Time Quantization Research Articles

Generalized Weyl Quantization and Time

This work presents quantization of time of arrival functions using generalized Stratonovich-Weyl quantization. We take into account the ordering problems involved, mainly the Born-Jordan and the symmetric ordering schemes. We call attention to the combination of the group theoretic methods usually employed in Weyl quantization with the implementation of different ordering schemes via integral kernel factors. It is possible to, and we do, apply the Pegg-Barnett method to the quantization of time to address physical issues such as boundedness and self-adjointness.

Оптимізація нелінійних імпульсних систем автоматичного регулювання з астатичними об’єктами

Currently, nonlinear pulse automatic control systems have become widespread, so there is a need to develop methods for their study. Pulse regulators are created on the basis of positional with the addition of pulse breakers. They can be represented as a non-linear element, a simple impulse element and a forming circle connected in series. The aim of the study was to determine the optimal parameters for setting up a relay-pulse controller for an astatic object with a delay. When determining the parameters of adjustment of the relay-pulse regulator for the quality indicator in the optimization of the automatic control system was taken as the total square deviation. Applying this criterion, the pulse duration of the regulator was determined. The time quantization interval is determined from the condition of ensuring the absolute stability of the automatic control system. Analytical dependences were obtained to determine the pulse duration and time quantization interval, which make it possible to determine the debugging parameters of the relay-pulse controller for a first-order astatic object with a delay. This ensures a minimum control error, and the control system is stable.

Intonacijos įtaka akustinei priegaidžių raiškai: eksperimentinis latvių bendrinės kalbos tyrimas

Straipsnyje, remiantis latvių bendrinės kalbos medžiaga, analizuojamas fonetinės priegaidžių ir frazės intonacijos sąveikos mechanizmas. Iš pradžių aptarus fonologines šios srities tyrimų problemas, argumentuota pasirinktoji tyrimo metodika – nuspręsta kalbamųjų prozodinių elementų akustinį ryšį apibūdinti rodikliais, gaunamais tiriamuosius objektus (su viena ar kita priegaide tariamų balsių tono kontūrus) skaidant į skirtingas laiko atkarpas. Priegaidžių diferencialumo lygmuo ir pobūdis nagrinėtas įvairiomis intonacinėmis sąlygomis: varijuota intonaciniais tipais, minimaliųjų porų (zâle „žolė“ – zãle „salė“; plâns „plonas“ – plãns „planas“) narių pozicijomis frazės kirčio (t. y. stiprioji / silpnoji frazės pozicija) ir centro (frazės inicialė, medialė arba finalė) atžvilgiu. Iš gautųjų duomenų padaryta keletas bendrojo pobūdžio išvadų. Pirma, akustinė priegaidžių raiška sietina su funkciniu jų krūviu frazėse ir poreikiu išskirti, pabrėžti kažkurio sakinio elemento dalykinį turinį. Antra, tiesioginį neigiamą frazės intonacijos poveikį priegaidėms loginio kirčio pozicijoje atspindi tono kontūrų suvienodinimas pagal bendrąją kitimo kryptį ir pobūdį. Trečia, priegaidės laikytinos veiksniu, vienaip ar kitaip modifikuojančiu frazės intonacijos implikuojamą bendrąjį akustinės energijos kiekį, jos kaitos laipsnį ir kryptį.

Quantization of the mean decay time for non-Hermitian quantum systems

We show that the mean time, which a quantum particle needs to escape from a system to the environment, is quantized and independent from most dynamical details of the system. In particular, we consider a quantum system with a general Hermitian Hamiltonian $\hat{H}$ and one decay channel, through which probability dissipates to the environment with rate $\Gamma$. When the system is initially prepared exactly in the decay state, the mean decay time $\langle T \rangle$ is quantized and equal to $w/(2\Gamma)$. $w$ is the number of distinct energy levels, i.e. eigenvalues of $\hat{H}$, that have overlap with the decay state, and is also the winding number of a transform of the resolvent in the complex plane. Apart from the integer $w$, $\langle T \rangle$ is completely independent of the system's dynamics. The complete decay time distribution can be obtained from an electrostatic analogy and features rare events of very large dissipation times for parameter choices close to critical points, where $w$ changes, e.g. when a degeneracy is lifted. Experiments of insufficient observation time may thus measure a too small value of $w$. We discuss our findings in a disordered tight-binding model and in the two-level atom in a continuous-wave field.

Abstract-algebraic interpretations of the energy–time uncertainty relation prove quantization of time

In modern physics, the general theory of relativity (GTR) successfully predicts the vital structure of gravity. The GTR confirmed that gravity is the distortion of four-dimensional spacetime [Formula: see text] by massive bodies. Such a prediction of the GTR is one of the vital successes towards the development goals of modern physics. Though, the central foundation for all the calculations of the GR is the hypothesis of continuum spacetime. In this paper, the author introduces a theorem of the quantum mechanical theory of time (QMT) to test whether the metric time is discrete or continuous. To prove the theorem, the author applied the set theory of cardinal numbers on the energy–time uncertainty relationship. The proof of the theorem confirmed that the metric time is discrete, and has an intrinsic quantum nature. The result implied that the continuum spacetime assumption of the GTR is found fundamentally erroneous. Therefore, spacetime is discrete and needs to be analyzed by the principles of quantum mechanics (QM).

Liouville's theorem and quantum mechanics - time quantization and reality

The chrono-topology, as introduced axiomatically in a different context, is also supported by Liouville's theorem of statistical mechanics. It is shown that, if time is quantized, the distribution function (d.f.) becomes real. An elementary solution, g, of the classical Liouville equation has been found in phase-space and time, which can be used to construct any differentiable d.f, F(g), satisfying the same Liouville equation. The conditions imposed on F(g) are reality and additivity. The reality requirement, {Im F(g)=0) quantizes: (i) F(g) and makes it time-independent, (ii). The time variable, (iii) The energy. As a verification of chronotopology, the Planck constant h has been calculated on the basis of the time quantization. The d.f. F(g) becomes, after the time quantization, a real generalized Maxwell-Boltzmann d.f, F(g) = exp[g(p, g; l1,l2,..,lN)], depending on Ν quantum numbers. These facts are significant for quantum theory, because they uncover an intrinsic relationship between Liouville's theorem and quantum mechanics.

A Mixed-Signal RF Pulse Width Modulator With High Time Resolution Utilizing Passive Delay Lines

We present a novel mixed-signal single-output outphasing RF Pulse Width Modulator (RF PWM) realized in 40nm CMOS. Two Digital-to-Time Converters (DTCs) synchronously phase shift an external LO according to two 9-bit outphasing input words. Coarse time quantization is provided by tapping the internal nodes of passive integrated LC delay lines. Finer resolution is added using switching capacitors of a Gm-C circuit attaining minimum time steps of 6ps/750fs respectively. “Hair-pin” inductors with minimized footprint have been employed for the silicon realization of each LC delay line. Measurement yields an ACLR of approx. −42 dBc from a 32 MHz BW multi-tone signal on a 2.65 GHz carrier.

Some Topological Aspects of Sampling Theorem and Reconstruction Formula

In this paper, we present a few thoughts regarding topological aspects of transferring a signal of a continuous time into its discrete counterpart and recovering an analog signal from its discrete-time equivalent. In our view, the observations presented here highlight the essence of the above transform-ations. Moreover, they enable deeper understanding of the reconstruction formula and of the sampling theorem. We also interpret here these two borderline cases that are associated with a time quantization step going to zero, on the one hand, and approaching its greatest value provided by the sampling theorem, on the other.

On the Quantization of Time, Space and Gravity

We combine the de Broglie Matter Wave Equation with the Heisenberg Uncertainty Principle to derive an equation for time as a wave. This happens to be the first time that these two statements have been combined in this manner to derive an equation for time. The result is astounding. Time turns out to be a minuscule blob of quantum electromagnetic energy in perpetual angular momentum. From this time equation, we derive an equation for space which turns out to also predict a string (like the string of string theory). We then combine the time equation with the space equation to derive an equation for the inverse of quantum gravity which is also surprisingly electromagnetic in nature. This last statement implies that space is multidimensional and gravity in multidimensional space is not quantized, but its inverse (which is single-dimensional) is.

A Fast-Transient and High-Accuracy, Adaptive-Sampling Digital LDO Using a Single-VCO-Based Edge-Racing Time Quantizer

A digital low-dropout (LDO) voltage regulator using a single-VCO-based edge-racing time quantizer (SVER TQ) was designed to achieve a fast-transient response and a high-accuracy of the output voltage. As the sampling frequency generated from the SVER TQ is scaled dynamically according to the magnitude of errors in the output voltage, its transient response can be improved without the increase in the power consumption in the steady state. For the SVER TQ, since two injected edges equally pass through all delay cells in a single VCO, the accuracy of regulation is not degraded by mismatches between the delay cells. The proposed digital LDO was fabricated in a 65-nm CMOS process, and it occupied a silicon area of 0.0488 mm2. In measurements, the digital LDO in this letter achieved a 0.29-ps-transient FOM and a sub-2-mV accuracy under a 0.5-V supply.

Quantization of time and the big bang via scale-invariant loop gravity

We consider the background-independent quantization of a general scale-invariant theory of gravity with matter, which supports a conserved Weyl current recently suggested as a natural flow of time. For scalar-metric systems, a conformal class of Ashtekar-Barbero connection variables is constructed, which can be quantized using spin networks. Crucially, the quantum states become separable into the eigen states of the generator of the scale transformation and spin-network states in the Einstein frame. The eigen values consist of additional quantum numbers including a new type of fundamental frequency ω and energy E=ħω with respect to a new local time τ carried by every spin-network vertex. The discretely distributed τ values as the “quanta of time” correspond to a functional time related to the integrated Weyl current in the classical theory. The Immirzi ambiguity of loop quantum geometry is removed by scale symmetry. To probe the quantum behaviour of the early Universe, the new formalism is applied to a scale-invariant homogenous and isotropic cosmological model coupled to a doublet of scalars with illustrative numerical simulations. The Einstein-frame volume is quantized in recently improved and regularized polymer representations with an arbitrary Immirzi parameter. The resulting unitary evolution of the quantum state of an expanding universe has a positive energy spectrum. A rescaling of the Immirzi parameter is equivalent to a translation in time without changing dynamics. The big bang can be identified in the past time limit when the expectation values of the Jordan-frame volume tend to zero. Remarkably, the quantized big bang is not replaced by a big bounce—a prevalent scenario in present loop quantum cosmology.

A Wide Dynamic Range and Low Bit Error Pixel TDC Suitable for Array Application

This brief presents a cascade pseudo 3-level time-to-digital converter (TDC) based on wideband phase-locked loops (PLLs) for photon time of flight measurement. In each pixel, a 9-bit pseudo random synchronous counter composed of linear feedback shift register is served as a high-level coarse TDC. Its counting clock is directly coming from the synchronous counter served as the middle-level TDC. The low-level fine TDC is based on time-interpolation technology and directly use the low-jitter multi-phase clock signal generated by the PLL to complete the fine quantization of the residue time. In addition, proper timing control and error suppression methods are implemented in the proposed TDC. The circuit is demonstrated in TSMC 0.35- ${\mu }\text{m}$ CMOS process. Under the condition of 10-MHz input reference frequency and 3.3-V supply voltage, the wideband PLL can be locked from 146 to 450 MHz. The resolution of the TDC will change from 856 to 278 ps. At 450 MHz, the measured DNL around $15\boldsymbol {\mu }\text{s}$ is–0.1 to 0.1 LSB and the INL is–0.05 to 0.2 LSB.

Guess-Work and Reasonings on Centennial Evolution of Surface Air Temperature in Russia. Part V: Stability Margin Towards Emergency

The paper presents a discussion on an opinion about the stability margin towards an emergency in local climate dynamics from the bifurcation analysis viewpoint. With this purpose we propose to attract the practice-oriented bifurcation analysis, where the conflict-of-units between notions used to understand natural evolution processes and notions used to describe desirable artificial regimes is resolved by integrating analytics on the basis of modified bifurcation diagrams. The discussion focuses on the phenomenon of interannual temperature variability, where local annual maximums and minimums are analyzed with daily details in both time and temperature coordinates. This phenomenon is considered via the probable, periodical and regulator conceptions. Advantages of the regulator conception are verified by results of processing the data of temperature meteorological observations on daily means over the last 135 years. This conception is based on the HDS-hypothesis, in accordance to which local climate dynamics is determined by the natural competition between the amplitude quantization (restricted by the temperature Hysteresis) and time quantization (caused by the Double Synchronization). Thus an alternation between three elementary processes with the same period (year) and different patterns of annual warming–cooling cycles is supposed as a typical behavior for local climate systems, and the idea on high-dynamic local climate ensembles is developed instead of the conventional opinion on quasi-static local climate norms. Mechanisms of temperature changes due to abrupt shifts (so-called change-points) of the HDS-regulator parameters are distinguished from mechanisms of temperature changes due to bifurcations. The notion of a stability margin is used as a distance to an emergency and is visualized in the parametrical space. So, in spite of the mechanisms of temperature changes with/without bifurcations are different, their conflict-free sewing becomes conceptually possible in the context of the stability margin towards emergencies determined relatively bifurcation boundaries in the parametrical space. Since the discussed dynamics is not supposed to exist in terms of the traditional estimations concerning the observed local climate changes, then we believe that the paper would be interesting for scientists in the field of bifurcation analysis as well as for scientists and specialists, activity areas of which relate to the contemporary challenges connected with climate changes.

Nonfragile Quantized Dissipative Filter for Nonlinear Networked Systems

To address the problem of filter parameter perturbation in nonlinear networked systems, a nonfragile quantized dissipative filter is designed by considering the coexistence of random one-step time delay, multipacket losses, and quantization error. We acquired the sufficient conditions for the existence of filter by choosing appropriate Lyapunov function as well as utilizing linear matrix inequality. Furthermore, we obtained the parameter expressions of the designed filter. The designed filter could meet the performance requirements of stability and dissipativity for the filter error system under the condition of allowed time delays, packet loss probability, and quantization density. The effectiveness of the designed filter is verified by numerical simulation.

FLINT+: A runtime-configurable emulation-based stochastic timing analysis framework

ASICs for Stochastic Computing conditions are designed for higher energy-efficiency or performance by sacrificing computational accuracy due to intentional circuit timing violations. To optimize the stochastic behavior, iterative timing analysis campaigns have to be carried out for a variety of circuit timing corner cases. However, the application of common event-driven logic simulators usually leads to excessive analysis runtimes, increasing design time for hardware developers. In this paper, a gate-level netlist-oriented FPGA-based timing analysis framework is proposed, offering a runtime-configuration mechanism for emulating different timing corner cases in hardware without requiring multiple FPGA bitstreams. Logic gates are instrumented with a quantization-based delay model and a critical path selection algorithm is used to reduce the FPGA resource overhead. For an exemplary design space exploration of stochastic CORDIC units, speed-up factors of up to 48 for 10 ps or 476 for 100 ps timing quantization are achieved while maintaining timing behavior deviations lower than 1.5% or 4% to timing simulations, respectively.

Discrete random sampling: Theory and practice in machine monitoring

Abstract Random sampling was first introduced in the 1960’s (Beutler and Leneman, 1966 [1] ), and was then reused in the Compressive Sensing theory (published in 2006 (Donoho, 2006 [2])) for having two important advantages: anti-aliasing property and low sampling rate. These advantages decrease the demand of high speed acquisition and big data storage. In this paper, a brief review of the principal random sampling modes is presented: Additive Random Sampling (ARS) and Jittered Random Sampling (JRS) that both use probability distributions: uniform or Gaussian (Wojtiuk, 2000; Ben Romdhane, 2009; Luo, 2012; Lo and Purvis, 1997 [3–6]). In fact, the stationarity of the random point process is the essential criterion to guarantee the anti-aliasing property (Bilinksis and Mikelson, 1992 [7]). Accordingly, these modes of sampling are studied and used in simulation and hardware implementation. In addition, a study of the time quantization effect is done to explore the different aspects of discrete random sampling (Ben Romdhane, 2009; Luo, 2012 [4,5]). The performance of this sampling is approved by simulation and practice, using respectively Matlab and Arduino microcontroller, respectively, for acquiring signals at a randomly spaced clock. A database was created in order to observe the impact of statistical parameters such as the mean and the standard deviation for Gaussian distribution, and the interval endpoints of uniform distribution. In conclusion, the ARS with uniform distribution has been proved to have less limitations (Ben Romdhane, 2009 [4]), whereas the spectrum of sampled signal is free of alias and the sampling frequency is reduced (a much smaller than Nyquist-Shannon sampling rate). In order to take advantage of this mode, it is applied on vibration signals to enhance remoted machine monitoring.

A Fully Integrated Digital LDO With Built-In Adaptive Sampling and Active Voltage Positioning Using a Beat-Frequency Quantizer

This paper proposes a fully integrated digital low-dropout (DLDO) regulator using a beat-frequency (BF) quantizer implemented in a 65-nm low power (LP) CMOS technology. A time-based approach, replacing the conventional voltage quantizer by a pair of voltage-controlled oscillator and a time quantizer, makes the design highly digital. A D-flip-flop is utilized as a BF generator, which is used as the sampling clock for the DLDO. The variable sampling frequency in the BF DLDO can achieve fast response, LP consumption, and excellent stability at the same time. In addition to that, the DLDO has a built-in active voltage positioning (AVP) for lower peak-to-peak voltage deviation during load step. The load capacitor is only 40 pF, and the total core area of the DLDO is 0.0374 mm2. A 50-mA step in load current produces a voltage droop of 108 mV, which is recovered in 1.24 $\mu \text{s}$ . It can operate for a wide input voltage from 0.6 to 1.2 V while generating a 0.4–1.1-V output for a maximum load current of 100 mA. The peak current efficiency is 99.5% and the figure of merit (FOM) is 1.38 ps.

Unruh effect as a result of quantization of spacetime

A way to encode acceleration directly into fields has recently being proposed, thus establishing a new kind of fields, the accelerated fields. The definition of accelerated fields points to the quantization of space and time, analogously to the way quantities like energy and momentum are quantized in usual quantum field theories. Unruh effect has been studied in connection with quantum field theory in curved spacetime and it is described by recruiting a uniformly accelerated observer. In this work, as a first attempt to demonstrate the utility of accelerated fields, we present an alternative way to derive Unruh effect. We show, by studying quantum field theory on quantum spacetime, that Unruh effect can be obtained without changing the reference frame. Thus, in the framework of accelerated fields, the observational confirmation of Unruh effect could be assigned to the existence of quantum properties of spacetime.

Hybrid co-simulation: it\u2019s about time

Model-based design methodologies are commonly used in industry for the development of complex cyber-physical systems (CPSs). There are many different languages, tools, and formalisms for model-based design, each with its strengths and weaknesses. Instead of accepting some weaknesses of a particular tool, an alternative is to embrace heterogeneity, and to develop tool integration platforms and protocols to leverage the strengths from different environments. A fairly recent attempt in this direction is the functional mock-up interface (FMI) standard that includes support for co-simulation. Although this standard has reached acceptance in industry, it provides only limited support for simulating systems that mix continuous and discrete behavior, which are typical of CPS. This paper identifies the representation of time as a key problem, because the FMI representation does not support well the discrete events that typically occur at the cyber-physical boundary. We analyze alternatives for representing time in hybrid co-simulation and conclude that a superdense model of time using integers only solves many of these problems. We show how an execution engine can pick an adequate time resolution, and how disparities between time representations internal to co-simulated components and the resulting effects of time quantization can be managed. We propose a concrete extension to the FMI standard for supporting hybrid co-simulation that includes integer time, automatic choice of time resolution, and the use of absent signals. We explain how these extensions can be implemented modularly within the frameworks of existing simulation environments.

A low data-rate fluorescence lifetime imaging system with CMM pre-processed in-pixel

A low-data-rate implementation of fluorescence lifetime imaging based on pre-processing center of mass method (CMM) in pixel is proposed. The system utilizes gated ring oscillators (GROs) and two counters to integrate photon time-of-arrival. The electric states of GROs between two oscillations can be held and restored. Time quantization and integration can be flexibly realized by two counters. Each pixel includes a SPAD, quenching circuits, time-to-digital converters (TDCs), counters and registers. Pre-processing of CMM is implemented in pixel to reduce data rate and improve the frame rate. Estimating different theoretical lifetimes with software post calibrations, the system shows an estimation error below 2% within the solvable range under 1% excitation rate and 40MHz synchronous clock. The power consumption of each pixel is 192.6 μW. The data rate per pixel is 0.01 Mbps and the maximum frame rate is 400 fps. Design of video-rate system with large SPAD array is practical to carry out.