Quantum control based on three forms of Lyapunov functions

This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

QBIoT:A Quantum Blockchain Framework for IoT with an Improved Proof-of-Authority Consensus Algorithm and a Public-Key Quantum Signature

The Internet of Things(IoT)is a network system that connects physical devices through the Internet,allowing them to interact.Nowadays,IoT has become an integral part of our lives,offering convenience and smart functionality.However,the growing number of IoT devices has brought about a corresponding increase in cybersecurity threats,such as device vulnerabilities,data privacy concerns,and network susceptibilities.Integrating blockchain technology with IoT has proven to be a promising approach to enhance IoT security.Nevertheless,the emergence of quantum computing poses a significant challenge to the security of traditional classical cryptography used in blockchain,potentially exposing it to quantum cyber-attacks.To support the growth of the IoT industry,mitigate quantum threats,and safeguard IoT data,this study proposes a robust blockchain solution for IoT that incorporates both classical and post-quantum security measures.Firstly,we present the Quantum-Enhanced Blockchain Architecture for IoT(QBIoT)to ensure secure data sharing and integrity protection.Secondly,we propose an improved Proof of Authority consensus algorithm called“Proof of Authority with Random Election”(PoARE),implemented within QBIoT for leader selection and new block creation.Thirdly,we develop a publickey quantum signature protocol for transaction verification in the blockchain.Finally,a comprehensive security analysis of QBIoT demonstrates its resilience against cyber threats from both classical and quantum adversaries.In summary,this research introduces an innovative quantum-enhanced blockchain solution to address quantum security concernswithin the realmof IoT.The proposedQBIoT framework contributes to the ongoing development of quantum blockchain technology and offers valuable insights for future research on IoT security.

Electrostatic Attraction and Repulsion Explained and Modelled Mathematically Using Classical Physics—A Detailed Mechanism Based on Particle Wave Functions

The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

A new group key management scheme based on keys tree, XOR operation and one-way function

By introducing XOR operation and one-way function chains to group key management schemes based on the keys tree, a new group key management scheme based on the keys tree, XOR operation and one-way function chains is proposed. Initialization, member adding and member evicting operations are introduced. The new scheme is compared with three other group key management schemes which are based on the keys tree： SKDC, LKH, and OFF. As far as transmission, computation and storage costs are concerned, the performance of the new group key management scheme is the best. The security problem of the new scheme is analyzed. This new scheme provides backward and forward security, i.e.. newly admitted group members cannot read previous multicast messages and evicted members cannot read future multicast messages, even with collusion by many arbitrarily evicted members.

Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time

The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.

Exact Wave Function of a Time-Dependent Quantum System

To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found.

One-way hash function based on hyper-chaotic cellular neural network

The design of an efficient one-way hash function with good performance is a hot spot in modern cryptography researches. In this paper, a hash function construction method based on cell neural network with hyper-chaos characteristics is proposed. First, the chaos sequence is gotten by iterating cellular neural network with Runge Kutta algorithm, and then the chaos sequence is iterated with the message. The hash code is obtained through the corre- sponding transform of the latter chaos sequence. Simulation and analysis demonstrate that the new method has the merit of convenience, high sensitivity to initial values, good hash performance, especially the strong stability.

The Normal Meromorphic Functions Family Concerning Higher Order Derivative and Shared Set by One-Way

Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.

Recent advances in quantum dot catalysts for hydrogen evolution:Synthesis,characterization,and photocatalytic application

Photocatalytic water splitting is beneficial for the effective mitigation of global energy and environmental crises.Owing to multi-exciton generation,impressive light harvesting,and excellent photochemical properties,the quantum dot(QD)-based catalysts reveal a considerable potential in photocatalytic hydrogen(H_(2))production compared with bulk competitors.In this review,we summarize the recent advances in QDs for photocatalytic H_(2) production by enumerating different synthetic and characterization strategies for QDs.Various QDs-based photocatalysts are introduced and summarized in categories,and the role of different QDs in varied systems,as well as the mechanism and key factors that enhance the photocatalytic H_(2) generation performance,is discussed.Finally,conclusions and future perspectives in the exploration of highly efficient QDs-based photocatalysts for innovative applications are highlighted.

MXene Quantum Dots/Copper Nanocomposites for Synergistically Enhanced N_(2)Electroreduction

Electrocatalytic N_(2) reduction reaction(NRR)represents an appealing solution for sustainable ammonia production,whereas exploring high-efficiency NRR catalysts is highly desired but extremely challenging.Herein,we combine Ti_(3) C_(2)T_(x)-MXene quantum dots(MQDs)with porous Cu nanosheets to design a novel heterostructured MQDs/Cu as an effective and durable NRR catalyst.Impressively,MQDs/Cu showed a synergistically enhanced NRR activity with an NH_(3) yield of 78.5 lg h^(-1) mg^(-1)(-0.5 V)and a Faradaic efficiency of 21.3%(-0.4 V),far superior to pure MQDs and Cu,and outperforming the majority of the state-of-the-art NRR catalysts.Density function theory computations demonstrated that the synergy of MQDs and Cu enabled the creation of interfacial Cu-Ti dimer as dual-active-centers to strongly activate the absorbed N 2 and promote the*N_(2)H formation,consequently resulting in the much reduced energy barriers and greatly enhanced NRR performance.

Single-particle distribution function of a quantum dot system at finite temperature

In the present paper, we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature. Unlike the proof given in our previous work （Phys. Rev. B 74 195414 （2006））, we take a different approach, which does not exploit the explicit expression of the Gibbs distribution function. Instead, we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable. As a result, we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability. Furthermore, the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.

Quantum phase distribution and the number-phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states：solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.

Quantum spin Hall insulators in chemically functionalized As(110)and Sb(110)films

We propose a new type of quantum spin Hall （QSH） insulator in chemically functionalized As （110） and Sb （110） film. According to first-principles calculations, we find that metallic As （110） and Sb （110） films become QSH insulators after being chemically functionalized by hydrogen （H） or halogen （C1 and Br） atoms. The energy gaps of the functionalized films range from 0.121 eV to 0.304 eV, which are sufficiently large for practical applications at room temperature. The energy gaps originate from the spin-orbit coupling （SOC）. The energy gap increases linearly with the increase of the SOC strength λ/λ0. The Z2 invariant and the penetration depth of the edge states are also calculated and studied for the functionalized films.

Quantum-Enhanced Blockchain: A Secure and Practical Blockchain Scheme

The rapid advancement of quantum technology poses significant security risks to blockchain systems.However,quantum technology can also provide solutions for enhancing blockchain security.In this paper,we propose a quantum-enhanced blockchain scheme to achieve a high level of security against quantum computing attacks.We first discuss quantum computing attacks on classic blockchains,including attacks on hash functions,digital signatures,and consensus mechanisms.We then introduce quantum technologies,such as a quantum hash function(QHF),a quantum digital signature(QDS),and proof of authority(PoA)consensus mechanism,into our scheme to improve the security of the blockchain system.Our security analysis demonstrates that our scheme offers superior security against quantum and classic attacks.Finally,we compare our scheme with previous works,showing that our scheme has achieved a perfect balance in terms of practicality,reliability,scalability,and efficiency.Overall,this work contributes to the ongoing research on quantum blockchain in the quantum era.

Platinum quantum dots-decorated MXene-derived titanium dioxide nanowire/Ti_(3)C_(2) heterostructure for use in solar-driven gas-phase carbon dioxide reduction to yield value-added fuels

Solar-driven photocatalytic CO_(2) reduction to produce valuable chemicals and fuels offers an attractive strategy in alleviating the energy crisis.Pt quantum dots(PtQDs)with TiO_(2) nanowire(TiO_(2)NW)/Ti_(3)C_(2) MXene heterostructures(Pt-TiO_(2)NW/Ti_(3)C_(2)) with tight interfacial contacts between the various components were prepared at room temperature via oxidation reactions.The incorporated PtQDs played crucial roles as electron conduction bridges supported by the cocatalyst effect,effectively enhancing the separation efficiencies of photoinduced electron/hole pairs and improving CO_(2) reduction under simulated solar light irradiation.The Pt-TiO_(2)NW/Ti_(3)C_(2) heterostructures exhibited remarkable carbon monoxide(CO)and methane(CH_(4)) production at respective rates of 38.14 and 36.15μmol g^(-1)after 10 h of simulated solar light irradiation,an apparent quantum yield of 1.68%,and 79.2%selectivity for CH4.The photocatalytic activities of the Pt-TiO_(2) NW/Ti_(3)C_(2) heterostructures for CO_(2) reduction were significantly enhanced compared to those of TiO_(2)NW/Ti_(3)C_(2) and the single-component photocatalysts,and they exhibited remarkable stabilities even after five cycles.In addition,the densities of states and electronic characteristics of Ti_(3)C_(2) MXene and Pt-TiO_(2)NW/Ti_(3)C_(2) were studied using density functional theory,and a synergistic mechanism of the improvement in CO_(2) photoreduction is proposed.

Message Authentication with a New Quantum Hash Function

To ensure the security during the communication,we often adopt different ways to encrypt the messages to resist various attacks.However,with the computing power improving,the existing encryption and authentication schemes are being faced with big challenges.We take the message authentication as an example into a careful consideration.Then,we proposed a new message authentication scheme with the Advanced Encryption Standard as the encryption function and the new quantum Hash function as the authentication function.Firstly,the Advanced Encryption Standard algorithm is used to encrypt the result of the initial message cascading the corresponding Hash values,which ensures that the initial message can resist eavesdropping attack.Secondly,utilizing the new quantum Hash function with quantum walks can be much more secure than traditional classical Hash functions with keeping the common properties,such as one-wayness,resisting different collisions and easy implementation.Based on these two points,the message authentication scheme can be much more secure than previous ones.Finally,it is a new way to design the message authentication scheme,which provides a new thought for other researchers in the future.Our works will contribute to the study on the new encryption and authentication functions and the combination of quantum computing with traditional cryptology in the future.

Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters

This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.

The Quantum Mechanics <i>Needs</i>the Principle of Wave-Function Collapse—But This Principle Shouldn’t Be <i>Misunderstood</i>

The postulate of the collapse of the wave-function stands between the microscopic, quantum world, and the macroscopic world. Because of this intermediate position, the collapse process cannot be examined with the formalism of the quantum mechanics (QM), neither with that of classical mechanics. This fact makes some physicists propose interpretations of QM, which avoid this postulate. However, the common procedure used in that is making assumptions incompatible with the QM formalism. The present work discusses the most popular interpretations. It is shown that because of such assumptions those interpretations fail, i.e. predict for some experiments results which differ from the QM predictions. Despite that, special attention is called to a proposal of S. Gao, the only one which addresses and tries to solve an obvious and major contradiction. A couple of theorems are proved for showing that the collapse postulate is necessary in the QM. Although non-explainable with the quantum formalism, this postulate cannot be denied, otherwise one comes to conclusions which disagree with the QM. It is also proved here that the idea of “collapse at a distance” is problematic especially in relativistic cases, and is a misunderstanding. Namely, in an entanglement of two quantum systems, assuming that the measurement of one of the systems (accompanied by collapse of that system on one of its states) collapses the other systems, too without the second system being measured, which leads to a contradiction.