Retardation in two-atom systems

We consider the old problem of two identical two-level atoms a fixed distance r apart, one excited at t = 0, the other unexcited, and the field in the vacuum state. We are interested specifically in the higher order retardation effects, which have not previously been discussed. We show the existence of an unexpected interference term in the probability for atom 1 to be excited which sets in two retardation times after atom 1 begins to decay.     

Coherent emission of a photon by many atoms

The theory ofWeisskopf andWigner of the natural line width is extended to a case where many atoms at given positions interact with one common quantized radiation field. At timet=0, one quantum of radiation energy is stored by the atoms, which however does not mean necessarily that exactly one of the atoms must be excited. We study the process of the creation of a photon in dependence on the positions of the atoms and on the state of the system of atoms att=0. The dimensions of the emitted wave train and the decay time of this excited atomic state depend sensitively on these parameters.     

Matter Density and Relativistic Models of Wave Function Collapse

Mathematical models for the stochastic evolution of wave functions that combine the unitary evolution according to the Schrödinger equation and the collapse postulate of quantum theory are well understood for non-relativistic quantum mechanics. Recently, there has been progress in making these models relativistic. But even with a fully relativistic law for the wave function evolution, a problem with relativity remains: Different Lorentz frames may yield conflicting values for the matter density at a space-time point. We propose here a relativistic law for the matter density function. According to our proposal, the matter density function at a space-time point x is obtained from the wave function ψ on the past light cone of x by setting the i-th particle position in |ψ|² equal to x, integrating over the other particle positions, and averaging over i. We show that the predictions that follow from this proposal agree with all known experimental facts.     

Spontaneous emission from cylindrical atomic cloud: Collective eigenstates and non-local effects

We consider collective emission of a single photon stored in a cloud of N two-level atoms (with energy ?ω) confined inside an infinite cylinder and discuss eigenstates of this system, their decay rates and collective frequency shifts. We found that states with wave number k_z ≥ ω/c do not decay and analogous to guiding modes in dielectric waveguides. Evolution of such states is qualitatively different in local (Markovian) and non-local regimes. We found that in the Markovian regime there is no photon emission. In contrast, non-local (memory) effects result in emission and reabsorption of the photon so that probability to find atoms excited oscillates with a collective Rabi frequency. Cross-over between local and non-local behavior can be observed by increasing radius of the cylinder or wave number k_z of the excited atomic state. Similar behavior can also be observed in slab geometry and tested in synchrotron experiments on collective excitation of solid-state samples by increasing thickness of the nuclear layer.     

A one dimensional microscopical model for the study of the coherence in the stopping power problem. Part 3

We consider the quantum mechanical problem of a particle being scattered inelastically by a chain ofN infinitely heavy, equidistantly spaced two-level atoms. In a previous paper (Süßmann, G., Szilas, P.: Z. Phys. B — Condensed Matter42, 253 (1981)) the time dependent problem of a Gaussian wave packet impinging on the target atoms has been studied and an explicit asymptotic expression for the reduced density matrix ρ _R of the particle has been given. We now introduce the coarse grained density matrix \(\bar \rho _R\) . The incoherenceI?1-Tr( \(\bar \rho _R^2\) ), i.e. the deviation of the state of the particle from a pure state, being small on certain conditions, we find a single particle wave function ψ with \(\psi (x',t)\psi ^* (x'',t) \approx \left\langle {x'\left| {\bar \rho _R (t)} \right|x''} \right\rangle\) and a nonlinear Hermitean HamiltonianH _ψ=p ²/2m+W _ψ such thati?ψ(x, t)=H _ψψ(x, t) describes the time evolution. Finally we also considerW _ψ within the framework of the phenomenological theory of nonlinear frictional operators.     

Another gravitational instability of flat space-time

Witten's demonstration of the instability of the five dimensional Kaluza-Klein ground state can be reduced to four, physical dimensions. One can then conclude that flat space-time at zero temperature with one of the spatial directions wrapped up is unstable. The decay rate is of order exp?L²/16πL²_p where L is the spatial periodicity and L_p is the Planck length. The post tunnelling evolution of the space-time is also discussed.     

Are quantum processes cosmologically induced?

Why, among ～10 ¹⁶ possibilities, does a wave function of a fast ion, spread over several centimeters, collapse in a crystal within a region measuring a few angstroms across? The most direct answer to this question would be the existence in this region of a cosmic particle, called a dybbuk, which induces the collapse. If dybbuks exist, deviations from conventional theory might be expected to occur for experiments involving ultrasmall space-time intervals less than the characteristic space-time interval of a dybbuk. It is shown that a dybbuk theory having the above characteristics can be constructed and can be tested experimentally by the decay of a0 ^? (J ^P) meson into two vector mesons.     

On the bound state in weakly coupled λ(ϕ6−ϕ4)2

We consider the λ(?⁶??⁴) quantum field theory in two space-time dimensions. Using the Bethe-Salpeter equation, we show that there is a unique two particle bound state if the coupling constant λ>0 is sufficiently small. Ifm is the mass of single particles then the bound state mass is given by $$_B (\lambda ) = 2m\left( {1 - \frac{9}{8}\left( {\frac{\lambda }{{m^2 }}} \right)} \right)^2 + \mathcal{O}\left( {\lambda ^3 } \right).$$      

Zr粉粒径对Zr/KClO4烟火剂燃烧特性的影响

 研究了烟火药激光器泵浦源传统配方Zr/KClO₄中Zr粉粒径对该配方燃烧特性的影响。结果表明：Zr粉从61.375 μm减小到18.675 μm,Zr/KClO₄混合物的点火温度从506.40 ℃降低到492.42 ℃,燃烧辐射脉宽由60 ms缩短到25 ms,峰值辐射强度增加1倍;在 200～1 100 nm波段内,随着Zr粉粒径的减小,可见光区内的辐射能所占的比例增强;针对掺钕激光介质的泵浦而言,Zr粉粒径为800目时,分布在激光介质的3个主要泵浦带内的辐射能最高,而且闪光脉宽最短。因此,在其它条件相同时,选择颗粒尺寸小的Zr粉有利于获得高的激光输出。     

Spin singlet mott states and evidence for spin singlet quantum condensates of spin-one bosons in lattices

We have investigated spin singlet Mott states of spin-one bosons with antiferromagnetic interactions. These spin singlet states do not break rotational symmetry and exhibit remarkably different macroscopic properties compared with nematic Mott states of spin-one bosons. We demonstrate that the dynamics of spin singlet Mott states is fully characterized by even- or odd-class quantum dimer models. The difference between spin singlet Mott states for even and odd numbers of atoms per site can be attributed to a selection rule in the low energy sectors of on-site Hilbert spaces; alternatively, it can also be attributed to an effect of Berry’s phases on bosonic Mott states. We also discuss evidence for spin singlet quantum condensate of spin-one atoms. Our main finding is that in a projected spin singlet Hilbert space, the low energy physics of spin-one bosons is equivalent to that of a Bose-Hubbard model for spinless bosons interacting via Ising gauge fields. The other major finding is spin-charge separation in some one-dimensional Mott states. We propose charge-e spin singlet superfluid for an odd number of atoms per lattice site and charge-2e spin singlet superfluid for an even number of atoms per lattice site in one-dimensional lattices. All discussions in this article are limited to integer numbers of bosons per site.     

Wave packets in graphene under external fields: Vortices formation

In this work we analyzed the time propagation of wave packets on a sheet of graphene under the action of external magnetic and electric fields in the Hall configuration. The treatment given in this work to the problem of particle propagation in graphene is based on the tight-binding model, not requiring to consider the linear approximation of the band structure around point K in the Brillouin zone. So, our calculation is able to describe the behavior of the particle in more general cases, not only the case of low lying excited states, the so-called massless Dirac electrons. Evaluating the time evolution of the wave function we assume as an initial state a Gaussian with a given velocity. We have considered the symmetric gauge for the vector potential. For specific cases one is able to show a very interesting effect such as the apparition of vortices, i.e., the initial wave is split into components each one of these forming vortices that remain stationaries as time goes. Moreover, for a packet with a wave vector near point K in the Brillouin zone, one is able to show the presence of the effect of zitterbewegung, that is, a trembling motion of the centroid of the wave packet. The inclusion of a dc electric field in the plane of the graphene lattice displaces the vortices in a direction perpendicular to the field.     

Interference of geometries in quantum gravity

The intensity of the wave function of a quantum particle is shown to undergo a spatial oscillation due to the influence of a quantum superposition of space-time geometries in a simply connected region, even though each geometry is flat in this region.     

Evidence for high-l rydberg states in atomic lithium excited by electron impact

By a time-of-flight technique we have studied the radiative decay of lithium atoms excited to high Rydberg levels by electron impact. The observed decay rates are consistent with large values for the orbital angular momentum quantum number l.     

Spontaneous decay in a system of two spatially separated atoms (One-dimensional case)

The problem of the dynamics and the spectrum of spontaneous radiation is solved for a system of two atoms in one-dimensional space. In order to single out, to the maximum possible degree, phenomena associated with the influence of spatially separated atoms on each other via the radiation field, the present analysis is performed precisely for the one-dimensional case. As a result, two effects are revealed and considered in detail: (i) the existence of stable (metastable) entangled superposition states at specific distances between the atoms and (ii) a considerable distinction between the spectra of photons emitted in two opposite directions from the system where only one of the atoms is initially excited. The possibilities of observing these effects are discussed.     

Time evolution of quasi-stationary states

In this paper we study the time evolution of prepared states in some quantum mechanical models, and discuss the probability of decay and the rate of energy dissipation and their dependence on the form of the interaction. First we consider solvable models with divergent matrix elements for the operatorH ², whereH is the Hamiltonian of the system. We study two specific examples, one with well-defined eigenvalues and the other with renormalizable interaction. The time development of the initial state in the latter case depends on the cut-off parameter. In the second part of the paper, we show the possibility of existence of decaying states with long lifetime, where the amplitude of the initial state decreases like a Bessel function. In the third part, we determine the time development of a prepared state in a simple many-boson problem. Finally we study the problem of penetration of a wave packet through two phase-equivalent potential barriers, and we conclude that from the scattering phase shifts alone, it is not possible to determine the lifetime or the mode of decay of an unstable particle uniquely.     

Bethe ansatz study of 1+1 dimensional Hubbard model

A wave function of Bethe ansatz form is used to obtain approximate solutions for a 1+1 dimensional Hubbard model. In this model a helical structure with infinite diameter is constructed to mimic the square lattice. Betheansatz analysis is performed along the helical line. By including the hopping integrals in perpendicular direction, the solutions show some recovery of two dimensional character. At half-filling, the system undergoes Mott transition, the critical value of on-site repulsion obtained by this scheme is smaller than that of the mean-field theory. For a given particle density, the energy level of corresponding one dimensional model is extended to a band. The relation of the results to the properties of two dimensional strong-correlation system is discussed.     

The Λ particle as a probe of deeply bound single particle states in heavy nuclei

Decay rates of excited states in heavy hypernuclei have been calculated using shell model wave functions. The nuclear Auger effect determines the widths of the states in most cases. The exception is the radiative decay for theΛ particle in the 1p and in exceptional cases also 1d shell. In general, the natural widths of the highly excited states below the threshold for theΛ emission are smaller than the spacing between theΛ shells. Spectroscopy ofΛ bound states in heavy hypernuclei thus seems to be feasible.     

正冲击波后固壁表面颗粒的上升运动

为揭示固壁表面颗粒的冲击波夹卷本质,模拟垂直于固壁表面的正冲击波后单个颗粒的上升运动。假定颗粒初始时刻处于气载状态（因波的反射或碰撞离开壁面）,受Saffman升力、气动阻力和重力作用。模型方程为波后定常气流边界层方程和颗粒运动常微分方程,分别用单参数法和四阶龙格库塔法求解。计算颗粒速度与轨迹表明：颗粒的冲击波卷扬动力,源于边界层内强剪切流提供的Saffman力;在所考察的冲击波强度和颗粒尺寸范围内,颗粒的上升高度不依赖于冲击波强度;上升高度按颗粒尺寸变化,即尺寸越大,高度越大。比较分析单颗粒和颗粒层的结果,认为实验中颗粒云内大尺寸颗粒少的原因是由于这些颗粒不易从颗粒层中逸出。部分计算结果与实验结果较为符合,验证了所建模型与假设的合理性。