Time Quantization Research Articles

Confined Quantum Time of Arrivals

We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For the spatially confined particle, we show that the problem admits a solution in the form of an eigenvalue problem of a compact and self-adjoint time of arrival operator derived by a quantization of the classical time of arrival, which is canonically conjugate with the Hamiltonian in a closed subspace of the Hilbert space.

Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

The historical Ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium. This approach represents a special case in the dynamics of N uncoupled two-state systems. In this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change. Analytical solutions for the probability distribution of the system’s state as well as the fluctuation distribution are derived. Interestingly, close inspection of the fluctuation distribution reveals an intrinsic time scale. Sampling the system’s state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes. For faster measurements a power law extends roughly over log10 N orders of magnitude followed by an exponential tail. At some point, further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind. Since the generic solution is rather unwieldy, we derive and discuss simple and intuitive analytical solutions in the limit of small p and large N . Furthermore, we relax the quantization of time by considering a complementary approach in continuous time. Finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features.

Time quantization andq-deformations

We extend to quantum mechanics the technique of stochastic subordination, by means of which one can express any semi-martingale as a time-changed Brownian motion. As examples, we considered two versions of the q-deformed harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules.

On filtering in Markovian term structure models: an approximation approach

We consider a parametrization of the Heath-Jarrow-Morton (HJM) family of term structure of interest rate models that allows a finite-dimensional Markovian representation of the stochastic dynamics. This parametrization results from letting the volatility function depend on time to maturity and on two factors: the instantaneous spot rate and one fixed-maturity forward rate. Our main purpose is an estimation methodology for which we have to model the observations under the historical probability measure. This leads us to consider as an additional third factor the market price of interest rate risk, that connects the historical and the HJM martingale measures. Assuming that the information comes from noisy observations of the fixed-maturity forward rate, the purpose is to estimate recursively, on the basis of this information, the three Markovian factors as well as the parameters in the model, in particular those in the volatility function. This leads to a nonlinear filtering problem, for the solution of which we describe an approximation methodology, based on time discretization and quantization. We prove the convergence of the approximate filters for each of the observed trajectories.

Obstacles on the Way Towards the Quantisation of Space, Time and Matter — and Possible Resolutions

Most attempts at obtaining theories that unify quantum mechanics with general relativity require violation of locality and/or causality to some degree. Here, we suggest that these problems actually are very deep and fundamental; hence they may require reconsideration of both quantum mechanics and general relativity at a very fundamental level. An approach called ‘deterministic quantisation’ is sketched.

The Effect of Atmospheric Drag on Satellite Orbits During the Bastille Day Event

Geomagnetic storms driven by solar eruptions are known to have significant effects on the total density of the upper atmosphere in the altitude range 250–1000 km. This in turn causes a measurable effect on the orbits of resident space objects in this altitude range. We analyzed a sample of these orbits, both from sensor data and from orbital element sets, during the period surrounding the 14 July 2000 solar activity. We present information concerning the effects of this event on the orbits of resident space objects and how well accepted atmospheric models were able to represent it. As part of this analysis, we describe a technique for extracting atmospheric density information from orbital element sets. On daily time scales, the effect of geomagnetic activity appears to be more important than that of prompt radiation. However, the limitations in time and amplitude quantization of the accepted solar indices are evident. A limited comparison is also made with previous solar storm events.

Barnett-Pegg formalism of angle operators, revivals, and flux lines

We use the Barnett-Pegg formalism of angle operators to study a rotating particle with and without a flux line. Requiring a finite dimensional version of the Wigner function to be well defined we find a natural time quantization that leads to classical maps from which the arithmetical basis of quantum revivals is seen. The flux line, that fundamentally alters the quantum statistics, forces this time quantum to be increased by a factor of a winding number and determines the homotopy class of the path. The value of the flux is restricted to the rational numbers, a feature that persists in the infinite dimensional limit.

A numerical experiment in DLCQ: microcausality, continuum limit and all that

Issues related with microcausality violation and continuum limit in the context of (1+1) dimensional scalar field theory in discretized light-cone quantization (DLCQ) are addressed in parallel with discretized equal time quantization (DETQ) and the fact that Lorentz invariance and microcausality are restored if one can take the continuum limit properly is emphasized. In the free case, it is shown with numerical evidence that the continuum results can be reproduced from DLCQ results for the Pauli–Jordan function and the real part of Feynman propagator. The contributions coming from k + near zero region in these cases are found to be very small. In the interacting case, aspects related to the continuum limit of DLCQ results in perturbation theory in momentum space are discussed.

Timing quantization error in lidar speed-measurement devices

Minimizing the timing quantization error of lidar speed-measurement devices is an important step in reducing the magnitude of the speed-measurement errors associated with these devices. This paper presents a statistical model for the timing quantization error and demonstrates how this model can be used to select the values of key timing parameters. The values of these parameters must be carefully selected so that manufactured equipment meets current model lidar speed-measurement device performance standards established by the National Highway Traffic Safety Administration (NHTSA).

The massive Schwinger model in a fast moving frame

We present a non-perturbative study of the massive Schwinger model. We use a Hamiltonian approach, based on a momentum lattice corresponding to a fast moving reference frame, and equal time quantization.

Trans-Planckian particles and the quantization of time

Trans-Planckian particles are elementary particles accelerated such that their energies surpass the Planck value . There are several reasons to believe that trans-Planckian particles do not represent independent degrees of freedom in Hilbert space, but they are controlled by the cis-Planckian particles. A way to learn more about the mechanisms at work here, is to study black hole horizons, starting from the scattering matrix ansatz. By compactifying one of the three physical spatial dimensions, the scattering matrix ansatz can be exploited more efficiently than before. The algebra of operators on a black hole horizon allows for a few distinct representations. It is found that this horizon can be seen as being built up from string bits with unit length, each of which are described by a representation of the Lorentz group. We then demonstrate how the holographic principle works for this case, by constructing the operators corresponding to a field . The parameter t turns out to be quantized in units of , where R is the period of the compactified dimension.

The massive Schwinger model - a Hamiltonian lattice study in a fast moving frame

We present a non-perturbative study of the massive Schwinger model. We use a Hamiltonian approach, based on a momentum lattice corresponding to a fast moving reference frame, and equal time quantization. We present numerical results for the mass spectrum of the vector and scalar particle. We find good agreement with chiral perturbation theory in the strong coupling regime and also with other non-perturbative studies (Hamer et al., Mo and Perry) in the non-relativistic regime. The most important new result is the study of the $\theta$-action, and computation of vector and scalar masses as a function of the $\theta$-angle. We find excellent agreement with chiral perturbation theory. Finally, we give results for the distribution functions. We compare our results with Bergknoff's variational study from the infinite momentum frame in the chiral region.

Renormalization in light-cone gauge: how to do it in a consistent way

We summarize several basic features concerning canonical equal time quantization and renormalization of Yang-Mills theories in light-cone gauge. We describe a “two component” formulation which is reminiscent of the light-cone hamiltonian perturbation rules. Finally we review the derivation of the one-loop Altarelli-Parisi densities, using the correct causal prescription on the “spurious” pole.

Subnanosecond sampling all‐optical analog‐to‐digital converter using symmetric self‐electro‐optic effect devices

A system to convert an analog optical system to a digital one in an optical environment using basic symmetric self-electro-optic effect devices (S-SEEDs) is detailed. It is shown that quantization and binary encoding can readily be achieved using the logic capabilities of S-SEEDs. A quantizer prototype has been constructed and proper op- eration observed. The effect of the hysteresis inherent in the S-SEED is discussed and three techniques are proposed to eliminate the problems caused by hysteresis. The logic operations needed for the construction of the binary encoder with the minimum number of S-SEEDs are facili- tated using a reference beam. An alternate, efficient design of the binary encoder is also presented. Using a novel time quantization technique, a sampling rate in excess of 1 gigasamples/s is achievable. © 1996 So- ciety of Photo-Optical Instrumentation Engineers. Subject terms: analog-to-digital conversion; quantization; symmetric-self-electro- optic effect devices; hysteresis; binary encoding logic.

A New Approach to The Stochastic Estimation of Frequency Measurement Process in Digital Automatic Control Systems, with Technical Applications

The object of this report is the development of a method for numerical statistic characteristic calculation in digital frequency measurements for frequency modulated automatic control systems (ACS). In such systems valid data is transmitted using frequency modulation of a pulse signal sequence. The pulse data frequency is measured by a fixed number, N, of retrieval- storage cycle repetitions and calculation of the average number K(N) of pulses measured in N samples. The stochastic estimation problem for this process consists in the mean value M K(N) and variance DK(N) determination as functions of the retrieval-storage cycle time (i.e. the period of time quantization) fluctiations, \tau_{q}, the time of retrieval, \tau_{\tau} and the input signal phase, \varphi.

Uncertainty in end-point tension measurement in wires subject to high-velocity impact

This paper analyses sensor performance requirements in measuring end-point tension (in magnitude and direction) in cables subject to high-velocity impact. The work may be viewed as a tool to analyse and design end-point tension measurement devices for cable-like systems when wire dynamics is very rapid (> 10 kHz) and fully non-linear. Load effect, conversion time and ADC quantization effects are analysed in order to provide a full description of these uncertainty sources by simultaneous integration of the set of hyperbolic partial differential equations governing cable motion, and the set of ordinary differential equations describing the motion of the impacting object and sensor dynamics. Three-dimensional mathematical modelling of the wire is based on the theory of quasi-linear partial differential equations. Fully non-linear analysis of wire motion is thus accomplished without restrictions on displacement and deformation magnitudes. Numerical solution algorithms are based on the characteristics method. The main result is that the dynamic error due to sensor dynamics is the principal source of uncertainty. Moreover, the reduction of such uncertainty is not allowed by the actual force transducer devices, due to the high frequency response required.

Quantization of time: an implication of strictly-irreversible evolution of dynamically isolated quantum systems

Quantized time-lapses are determined to be an essential feature of the changes undergone by the energy-eigenfunction-evaluated matrix elements of statistical operators that evolve in accord with an intrinsic temporal discreteness characteristic of strictly-irreversible behavior. They are inversely proportional to their associated energy differences, with a proportionality constant that is universal. An analysis of appropriate experimental “quantum-beat” processes is described which may serve to evaluate the constant. Once it is, a fully-determinable dynamical theory of strictly-irreversible evolution is the result, in which, except for temporal-discreteness, the conventional description of quantum-mechanical systems is maintained.

Continuum light-cone quantization of Gross-Neveu models.

The Gross-Neveu models are quantized on the light cone, using an equation of motion approach tailored to the large [ital N] limit. Vacuum properties are exhibited and the fermion-antifermion integral equation of Tamm-Dancoff type is derived and solved, with particular attention paid to the issue of renormalization. The main results are verified in equal time quantization, by means of the infinite momentum frame.

Accuracy of digital measurement of dynamic magnetic characteristics of soft-magnetic materials

The errors of measurements of dynamic magnetic characteristics of soft-magnetic materials due to sampling in time and signal-level quantization during analog-digital conversion are analyzed considering the effect of the computing algorithm for sinusoidal signals.

Time and radiation time quantization and their application to the transport through a quantum dot turnstile

In this paper, we analyse the time in the time evolution operator and then give time a reasonable definition. We realize the radiation time quantization by supposing that a radiation-matter interaction process is an eigenstate of the time operator, which results in the quantized resonance time. We discuss the application to the transport through a quantum dot turnstile in an rf field.