Quantum mechanics based on position

The only observational quantity which quantum mechanics needs to address islocation. The typical primitive observation on a microsystem (e.g., photon) isdetection at alocation (e.g., by a photomultiplier looking at a grating). To analyze an experiment, (a) form a conceptual ensemble of replicas of it, (b) assign a wave function (in position representation) to its initial condition, (c) evolve the wave function by the Schrödinger equation (known, once and for all, as a function of the system's composition), (d) compute the probability for particle detection at various times and places. The initial wave function is chosen on the basis of experience with such treatments. Key experiments are thus treated: (i) time-of-flight, (ii) Stern-Gerlach, (iii) Franck-Hertz, (iv) photon recoil, (v) photoionization. Quantum states, dynamical variables, and measurements, and the usual postulates about them, are superfluous. The explicit treatments are nonrelativistic; the existence of relativistic generalizations is left open.     

Quantum mechanics without the position operator

The formula for the differential scattering cross section in quantum mechanics is derived without the usual assumption that the square of the -function is a position probability density for particles. It is argued that position, like time, may be basically a macroscopic parameter rather than a random variable for microparticles.This research was partly supported by a grant from the NSERC.     

基于非正交态的量子密钥验证方案

研究了量子密钥分发的验证问题,并利用非正交量子态设计了一个协议,该协议既能分发量子密钥,又能验证所分发的量子密钥的真实性,从而防止了以往所提出协议中可能存在的假冒问题 关键词： 量子密钥验证 量子密码 量子物理 密码学     

Quantum dissipative Higgs model

By using a continuum of oscillators as a reservoir, we present a classical and a quantum-mechanical treatment for the Higgs model in the presence of dissipation. In this base, a fully canonical approach is used to quantize the damped particle on a spherical surface under the action of a conservative central force, the conjugate momentum is defined and the Hamiltonian is derived. The equations of motion for the canonical variables and in turn the Langevin equation are obtained. It is shown that the dynamics of the dissipative Higgs model is not only determined by a projected susceptibility tensor that obeys the Kramers–Kronig relations and a noise operator but also the curvature of the spherical space. Due to the gnomonic projection from the spherical space to the tangent plane, the projected susceptibility displays anisotropic character in the tangent plane. To illuminate the effect of dissipation on the Higgs model, the transition rate between energy levels of the particle on the sphere is calculated. It is seen that appreciable probabilities for transition are possible only if the transition and reservoir’s oscillators frequencies to be nearly on resonance.     

Experimental verification of Foreman dislocation model

We present a strain analysis of an edge dislocation core, and a detailed discussion of the Foreman dislocation model. In order to examine the model, the quantitative measurement of strain field around an edge dislocation in aluminum is performed, and high-resolution transmission electron microscopy and geometric phase analysis are employed to map the strain field of the edge dislocation core in aluminum. The strain measurements are compared with the Foreman dislocation model, showing that they are in good agreement with each other when 0.7 ≤ a ≤ 1.5.     

Quantum logics,physical space,position observables and symmetry

The concepts of physical space, localizability, position and symmetry are incorporated in the quantum logic approach to axiomatic quantum mechanics. The corresponding structure then reduces to the usual von Neumann Hilbert space model for quantum mechanics.     

Quantum nondemolition measurement of transverse atomic position in Kapitza-Dirac atomic beam scattering

It is demonstrated that one can measure the distribution of the transverse position of an atom crossing one or more optical cavities by monitoring the phase of the standing wave fields in the cavities. For the atom-field interaction the Kapitza-Dirac regime is assumed; it is shown that in this regime the method represents a quantum nondemolition measurement of the atomic position. On the other hand it can be applied to prepare narrow distributions of the transverse atomic position. In order to show this, a numerical simulation is performed, which illustrates the collapse of a broad initial Gaussian wavepacket, which can be coherent or incoherent, to a distribution with narrow peaks. Preparing the cavity fields in a squeezed state, one can greatly enhance the impact of the cavity field measurements on the atomic density matrix.     

Experimental verification of an interpolation algorithm for improved estimates of animal position

This article presents experimental verification of an interpolation algorithm that was previously proposed in Jaffe [J. Acoust. Soc. Am. 105, 3168-3175 (1999)]. The goal of the algorithm is to improve estimates of both target position and target strength by minimizing a least-squares residual between noise-corrupted target measurement data and the output of a model of the sonar's amplitude response to a target at a set of known locations. Although this positional estimator was shown to be a maximum likelihood estimator, in principle, experimental verification was desired because of interest in understanding its true performance. Here, the accuracy of the algorithm is investigated by analyzing the correspondence between a target's true position and the algorithm's estimate. True target position was measured by precise translation of a small test target (bead) or from the analysis of images of fish from a coregistered optical imaging system. Results with the stationary spherical test bead in a high signal-to-noise environment indicate that a large increase in resolution is possible, while results with commercial aquarium fish indicate a smaller increase is obtainable. However, in both experiments the algorithm provides improved estimates of target position over those obtained by simply accepting the angular positions of the sonar beam with maximum output as target position. In addition, increased accuracy in target strength estimation is possible by considering the effects of the sonar beam patterns relative to the interpolated position. A benefit of the algorithm is that it can be applied "ex post facto" to existing data sets from commercial multibeam sonar systems when only the beam intensities have been stored after suitable calibration.     

Quantum orders in an exact soluble model

We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: H=16g Sum S(y)(i)S(x)(i + empty set x)S(y)(i + empty set x + empty set y)S(x)(i + empty set y). We show that the ground states for g < 0 and g > 0 have different quantum orders described by Z2A and Z2B projective symmetry groups. The phase transition at g = 0 represents a new kind of phase transition that changes quantum orders but not symmetry. Both the Z2A and Z2B states contain Z2 lattice gauge theories at low energies. They have robust topologically degenerate ground states and gapless edge excitations.     

Quantum chaos in the two-center shell model

Within an axially symmetric two-center shell model single-particle levels with Ω=1/2 are analyzed with respect to their level-spacing distributions and avoided level crossings as functions of the shape parameters. Only for shapes sufficiently far from any additional symmetry, ideal Wigner distributions are found as signature for quantum chaos.     

Quantum probability model for spin

We present a realistic model in which spin measurements are represented by functions. By employing a simple amplitude density, we derive the usual spin distributions for the spin-1/2 case. Higher order spin measurements are represented by sums of spin-1/2 measurements. We treat the spin-1 and spin-3/2 cases explicitly and show that the model applies to spins of any order.     

Quantum graviton creation in a model universe

Quantization in the spatially inhomogeneous, anisotropic, Gowdy three-torus solution of Einstein's equations leads to the production of gravitons from empty space. The creation of pairs of gravitons occurs only in wave modes with wavelength exceeding the horizon size at an initial time. The final number of created gravitons in any mode is proportional to the number of causally unconnected regions at the initial time over the wavelength of that mode. At large times, graviton number is well defined since the solution is in WKB form. The creation process produces the anisotropic collisionless radiation identical to that discussed by Doroshkevich, Zel'dovich, and Novikov which characterizes the large time classical solution. Near the singularity, the model behaves like an empty Bianchi Type I universe at each point in space (local Kasner). The canonical methods of Arnowitt, Deser, and Misner yield a reduced Hamiltonian from which the classical equations of motion are obtained. The quantization of the rapidly varying gravitational field component resembles the procedures used by Parker or Zel'dovich et al. to study particle creation in curved spacetime.     

Quantum correlation in one-dimensional extended quantum compass model

We study the correlations in the one-dimensional extended quantum compass model in a transverse magnetic field. By exactly solving the Hamiltonian, we find that the quantum correlation of the ground state of one-dimensional quantum compass model is vanishing. We show that quantum discord can not only locate the quantum critical points, but also discern the orders of phase transitions. Furthermore, entanglement quantified by concurrence is also compared.     

Quantum statistics in a simple model of space-time

A classification of particles in two classes is proposed in the framework of a model of space-time previously introduced. One of them is constituted by particles being represented by sets of sets of preparticles. The other kind is constituted by particles represented by cuts or discontinuities in a space-time. We prove here that particles of the first and second kind follow the Bose-Einstein and Fermi-Dirac statistics, respectively.A short communication was presented at the Sanibel Symposium (Part III): On Fundamentals of Quantum Statistics and Quantum Theory, Palm Coast, Florida, March 17–20, 1980     

Quantum glass phases in the disordered Bose-Hubbard model

The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.     

Quantum phase transition in the two-band hubbard model

The interaction between itinerant and Mott localized electronic states in strongly correlated materials is studied within dynamical mean field theory in combination with the numerical renormalization group method. A novel nonmagnetic zero temperature quantum phase transition is found in the bad-metallic orbital-selective Mott phase of the two-band Hubbard model, for values of the Hund's exchange which are relevant to typical transition metal oxides.