The symmetry properties of correlated wave functions

The resolution of a correlated wave function Ψ about an orbital approximation Ψ₀ for any state of an N-electron system is discussed with particular reference to the symmetry conditions which the n-electron correlation functions of X_n must satisfy in order that Ψ have the correct symmetry properties for the state in question. It is shown how for a closed-shell state the symmetry properties of the correlation functions are determined by those of the spin-orbital products which they replace in Ψ₀, and how this is not in general true for an open-shell state. It is shown how the symmetry properties of an n-electron correlation function can always be uniquely defined by those of the (N-n)-electron spin-orbital product to which it is coupled in X_n , and the general symmetry conditions which the correlation functions must satisfy are derived.     

增加光子位移福克态的量子统计性质

引入了增加光子位移福克态 a^+m| α,n〉,其中 | α,n〉是位移福克态,m是整数.用数值计算的方法研究了这种态的量子统计性质.结果表明,在位移福克态上增加光子后可以使原有的光场呈现较强的压缩,并能使光场的亚泊松特性得到明显增强.     

Random anisotropy disorder in superfluid 3He-A in aerogel

Anisotropic superfluid ³He-A in aerogel provides an interesting example of a system with continuous symmetry in the presence of random anisotropy disorder. Recent NMR experiments allow us to discuss two regimes of the orientational disorder that have different NMR properties. One of them, the (c) state, is identified as the pure Larkin-Imry-Ma state. The structure of another state, the (f) state, is not very clear: probably, it is the Larkin-Imry-Ma state contaminated by the network of the topological defects pinned by the aerogel. The text was submitted by the author in English.     

On the Orthocomplementation of State–Property–Systems of Contextual Systems

We adopt an operational approach to quantum mechanics in which a physical system is defined by the mathematical structure of its set of states and properties. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the case N=2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the two states involved, but also on the measurement context which induces the state transition.     

Fluorescence Properties of Donor–Acceptor-Substituted Pyrazoloquinolines

The photophysical properties of three newly synthesized pyrazoloquinolines, composed of N,N-dimethylaniline as donor subunit and various substituted forms of the acceptor pyrazoloquinoline (DPPQ), were investigated by absorption as well as by stationary and time resolved fluorescence spectroscopy. These compounds show generally highly efficient emission in nonpolar and medium polar solvents; the dipole moment of the emitting state increases and the quantum yield decreases with solvent polarity. These results are explained by state reversion in polar solvents: At low polarities emission originates from a state localized on the DPPQ moiety, whereas in the high-polarity regime the next excited state of charge transfer character, in which an electron is promoted from the amino nitrogen lone pair into an excited orbital of the DPPQ moiety, becomes the fluorescent state. This view is corroborated by semiempirical calculations including the solvent reaction field, low-temperature fluorescence measurements, and the observation of effects of protonation on the spectroscopic and photophysical properties.     

Magnetism and phase separation in the ground state of the Hubbard model

We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilize a Néel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed. Received 9 January 2002 Published online 25 June 2002     

多模复共轭奇、偶相干态光场的N次方Y压缩与N次方H压缩

利用新近提出的多模辐射场的广义非线性等阶高阶压缩理论,对多模复共轭奇、偶相干态光场的N次方Y压缩与N次方H压缩特性进行了详细研究.结果发现:①多模复共轭奇相干态光场,压缩阶数N为偶数时,只存在N-Y最小测不准态;而当腔模总数q与压缩阶数的乘积q·N为偶数时,只存在N-H最小测不准态;此外,无论N及q·N为何值,不呈现N次方Y压缩与N次方H压缩效应.②多模复共轭偶相干态光场在一定条件下可呈现出周期性变化的任意阶的N次方Y压缩与N次方H压缩效应.③多模偶相干态光场与多模复共轭偶相干态光场两者的压缩效果和压缩特性完全相同,这种现象称为“压缩简并”.     

Representation Theorem of Observables on a Quantum System

An orthomodular lattice (OML) with a conditional state can be used as a model for noncompatible events (a quantum system). In this paper we will study some properties of a conditional state and an s-map which are defined on an OML. We show conditions when a quantum system has the same properties as the classical probability space.     

Complementarity Relations for Multi-Qubit Systems

No Heading We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the degree to which single particle properties are possessed by an individual member of the system is limited by the bipartite entanglement that exists between that qubit and the remainder of the system. This result implies that the phenomenon of entanglement sharing is one specific consequence of complementarity. The second expression, which holds for an arbitrary state of two qubits, pure or mixed, quantifies a tradeoff between the amounts of entanglement, separable uncertainty, and single particle properties that are encoded in the quantum state. The separable uncertainty is a natural measure of our ignorance about the properties possessed by individual subsystems, and may be used to completely characterize the relationship between entanglement and mixedness in two-qubit systems. The two-qubit complementarity relation yields a useful geometric picture in which the root mean square values of local subsystem properties act like coordinates in the space of density matrices, and suggests possible insights into the problem of interpreting quantum mechanics.     

Unified approach to superposition states of the quantized radiation field

Summary In the recent years various and interesting superposition states of the quantized radiation field were investigated in the literature, such as that involving two number states by Wodkiewiczet al.; that involving two coherent states by Hillery and Gerryet al.; that involving two squeezed states by Xinet al., etc. Here we study a general one-parameter superposition state which unifies those states and others in the literature, all becoming a particularization of ours. General expressions characterizing the physical properties of the field are obtained. The role played by the present superposition state as an alternative interpolating state is also discussed. The authors of this paper have agreed to not receive the proofs for correction.     

Lattices of Quantum Automata

We defined and studied three different types of lattice-valued finite state quantum automata (LQA) and four different kinds of LQA operations, discussed their advantages, disadvantages, and various properties. There are four major results obtained in this paper. First, no one of the above mentioned LQA follows the law of lattice value conservation. Second, the theorem of classical automata theory, that each nondeterministic finite state automaton has an equivalent deterministic one, is not necessarily valid for finite state quantum automata. Third, we proved the existence of semilattices and also lattices formed by different types of LQA. Fourth, there are tight relations between properties of the original lattice l and those of the l-valued lattice formed by LQA.     

Exact theorems concerning CP and CPT violations in <Emphasis Type="Italic">C</Emphasis>=−1 entangled state of pseudoscalar neutral mesons

Neutral pseudoscalar mesons in an entangled or Einstein–Podolsky–Rosen state are routinely produced in ϕ and B factories. Based on the peculiar properties of an entangled state, we present some general exact theorems about parameters characterizing CP and CPT violations, by using various asymmetries defined for the correlated decays of the two entangled mesons, which are rigorously calculated.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Colossal resistive switching behavior and its physical mechanism of Pt/<Emphasis Type="Italic">p</Emphasis>-NiO/<Emphasis Type="Italic">n</Emphasis>-Mg<Subscript>0.6</Subscript>Zn<Subscript>0.4</Subscript>O/Pt thin films

A heterojunction structure of p-NiO/n-Mg_0.6Zn_0.4O with an aim to tuning or improving the resistive switching properties was fabricated on Pt/TiO₂/SiO₂/Si substrates by the sol-gel spin-coating technique. The Pt/NiO/Mg_0.6Zn_0.4O/Pt heterojunction thin-film device shows excellent resistive switching properties, such as a reduced threshold current of 1 μA for device initiation, a small dispersion of reset voltage ranging from 0.54 to 0.62 V, long retention time and a high resistance ratio of high-resistance state to low-resistance state about six orders of magnitude. These results indicate that the resistive switching properties can be greatly improved by constructing the p-NiO/n-Mg_0.6Zn_0.4O heterojunction for nonvolatile memory applications. The physical mechanism responsible for colossal resistive switching properties of the heterojunction was analyzed based on interfacial defect effect and formation and rapture of conductive filaments.     

Thermodynamic Properties of an Atom Inside a Kerr Nonlinear Blackbody

Thermodynamic properties of a Kerr nonlinear blackbody (KNB) are investigated. It is found that below a transition temperature T _c , the free energy of a KNB radiation is larger than that in a normal blackbody. At the transition from KNB radiation state to a normal blackbody radiation state, the photon system undergoes a first-order phase transition. The thermodynamic system of an atom interacting with a KNB radiation bath is also investigated by using a thermodynamic perturbation theory. It is found that below a transition temperature T _c , the increment of the free energy of the atom is larger than that in a normal blackbody. Above T _c , the KNB becomes a normal blackbody, and the properties in a KNB turn to be the same as those in normal blackbody radiation.     

Properties of the q-Analogue of a Squeezed Vacuum State

We constructed a normalizable q-analogue of squeezed vacuum state using the technique of integration within an ordered product (IWOP) of operators and the properties of the inverses of q-deformed creation and annihilation operatots. We also study its nonclassical properties and phase probability distribution.     

Spin Squeezing of Superposition of Multi-Qubit GHZ State and W State

We investigate the properties of spin squeezing in a general superposition of multi-qubit GHZ state and W state. It is shown that the mean spin direction is determined by the coefficients of superposition and the relative phase between the GHZ state and the W state; while the length of mean spin and spin squeezing parameter are only determined by coefficient of superposition.     

Quantum Fisher Information of Superposition of Many-Body GHZ-Class State and <Emphasis Type="Italic">W</Emphasis> State

We investigate the properties of quantum Fisher information in a general superposition of many-body GHZ-class state and W state. It is shown that mean spin direction is determined by the superposed coefficients and the relative phase between the GHZ-class state and the W state and it is independent of the relative phase between the GHZ-class state; while mean spin length and quantum Fisher information are only determined by the superposed coefficients.     

Random quantum states

This paper examines the statistical properties of random quantum states, for four different kinds of random state:(1) a pure state chosen at random with respect to the uniform measure on the unit sphere in a finite-dimensional Hilbert space;(2) a random pure state in a real space;(3) a pure state chosen at random except that a certain expectation value is fixed;(4) a random mixed state with fixed eigenvalues. For the first two of these, we give examples of simple states of a model system, the kicked top, which have the statistical properties of random states. Interestingly, examples of both kinds of randomness can be found in the same system. In studying the last two kinds of random state, we obtain new results concerning the application of information theory to quantum systems.     

Reproducing kernel Hilbert spaces and extremal problems for scattering of particles with arbitrary spins

In this paper each helicity amplitude of the two-body scattering of particles with arbitrary spins is considered as an element of a special class of Hilbert spacesH ^[u]. This space, which is called reproducing kernel Hilbert space (RKHS) has many special properties that appear to make it a natural space of functions to associate with the scattering helicity amplitudes. Some of the special properties of the RKHS are developed and then used to characterization of reproducing kernel (RK) ofH ^[u] as the solution to certain extremal problems. Then, it was shown that the optimal scattering state from the RKHS of the helicity amplitudes is analogous to the coherent state from the RKHS of the wave functions. The essential characteristic features of the scattering of particles with arbitrary spins in the optimal state dominance limit are established. An important alternative to the partial wave helicity analysis in terms of a fundamental set of optimal states is presented.