Space: An Alternative Approach to Noninteger Electron NumberSCI北大核心CSCD

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.     

Noncommutative Berezin transforms and multivariable operator model theory

In this paper, we initiate the study of a class of noncommutative domains of n-tuples of bounded linear operators on a Hilbert space H, where m?2, n?2, and p is a positive regular polynomial in n noncommutative indeterminates. These domains are defined by certain positivity conditions on p, i.e.,

     

Hartree-Fock exchange fitting basis sets for H to Rn

For elements H to Rn (except Lanthanides), a series of auxiliary basis sets fitting exchange and also Coulomb potentials in Hartree–Fock treatments (RI-JK-HF) is presented. A large set of small molecules representing nearly each element in all its common oxidation states was used to assess the quality of these auxiliary bases. For orbital basis sets of triple zeta valence and quadruple zeta valence quality, errors in total energies arising from the RI-JK approximation are below ∼1 meV per atom in molecular compounds. Accuracy of RI-JK-approximated HF wave functions is sufficient for being used for post-HF treatments like Møller–Plesset perturbation theory, MP2. Compared to nonapproximated treatments, RI-JK-HF leads to large computational savings for quadruple zeta valence orbital bases and, in case of small to midsize systems, to significant savings for triple zeta valence bases. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008     

Molecular structure and vibrational spectra of indole and 5-aminoindole by density functional theory and ab initio Hartree–Fock calculations

The molecular geometry and vibrational frequencies of indole and 5-aminoindole in the ground state have been calculated by using the Hartree–Fock and density functional method with 6-311++G(d,p) basis set. The optimized geometrical parameters obtained by DFT calculations are in good agreement with the experimental values. Comparison of the observed fundamental vibrational frequencies of indole and 5-aminoindole with the calculated results by density functional and Hartree–Fock methods indicates that B3LYP is superior to the scaled Hartree–Fock approach for molecular vibrational problems. The theoretical spectrograms for FT-IR spectrum of 5-aminoindole have been constructed.