A Bayesian account of quantum histories

We investigate whether quantum history theories can be consistent with Bayesian reasoning and whether such an analysis helps clarify the interpretation of such theories. First, we summarise and extend recent work categorising two different approaches to formalising multi-time measurements in quantum theory. The standard approach consists of describing an ordered series of measurements in terms of history propositions with non-additive ‘probabilities.’ The non-standard approach consists of defining multi-time measurements to consist of sets of exclusive and exhaustive history propositions and recovering the single-time exclusivity of results when discussing single-time history propositions. We analyse whether such history propositions can be consistent with Bayes’ rule. We show that certain class of histories are given a natural Bayesian interpretation, namely, the linearly positive histories originally introduced by Goldstein and Page. Thus, we argue that this gives a certain amount of interpretational clarity to the non-standard approach. We also attempt a justification of our analysis using Cox’s axioms of probability theory.     

Exact Solution of a Cellular Automaton for Traffic

We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g., cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with simultaneous updating of all sites. It is equivalent to a special case (v _max=1) of the Nagel–Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short-range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two-point functions, and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time-discrete updating procedures. Through use of this mapping, our results also give new results for these models.     

Time-Symmetric Quantum Mechanics

A time-symmetric formulation of nonrelativistic quantum mechanics is developed by applying two consecutive boundary conditions onto solutions of a time- symmetrized wave equation. From known probabilities in ordinary quantum mechanics, a time-symmetric parameter P₀ is then derived that properly weights the likelihood of any complete sequence of measurement outcomes on a quantum system. The results appear to match standard quantum mechanics, but do so without requiring a time-asymmetric collapse of the wavefunction upon measurement, thereby realigning quantum mechanics with an important fundamental symmetry.     

Directional Mode-Locking of Dynamics of Two-Dimensional Superparamagnetic Colloidal System in a Periodic Pinning Array

Using Langevin simulations,we study numerically the directional mode-locking of the dynamics of twodimensional superparamagnetic colloidal system in a periodic pinning array.When the colloidal particles are initially commensurate with the pinning sites,there appear mode-locking steps in the average velocity of colloidal particles along certain directions of the external driving force.With an increase in the pinning strength,the width of the step increases linearly but the velocity at the step decreases parabolically.     

Effect of light polarization on multi-photon ionization of the one-electron atom

On the basis of the one-electron model of an atom or ion (nuclear charge Z « 137) the complete ratio of probabilities for multi-photon ionization by circularly and linearly polarized light is derived (in contrast to previous expressions giving its maximal value only).     

Photodetachment of F− by short laser pulses. Comparison between experiments and numerical results

Recently, angle-resolved photoelectron spectra have been measured by exposing negative F^? ions to linearly or circularly polarized infrared femtosecond laser fields. We compare the experimental results with numerical calculations carried out in the framework of a Keldysh-type theory modified to account for both the time shape and the spatial inhomogeneity of the pulse. In order to account for the finite duration of the laser pulse, our results have been obtained through calculations of photodetachment probabilities. By using the saddle-point method it is possible to show that the transition amplitude may be written as a coherent sum of terms giving rise to interferences. This circumstance suggests that some particular features of the experimental results may be described in terms of quantum interferences in the time domain.     

Investigation of quark distributions in a family of pentaquarks using the Thomas-Fermi quark model

Using the Thomas-Fermi quark model,a collective,spherically symmetric density of states is created to represent a gas of interacting fermions with various degeneracies at zero temperature.Over a family of pentaquarks,uudcc,color interaction probabilities were obtained after averaging over all the possible configurations.Three different functions are developed for light,charm,and anti-charm quarks and are assumed to be linearly related by some proportionality constants.Interesting patterns of quark distributions are observed while analyzing the quark function consistency conditions for such constants.     

Symmetry properties of fluctuations in an actively driven rotor

We investigate rotational dynamics of an actively driven rotor through experiments and numerical simulations. While probability density distributions of rotor angular velocity are strongly non-Gaussian, relative probabilities of observing rotation in opposite directions are shown to be linearly related to the angular velocity magnitude. We construct a stochastic model to describe transitions between different states from rotor angular velocity data and use the stochastic model to show that symmetry properties in probability density distributions are related to the detailed fluctuation relation(FR) of entropy productions.     

Quantum Superimposing Multiple Anti-Cloning Machine

We prove that the nonorthogonal states randomly selected from a set can evolve into a linear superposition of multiple copies of anti-cloned state (an orthogonal state along with the original) with failure branch if and only if the input states are linearly independent. We derive a bound on the success probabilities of our machine. We show that probabilistic anti-cloning and multiple anti-cloning machines are special cases of our machine. The results for a single input state are also generalized into the case of several input copies of a state.     

Two proofs of Fine's theorem

Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also sufficient conditions. Here two transparent and self-contained proofs of Fine's theorem are presented. The first is a physically motivated proof using an explicit local hidden variables model. The second is an algebraic proof which uses a representation of the probabilities in terms of correlation functions.     

Tone model integration based on discriminative weight training for Putonghua speech recognition

A discriminative framework of tone model integration in continuous speech recognition was proposed. The method uses model dependent weights to scale probabilities of the hidden Markov models based on spectral features and tone models based on tonal features. The weights are discriminatively trained by minimum phone error criterion. Update equation of the model weights based on extended Baum-Welch algorithm is derived. Various schemes of model weight combination are evaluated and a smoothing technique is introduced to make training robust to over fitting. The proposed method is ewluated on tonal syllable output and character output speech recognition tasks. The experimental results show the proposed method has obtained 9.5% and 4.7% relative error reduction than global weight on the two tasks due to a better interpolation of the given models. This proves the effectiveness of discriminative trained model weights for tone model integration.     

Generation and Amplification of Cherenkov Superradiance Pulses by Electron Beams with Energy Chirp

We propose a method for increasing the peak power of a superradiance pulse by varying the electron energy along an electron bunch. A one-dimensional time-dependent model describing the evolution of an electromagnetic pulse as well as direct numerical simulations based on the KARAT code show that the power of generated pulses becomes several times greater if the particle energy increases linearly along the bunch. A similar method can be applied to increase the peak power in the case of amplification of a short electromagnetic pulse (and a superradiance pulse generated by an external source) propagated along a quasi-continuous electron beam with a certain particle-energy profile.     

The Quantum Harmonic Oscillator in the ESR Model

The ESR model proposes a new theoretical perspective which incorporates the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional on detection instead of absolute. We have provided in some previous papers mathematical representations of the physical entities introduced by the ESR model, namely observables, properties, pure states, proper and improper mixtures, together with rules for calculating conditional and overall probabilities, and for describing transformations of states induced by measurements. We study in this paper the relevant physical case of the quantum harmonic oscillator in our mathematical formalism. We reinterpret the standard quantum rules for probabilities, provide new expressions for absolute probabilities, and show how the standard state transformations must be modified according to the ESR model.     

Probability sum rules and consistent quantum histories

An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal decoherence are all calculated by using a projection operator to describe each possibility for the state at each time. Weak decoherence requires more sum rules. They bring in additional variables, that require different measurements and a different way to calculate probabilities, and raise questions of operational meaning. The example shows that extending the linearly positive probability formula from weak to minimal decoherence gives probabilities that are different from those calculated in the usual way using the Born and von Neumann rules and a projection operator at each time.     

The effect of damping and mass ratio on the stability of a tube bank

Experiments have been conducted in a wind tunnel on a parallel triangular tube array with a pitch ratio of 1·375. The aerodynamic component of damping was determined as a function of flow velocity. This damping was found to increase linearly with flow to about 50% of the stability threshold and then to decrease. Additionally, six different sets of tubes were tested to examine the effect of mass ratio on fluid-elastic stability. The results were compared with similar experiments in which damping alone was varied. It is seen that damping and mass ratio do not appear to be linearly dependent parameters which is contrary to the assumption used commonly in the stability analysis of tube banks. More importantly, however, the stability threshold is substantially less dependent on both damping and mass ratio than indicated by conventional theory.     

Present,predicted, and hidden probabilities

The general properties of measurements in microphysics are studied and the three types of probabilities that, according to the authors, appear in wave mechanics are set up. Such a distinction, together with the principle of the localization of the corpuscle as was laid down at the very introduction of the theory of the double solution, provides a good grasp of certain phenomena whose explanation according to the usual theory (which makes no use of permanent localization and where the three types of probabilities are intermingled) leads to paradoxical or self-contradictory situations.     

High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators

This paper studies parametric resonance of coupled micromechanical oscillators under periodically varying nonlinear coupling forces. Different from most of previous related works in which the periodically varying coupling forces between adjacent oscillators are linearized, our work focuses on new physical phenomena caused by the periodically varying nonlinear coupling. Harmonic balance method (HBM) combined with Newton iteration method is employed to find steady-state periodic solutions. Similar to linearly coupled oscillators studied previously, the present model predicts superharmonic parametric resonance and the lower-order subharmonic parametric resonance. On the other hand, the present analysis shows that periodically varying nonlinear coupling considered in the present model does lead to the appearance of high-order subharmonic parametric resonance when the external excitation frequency is a multiple or nearly a multiple (≥3) of one of the natural frequencies of the oscillator system. This remarkable new phenomenon does not appear in the linearly coupled micromechanical oscillators studied previously, and makes the range of exciting resonance frequencies expanded to infinity. In addition, the effect of a linear damping on parametric resonance is studied in detail, and the conditions for the occurrence of the high-order subharmonics with a linear damping are discussed.     

Incompatible stochastic processes and complex probabilities

The definition of conditional probabilities is based upon the existence of a joint probability. However, a reconstruction of the joint probability from given conditional probabilities imposes certain constraints upon the latter, so that if several conditional probabilities are chosen arbitrarily, the corresponding joint probability may not exist. Such an incompleteness in conditional probabilities can be eliminated by introducing complex probabilities. The physical meaning of the new mathematical formalism, as well as its relation to quantum probabilities, is discussed.     

Random motion with interfacial contact: Driven diffusion vis-à-vis mechanical activation

Rolling of a small sphere on a patterned support of an elastomer is governed by a non-linear friction. No motion occurs when the external field is weaker than the frictional resistance. However, with the intervention of an external noise, a viscous friction like behavior emerges; thus the sphere rolls with a uniform drift velocity that is proportional to the applied field. At a very low noise strength, the sphere exhibits a stick-slip behavior with motion occurring always along the bias. With the increase in the noise strength, the sphere exhibits a diffusive drift accompanied with forward and backward displacements. During this stage of driven diffusive motion, the ratio of the integrated probabilities of the negative-to-positive work fluctuations decreases monotonically with the time of observation, from which a temperature like intensive parameter can be estimated. This parameter conforms to Einstein??s ratio of diffusivity and mobility that increases almost linearly, even though the diffusivity increases super-linearly, with the strength of the noise. A new barrier crossing experiment is introduced that can be performed either with a hard (e.g. a steel ball) or with a soft (e.g. a water drop) sphere in contact with a periodically undulated substrate. The frequency of barrier crossing follows a transition state equation allowing a direct estimation of the effective temperature. These experiments as well as certain numerical simulations suggest that the effective temperature of a system controlled by a non-linear friction may not have a unique value.     

Multiphoton ionization of the hydrogen atom exposed to circularly or linearly polarized laser pulses

This paper studies the multiphoton ionization of the hydrogen atom exposed to the linearly or circularly polarized laser pulses by solving the time-dependent Schr?dinger equation. It finds that the ratio of the ionization probabilities by linearly and circularly polarized laser pulses varies with the numbers of absorbing photons. With the same laser intensity, the circularly polarized laser pulse favors to ionize the atom with more ease than the linearly polarized laser pulse if only two or three photons are necessary to be absorbed. For the higher order multiphoton ionization, the linearly polarized laser pulse has the advantage over circularly polarized laser pulse to ionize the atom.