Quantum n-Vector Anharmonic Crystal II: Displacement Fluctuations

Based on the 1/n-expansion derived in a previous paper, the displacement fluctuations are analyzed in a quantum n-vector model of anharmonic crystal in the large n regime. It is shown that in the ferroelectric phase the n limit of the local fluctuation field has faster large-distance correlation decay than its Hartree–Fock approximation. Also, the critical exponent of the global displacement fluctuation is strictly smaller there than the Hartree–Fock exponent. In particular, the displacement fluctuations may be normal in the ferroelectric phase in spite of the Hartree–Fock prediction.     

On the Classification of q-Algebras

The problem is the classification of the ideals of free differential algebras, or the associated quotient algebras, the q-algebras; being finitely generated, unital C-algebras with homogeneous relations and a q-differential structure. This family of algebras includes the quantum groups, or at least those that are based on simple (super) Lie or Kac–Moody algebras. Their classification would encompass the so far incompleted classification of quantized (super) Kac–Moody algebras and of the (super) Kac–Moody algebras themselves. These can be defined as singular limits of q-algebras, and it is evident that to deal with the q-algebras in their full generality is more rational than the examination of each singular limit separately. This is not just because quantization unifies algebras and superalgebras, but also because the points q=1 and q=–1 are the most singular points in parameter space. In this Letter, one of two major hurdles in this classification program has been overcome. Fix a set of integers n ₁,...,n _k, and consider the space of homogeneous polynomials of degree n ₁ in the generator e ₁, and so on. Assume that there are no constants among the polynomials of lower degree, in any one of the generators; in this case all constants in the space have been classified. The task that remains, the more formidable one, is to remove the stipulation that there are no constants of lower degree.     

On the Eigenstates of the Elliptic Calogero–Moser Model

It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (–1) of the elliptic Calogero–Moser model, where (1, ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero–Sutherland model, if exp(2–1) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero–Moser model which converge to the ones of the Calogero–Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2–1). With some assumptions, we show analogous results for N-particle and l is positive integer cases.     

滚转角误差的光学精密测量技术研究

提出了基于两点法的精密移动台滚转角测量新方法,可以将移动台滚转角误差与参考镜角形状误差分离开来.实验结果表明,滚转角误差的测量重复性精度可达0.05',这个值是由测量系统稳定性决定的.     

AN EXTENSION OF “POPPER'S EXPERIMENT” CAN TEST INTERPRETATIONS OF QUANTUM MECHANICS

Karl Popper proposed a way to test whether a proposed relation of a quantum-mechanical state to perceived reality in the Copenhagen interpretation (CI) of quantum mechanics—namely that the state of a particle is merely an expression of what is known about the system—is in agreement with all experimental facts. A conceptual flaw in Popper's proposal is identified and an improved version of his experiment (called Extension step 1)—which fully serves its original purpose—is suggested. The main purpose of this paper is to suggest to perform this experiment. The results of this experiment predicted under the alternative assumptions that the CI or the many-worlds interpretation (MWI) is correct are shown to be identical. Only after a further modification (called Extension step 2) (the use of an ion isolated from the macroscopic environment as particle detector) the predictions using the respective interpretations become qualitatively different. This is because what is known by a human observer H can fail as a basis for the prediction of the statistical distribution of measurement results within the MWI in special cases: The temporal evolution of a system un-entangled with H (like the isolated ion) can depend on another system's state components that are entangled with states ortogonal to H. Thus—within the CI—for H they are known not to exist. Yet H can infer their existence by studying the evolution of the ion.     

Dead-time free measurement of dipole-dipole interactions between electron spins

A four-pulse version of the pulse double electron-electron resonance (DEER) experiment is presented, which is designed for the determination of interradical distances on a nanoscopic length-scale. With the new pulse sequence electron-electron couplings can be studied without dead-time artifacts, so that even broad distributions of electron-electron distances can be characterized. A version of the experiment that uses a pulse train in the detection period exhibits improved signal-to-noise ratio. Tests on two nitroxide biradicals with known length indicate that the accessible range of distances extends from about 1.5 to 8 nm. The four-pulse DEER spectra of an ionic spin probe in an ionomer exhibit features due to probe molecules situated both on the same and on different ion clusters. The former feature provides information on the cluster size and is inaccessible with previous methods.     

Mesoscopic and macroscopic dipole clusters: Structure and phase transitions

A two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. This system can be used as a model for rare electrons in semiconductor structures near a metal electrode, indirect excitons in coupled quantum dots etc. For clusters of N ≤ 80 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are found. Monte-Carlo and molecular dynamic methods are used to study the order-disorder transition (the “melting” of clusters). In mesoscopic clusters (N < 37) there is a hierarchy of transitions: at lower temperatures an intershell orientational disordering of pairs of shells takes place; at higher temperatures the intershell diffusion sets in and the shell structure disappears. In “macroscopic” clusters (N > 37) an orientational “melting” of only the outer shell is possible. The most stable clusters (having both maximal lowest nonzero eigenfrequencies and maximal temperatures of total melting) are those of completed crystal shells which are concentric groups of nodes of 2D hexagonal lattice with a number of nodes placed in the center of them. The picture of disordering in clusters is compared with that in an infinite 2D dipole system. The study of the radial diffusion constant, the structure factor, the local minima distribution and other quantities shows that the melting temperature is a nonmonotonic function of the number of particles in the system. The dynamical equilibrium between “solid-like” and “orientationally disordered” forms of clusters is considered.     

A one-dimensional lattice model for a quantum mechanical free particle

Two types of particles, A and B with their corresponding antiparticles, are defined in a onedimensional cyclic lattice with an odd number of sites. In each step of time evolution, each particle acts as a source for the polarization field of the other type of particle with nonlocal action but with an effect decreasing with the distance: . It is shown that the combined distribution of these particles obeys the time evolution of a free particle as given by quantum mechanics.     

Efficient population transfer by delayed pulses despite coupling ambiguity

In traditional schemes of multilevel multilaser excitation, each laser pulse interacts with only one pair of states, and the rotating wave approximation (RWA) is applicable. Here we study the population transfer process in a three-state system when each of the two lasers interacts with each of the pair of states and when the Rabi frequencies characterizing the interaction strengths of the system are comparable to or larger than the difference of the transition frequencies. We show that complete and robust population transfer is possible under conditions more general than those hitherto considered necessary for stimulated Raman adiabatic passage (STIRAP) or for successive π pulses. Using adiabatic Floquet theory we show that successful population transfer can be interpreted as adiabatic passage by means of a transfer state which connects the initial and final states. The Floquet picture offers a convenient interpretation of the population transfer as accompanied by multiple absorption of photons from or emission into the laser fields.     

飞秒激光控制的量子分子动力学研究——多维三能级系统

结合MCTDH方法和优化控制理论，以具有三个电子能级，三个振动自由度的吡嗪分子为例，模拟了优化飞秒激光作用下的量子分子动力学过程. 在对多维两能级系统的优化控制模拟的基础上，以三能级中的两个激发态为目标态，考虑了不同的目标态对多维系统量子动力学过程的影响. 关键词： 飞秒激光控制 MCTDH 方法 量子分子动力学