Dynamics and statics of DNA-programmable nanoparticle self-assembly and crystallization

DNA linker mediated self-assembly is emerging as a very general strategy for designing new materials. In this Letter, we characterize both the dynamics and thermodynamics of nanoparticle-DNA self-assembly by molecular dynamics simulations from a new coarse-grained model. We establish the general phase diagram and discuss the stability of a previously overlooked crystalline phase (D-bcc). We also characterize universal properties about the dynamics of crystallization. We point out the connection to f-star polymer systems and discuss the implications for ongoing experiments as well as for the general field of DNA mediated self-assembly.     

二相介质中一种位错构型的弹性场及所受的力

本文建立了二相介质中与相界斜交位错的一种理想构型。根据位错各向异性弹性理论的普遍方法,以及关于界面的Gebbia-Eshelby定理,计算得到此位错在两相中的弹性场,以及位错线段所受“像力”的数值解。本文所提出的模型及算法具有一般适用性。结果可用于进一步计算此位错与其它缺陷的相互作用。对于考虑这种斜交位错在无扩散相变中的作用,本工作也是一个有意义的起点。 关键词：     

几何相位的伽利略变换性质

对几何相位的伽利略变换性质结果表明：通常实验中所测量体系的几何相位的确是伽利略不变的.但一般量子体系的几何相位不具有伽利略不变性.还仔细考察了几何相位在伽利略boost作用下变化的物理起源.文章最后通过对假想实验的分析，进一步证明几何相位对参考系的依赖并不意味着相应物理可观测量的非伽利略协变性.     

Real-time quantitative phase imaging with a spatial phase-shifting algorithm

This Letter reports on the use of a spatial phase-shifting algorithm in a fast, straightforward method of real-time quantitative phase imaging. The computation time for phase extraction is five times faster than a Fourier transform and twice as fast as a Hilbert transform. The fact that the phase extraction from an interferogram of 512 × 512 pixels takes less than 8.93 ms with a typical desktop computer suggests the proposed method can be readily applied to high-speed dynamic quantitative phase imaging. The proposed method of quantitative phase imaging is effective and sufficiently general for application to the dynamic phenomena of biological samples.     

Mutual Information of Pauli Channels with Correlated Noise

A general formula for the mutual information of the Paufi channels with memory modelled by correlated noise is derived. It is shown that the mutual information depends on the channel shrinking factor, the input state parameter and the channel memory coefficient. The analyses based on the general formula reveal that the entanglement is always a useful resource to enhance the mutual information of some Pauli channels, such as the bit flip channel and the bit-phase flip channel. Our analyses also show that the entanglement is not advantageous to the reliable transmission of classical information for some Pauli channels at any time, such as the phase flip channel and the phase damping channel.     

绝热演化中一般量子态的几何相位

在绝热演化中的几何相位（即Berry相位）被推广到包括非本征态的一般量子态.这个新的几何相位同时适用于线性量子系统和非线性量子系统.它对于后者尤其重要因为非线性量子系统的绝热演化不能通过本征态的线性叠加来描述.在线性量子系统中,新定义的几何相位是各个本征态Berry相位的权重平均.     

Pseudo-gap phase and duality in a holographic fermionic system with dipole coupling on Q-lattice

We classify the different phases by the "pole-zero mechanism" for a holographic fermionic system which contains a dipole coupling with strength p on a Q-lattice background. A complete phase structure in p space can be depicted in terms of Fermi liquid, non-Fermi liquid, Mott phase and pseudo-gap phase. In particular, we find that in general the region of the pseudo-gap phase in p space is suppressed when the Q-lattice background is dual to a deep insulating phase, while for an anisotropic background, we have an anisotropic region for the pseudo-gap phase in p space as well. In addition, we find that the duality between zeros and poles always exists regardless of whether or not the model is isotropic.     

On the theory of scattering by complex potentials

The scattering problem for a non-relativistic spinless particle under the influence of a complex effective potential, which is spherically symmetric and tends to zero faster than 1/r at infinity, is considered. Certain general relations, which illuminate the influence of the imaginary part of the potential on the scattering process, are derived with the use of the expression for the probability current density. The rigorous phase-integral method developed by N. Fröman and P. O. Fröman is used for obtaining an exact, general formula for the scattering matrix, or, equivalently, for the phase shift. The formula is expressed in terms of phase-integral approximations of an arbitrary order and certain quantities defined by convergent series. Estimating the latter quantities and omitting small corrections, an approximate formula is derived for the phase shift, valid for the case that only one complex turning point contributes essentially to the phase shift. Criteria for classifying a scattering problem as such a one-turning-point problem are given. The treatment is made general enough to also cover situations of interest in Regge-pole or complex angular momentum theory.     

用算符分解方法计算非同调谐振子几何相位及其推广

将几何相位理论应用于非同调谐振子(isotonic oscillator缩写为IO)这类量子系统,运用算符分解方法计算了系统在二态体系的Aharonov-Anandan相位,推广至三态及多态体系,并讨论了AA相位更普遍的计算公式和变化规律.     

The Poincaré group as the symmetry group of canonical general relativity

This work reconsiders the formulation, due to Regge and Teitelboim, of the phase space approach to general relativity in the asymptotically flat context, phrasing it in the language of symplectic geometry. The necessary boundary conditions at spatial infinity are spelled out in detail. Precise meaning is given to the statement that, as a result of these boundary conditions, the Poincaré group acts as a symmetry group on the phase space of general relativity. This situation is compared with the spi-picture of Ashtekar and Hansen, where a larger asymptotic symmetry group is obtained.     

Neutrino mixing and leptonic CP phase in neutrino oscillations

Oscillations of the Dirac neutrinos of three generations in vacuum are considered with allowance made for the effect of the CP-violating leptonic phase (analogue of the quark CP phase) in the lepton mixing matrix. The general formulas for the probabilities of neutrino transition from one sort to another in oscillations are obtained as functions of three mixing angles and the CP phase. It is found that the leptonic CP phase can, in principle, be reconstructed by measuring the oscillation-averaged probabilities of neutrino transition from one sort to another. The manifestation of the CP phase as a deviation of the probabilities of direct processes from those of inverse processes is an effect that is practically unobservable as yet.     

High intensity Compton scattering in a strong plane-wave field of general form

Photon emission by an electron embedded in a strong external field of general form is studied theoretically. The external field considered is a plane-wave electromagnetic field of any number of components, period and polarisation. Exact, Volkov solutions of the Dirac equation with the 4-potential of the general external field are obtained. The photon emission is considered in the usual perturbation theory using the Volkov solutions to represent the electron. An expression for the transition probability of this process is obtained after the usual spin and polarisation sums, trace calculation and phase space integration. The final transition probability in the general case contains a single sum over contributions from external field photons, an integration over one of the phase space components and the Fourier transforms of the Volkov phases. The validity of the general expression is established by considering specific external fields. Known specific analytic forms of the transition probability are obtained after substitution of the 4-potential for a circularly polarised and constant crossed external field. As an example usage of the general result for the transition probability, the case of two circularly polarised external fields separated by a phase difference is studied both analytically and numerically.     

Phase shifting algorithms for non-sinusoidal waveforms with phase shift errors

In phase shifting interferometry, phase errors due to harmonic components of a fringe signal can be minimized by applying synchronous phase shifting algorithms with more than four samples. However, when the phase shift calibration is inaccurate, these algorithms cannot eliminate the effects of a non-sinusoidal waveform. It is shown that by taking a number of samples beyond one period of the fringe pattern, phase errors due to the harmonic components of the fringe signal can be eliminated, even when there exists a constant error in the phase shift interval. A general procedure for constructing phase shifting algorithms that eliminate these errors is derived. A seven-sample phase shifting algorithm is derived as an example, in which the effect of the second harmonic component can be eliminated in the presence of a constant error in the phase shift interval.     

s-channel discontinuities of reggeon diagrams with planar vertices

The mutual relations between s-channel discontinuities of reggeon diagrams with planar triple-Regge vertices are discussed. It is shown that, in general, contributions coming from different cuttings are not simply related to each other as certain vertices acquire non-trivial phase factors depending on the nature of the cutting. For diagrams with only triple-Regge vertices this phase may be related to the triple-Regge phase. The complete four-reggeon vertices are not known in general. An approximation is considered which amounts to preserving only the absorptive part of triple- or four-reggeon amplitudes in certain parts of the diagrams. This approximation turns out to be equivalent to a simple absorbed multiperipheral model. The problem of exchange degeneracy breaking within the dual unitarisation Scheme is briefly discussed as an example.     

Quantum statistical mechanics on stochastic phase space

Within the context of the theory of stochastic phase spaces, introduced in some earlier papers, a systematic mathematical procedure is developed for expressing quantum mechanical observables as generalized functions on a stochastic phase space. The states in such a theory are normalized, positive semidefinite, continuous functions of the phase space variables, satisfying marginality conditions appropriate to the stochastic nature of the underlying phase space. The action of a general quantum mechanical observable on the state space is then shown to lead in general to formal differential operators of finite or infinite order. Explicit computations of some typical operators are made to illustrate the theory. As a useful practical application, the theory is employed to derive a Bloch equation from which the Husimi transform of the canonical equilibrium state is then computed, after expressing it as an infinite series in powers of .Supported in part by a research grant from the National Research Council of Canada.     

Absolute phase recovery of three fringe patterns with selected spatial frequencies

A new temporal approach is presented for the recovery of the absolute phase maps from their wrapped versions based on the use of fringe patterns of three different spatial frequencies. In contrast to the two-frequency method recently published, the method proposed is characterized by better anti-error capability as measured by phase error tolerance bound. A general rule for the selection of the three frequencies is presented, and its relationship to the phase error tolerance bound is derived. Theoretical analysis and experimental results are also presented to validate the effectiveness of the proposed three frequency technique.     

Berry phase of coupled two arbitrary spins in a time-varying magnetic field

In this paper, we investigate the Berry phase of two coupled arbitrary spins driven by a time-varying magnetic field where the Hamiltonian is explicitly time-dependent. Using a technique of time-dependent gauge transform the Berry phase and time-evolution operator are found explicitly in the adiabatic approximation. The general solutions for arbitrary spins are applied to the spin-1/2\ system as an example of explanation.