The logic of quantum mechanics derived from classical general relativity

For the first time it is shown that the logic of quantum mechanics can be derived from classical physics. An orthomodular lattice of propositions characteristic of quantum logic, is constructed for manifolds in Einstein’s theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves—a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparationand measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic.     

Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states

A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises. The orthogonality of these processes provides a natural way to construct binary or multi-valued logic circuitry with arbitrary number N of logic values by using analog circuitry. Moreover, the logic values on a single wire can be made a (weighted) superposition of the N distinct logic values. Fuzzy logic is also naturally represented by a two-component superposition within the binary case (N=2). Error propagation and accumulation are suppressed. Other relevant advantages are reduced energy dissipation and leakage current problems, and robustness against circuit noise and background noises such as 1/f, Johnson, shot and crosstalk noise. Variability problems are also non-existent because the logic value is an AC signal. A similar logic system can be built with orthogonal sinusoidal signals (different frequency or orthogonal phase) however that has an extra 1/N type slowdown compared to the noise-based logic system with increasing number of N furthermore it is less robust against time delay effects than the noise-based counterpart.     

Logical foundation of quantum mechanics

The subject of this article is the reconstruction of quantum mechanics on the basis of a formal language of quantum mechanical propositions. During recent years, research in the foundations of the language of science has given rise to adialogic semantics that is adequate in the case of a formal language for quantum physics. The system ofsequential logic which is comprised by the language is more general than classical logic; it includes the classical system as a special case. Although the system of sequential logic can be founded without reference to the empirical content of quantum physical propositions, it establishes an essential part of the structure of the mathematical formalism used in quantum mechanics. It is the purpose of this paper to demonstrate the connection between the formal language of quantum physics and its representation by mathematical structures in a self-contained way.     

The logic of quantum systems with diagonal singularities

The work of the Brussels-Austin groups on irreversibility over the last years has shown that Quantum Large Poincaré systems with diagonal singularity lead to an extension of the conventional formulation of dynamics at the level of mixtures which is manifestly time asymmetric. States with diagonal singularity acquire meaning as linear fractionals over the involutive Banach algebra of operators with diagonal singularity. We show in this paper that the logic of quantum systems with diagonal singularity is not the conventional logic of Hilbert space, because only finite combinations of prepositions are allowed.     

Nonordered quantum logic and its YES-NO representation

It is shown that an orthomodular lattice is an ortholattice in which aunique operation of bi-implication corresponds to the equality relation and that the ordering relation in the binary formulation of quantum logic as well as the operation of implication (conditional) in quantum logic are completely irrelevant for their axiomatization. The soundness and completeness theorems for the corresponding algebraic unified quantum logic are proved. A proper semantics, i.e., a representation of quantum logic, is given by means of a new YES-NO relation which might enable a proof of the finite model property and the decidability of quantum logic. A statistical YES-NO physical interpretation of the quantum logical propositions is provided.     

A Hilbert Space Realization of Nonlinear Quantum Mechanics as Classical Extension of Its Linear Counterpart

This paper studies the state-effect-probability structure associated with thequantum mechanics of nonlinear (homogeneous, in general nonadditive) operatorson a Hilbert space. Its aim is twofold: to provide a concrete representation ofthe features of nonlinear quantum mechanics on a Hilbert space, and to showthat the properties of the nonlinear version of quantum mechanics here describedhave the structure of a classical logic.     

Realization of XNOR logic function with all-optical high contrast XOR and NOT gates

In this article, we propose the realization of XNOR logic function by using all-optical XOR and NOT logic gates. Initially, both XOR and NOT gates are designed, simulated and optimized for high contrast outputs. T-shaped waveguides are created on the photonic crystal platform to realize these logic gates. An extra input is used to perform the inversion operation in the NOT gate. Inputs in both the gates are applied with out of phase so as to have a destructive interference between them and produce negligible intensity for logic ‘0'. The XOR and NOT gates are simulated using Finite Difference Time Domain method which results with a high contrast ratio of 55.23?dB and 54.83?dB, respectively at a response time of 0.136?ps and 0.1256?ps. Later, both the gates are cascaded by superimposing the output branch of the waveguide of XOR gate with the input branch of the waveguide of NOT gate so that it can be resulted with compact size for XNOR logic function. The resultant structure of XNOR logic came out with the contrast ratio of 12.27?dB at a response time of 0.1588?ps. Finally, it can be concluded that the proposed structures with fair output performance can suitably be applied in the design of photonic integrated circuits for high speed computing and telecommunication systems.     

Probabilistic forcing in quantum logics

It is shown that an orthomodular lattice can be axiomatized as an ortholattice with aunique operation of identity (bi-implication) instead of the operation of implication, and a corresponding algebraic unified quantum logic is formulated. A statisticalyes-no physical interpretation of the quantum logical propositions is then provided to establish a support for a novelyes-no representation of quantum logic which prompts a conjecture about a possible completion of quantum logic by means of probabilistic forcing.     

Multimode Interference All-Optical Logic Gates via Partially Nonlinear Propagation Region

We propose a new structure containing multimode interference waveguides with partial nonlinear Kerr-like material whose function is like a phase shifter for all-optical logic gates. It has the advantages of compactness and insensitivity to relative phase difference between the incident beams. In this paper, we analyze the structure by finite difference time domain method and demonstrate such logic gates as AND, NOT and XOR logics.     

A normalised residence time transport equation for the numerical simulation of combustion with high-temperature air

This study concerns the numerical simulation of turbulent non-premixed combustion in highly preheated air streams. One of the objectives is to settle an efficient computational procedure to proceed with the numerical simulation of large-scale industrial devices. It is also expected that the availability of such a computational framework may facilitate comprehensive sensitivity analyses as well as the development of mathematical models able to represent turbulence-chemistry interactions (TCI) in such conditions. Based on the salient physical ingredients that characterise scalar mixing, propagation, and self-ignition processes, a turbulent combustion modelling framework is thus introduced and applied to the numerical simulation of well-documented laboratory flames. In the corresponding geometries, the bulk flow velocities of the reactants streams can reach rather large values, which lead the flame to lift from the burner rim. Partially premixed flame edges thus stabilise the whole flame structure and the temperature of the oxidising stream can be increased by vitiation with burned gases so as to promote the corresponding flame-stabilisation processes. For sufficiently large values of the vitiated airstream temperature, self-ignition mechanisms may be triggered thus leading to a competition between mixing, propagation, and ignition processes. In this context, the ratio of the residence time to the self-ignition delay is thought to be a relevant variable to delineate the possible influence of ignition phenomena. Therefore, a modelled transport equation for this normalised residence time is considered. The performance of the corresponding modelling proposal is analysed with special emphasis placed on its ability to reproduce ‘memory’ or ‘lagrangian’ effects related to thermal aging processes. In this respect, it is noteworthy that the present set of computations makes use of tabulated quantities associated to (i) steady laminar one-dimensional diffusion flamelets, so as to describe the composition of combustion products, (ii) steady laminar one-dimensional premixed flamelets, to describe the flame brush propagation, and (iii) temporal evolution of zero-dimensional homogeneous mixtures to account for the possible occurrence of self-ignition phenomena. In particular, the tabulated self-ignition time value is used to evaluate the increase in the normalised residence time. Finally, two modelling parameters are put into evidence and studied through a detailed sensitivity analysis.     

Map for Simultaneous Measurements for a Quantum Logic

In this paper we will study a function of simultaneous measurements for quantum events (s-map) which will be compared with the conditional states on an orthomodular lattice as a basic structure for quantum logic. We will show the connection between s-map and a conditional state. On the basis of the Rényi approach to the conditioning, conditional states, and the independence of events with respect to a state are discussed. Observe that their relation of independence of events is not more symmetric contrary to the standard probabilistic case. Some illustrative examples are included.     

Logicoalgebraic structures II. Supports in test spaces

Test spaces are mathematical structures that underlie quantum logics in much the same way that Hilbert space underlies standard quantum logic. In this paper, we give a coherent account of the basic theory of test spaces and show how they provide an infrastructure for the study of quantum logics. IfL is the quantum logic for a physical systemL, then a support inL may be interpreted as the set of all propositions that are possible whenL is in a certain state. We present an analog for test spaces of the notion of a quantum-logical support and launch a study of the classification of supports.     

Largep T prompt photon production at HERA

We examine the possibility of using direct photon production at HERA as a means of obtaining information about the photon structure and fragmentation functions. Estimates of the cross section for inclusive prompt photon production at theep collider HERA are made completely in next-to-leading order QCD. Using parton distributions for the photon evolved in next-to-leading order QCD for the first time, we show that theO( _s ) corrections to the processes involving these functions are significant in the regions where they dominate. This can have important consequences for the possibility of measuring the gluon content of the photon using these processes at HERA. Moreover, we show that it may not be straightforward to separate the various contributions to the cross section in theep lab frame.     

All optical NOR and NAND gate based on nonlinear photonic crystal ring resonators

In this paper we proposed optical NOR and NAND gates. By combining nonlinear Kerr effect with photonic crystal ring resonators first we designed a structure, whose optical behavior can be controlled via input power intensity. The switching power threshold obtained for this structure equal to 2 kW/μm². For designing the proposed optical logic gates we employed two resonant rings with the same structures, both rings at the logic gates were designed such that their resonant wavelength be at λ = 1550 nm. Every proposed logic gate has one bias and two logic input ports. We used plane wave expansion and finite difference time domain methods for analyzing the proposed structures.     

Nonstandard extension of quantum logic and Dirac's bra-ket formalism of quantum mechanics

An extension of the quantum logical approach to the axiomatization of quantum mechanics usingnonstandard analysis methods is proposed. The physical meaning of a quantum logic as a lattice of propositions is conserved by its nonstandard extension. But not only the usual Hubert space formalism of quantum mechanics can be derived from the nonstandard extended quantum logic. Also the Dirac bra-ket quantum mechanics can be derived as a consequence of such an extended quantum logic.     

Interaction of Short Laser Pulses in Wavelength Range from Infrared to X‐ray with Metals,Semiconductors, and Dielectrics

Laser‐matter interaction is defined by an electronic band structure of condensed matter and frequency ω_L of electromagnetic radiation. In the range of moderate fluences, the energy absorbed by electrons from radiation finally thermalizes in the ion thermal energy. The thermalization processes are different for optical as compared with X‐ray quanta and for metals relative to semiconductors and dielectrics, since the light absorption and electron‐electron, electron‐ion dynamics are sensitive to the electron population in a conduction band and the width of a forbidden gap. Although the thermalization processes are different, the final state is simply a heated matter. Laser heating creates powerful stresses in a target if duration of a laser pulse τ_L is short in acoustic time scale. Nucleation and material removal take place under such stresses. Such way of removal is called here the spallative ablation. Thus the spallative ablation is an ablation mechanism universally important for qualitatively different materials and quanta (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantum Set Theory

The complete orthomodular lattice of closed subspaces of a Hilbert space is considered as the logic describing a quantum physical system, and called a quantum logic. G. Takeuti developed a quantum set theory based on the quantum logic. He showed that the real numbers defined in the quantum set theory represent observables in quantum physics. We formulate the quantum set theory by introducing a strong implication corresponding to the lattice order, and represent the basic concepts of quantum physics such as propositions, symmetries, and states in the quantum set theory.     

Binary logic is rich enough

Given a finite ortholatticeL, the *-semigroup is explicitly built whose annihilator ortholattice is isomorphic toL. Thus, it is shown that any finite quantum logic is the additive part of a binary logic. Some areas of possible applications are outlined.     

Terabit all-optical logic based on ultrafast two-dimensional transmission gating

Terabit all-optical complementary logic is proposed using two successive time slots to represent a unique logical status. An organic molecular thin film is used as an array of optically controlled optical switches. By utilizing the planar structure of the film and its ultrafast optical response, proof-of-principle fully optical NOT and AND logic operations were demonstrated with 400-fs interval pulses.     

二维光子晶体全光异或门的设计及研究

分析了二维光子晶体马赫-曾德尔干涉仪的传输特性,将二维光子晶体波导、环形腔和马赫-曾德尔干涉仪有效结合,提出了一种基于二维光子晶体马赫-曾德尔干涉仪的异或门设计。用平面波展开法分析二维光子晶体能带结构,并用时域有限差分法验证光信号在该器件中的电场稳态分布。结果表明,该结构能够实现异或逻辑,且具有高逻辑对比度7.88 dB,快速响应周期0.388 ps和高传输速率7.87 Tbit/s;并且该器件结构尺寸仅为13 μm×14 μm,易于集成。该异或逻辑结构中引入了二维光子晶体马赫-曾德尔干涉仪,使得光子晶体逻辑门结构的设计更加多样,并为二维光子晶体半加器与全加器的设计提供了基础,具有重要的研究意义。