Creation And Annihilation Research Articles

Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy

Not all complete set of spinors can be used as expansion coefficients of a quantum field. In fact, Steven Weinberg established the uniqueness of Dirac spinors for this purpose provided: (a) one paid due attention to the multiplicative phases for each of the spinors, and (b) one paired these to creation and annihilation operators in a specific manner. This is implicit in his implementation of the rotational symmetry for the spin half quantum field. Among the numerous complete set of spinors that are available to a physicist, Elko occupies a unique status that allows it to enter as expansion coefficients of a quantum field without violating Weinberg’s no go theorem. How this paradigm changing claim arises is the primary subject of this communication. Weinberg’s no go theorem is evaded by exploiting a uniquely special feature of Elko that allows us to introduce a doubling of the particle-antiparticle degrees of freedom from four to eight. Weinberg had dismissed this degeneracy on the ground that, “no examples are known of particles that furnish unconventional representations of inversions.” Here we will find that this degeneracy, once envisioned by Eugene Wigner, in fact gives rise to a quantum field that has all the theoretical properties required of dark matter.

Distinguishing pure and thermal states by Landauer’s principle in open systems

Starting from Polchinski’s thought experiment on how to distinguish between pure and thermal states, we construct a specific system to study the interaction between qubit and cavity quantum field theory (QFT) in order to provide a more operational point of view. Without imposing any restrictions on the initial states of qubit and cavity QFT, we compute the evolution of the system order by order by the perturbation method. We choose Landauer’s principle, an important bound in quantum computation and quantum measurement, as the basis for the determination of the thermal state. By backtracking the initial state form, we obtain the conditions that must be satisfied by the cavity QFT: the expectation value of the annihilation operator should be zero, and the expectation value of the particle number operator should satisfy the Bose–Einstein distribution. We also discuss the difference between the thermal state and a possible alternative to the thermal state: the canonical thermal pure quantum (CTPQ) state.

Non-Gaussian feature of the output field from a double qubit-cavity ultrastrong coupling system

Abstract We investigate the non-Gaussian feature of radiation in a circuit QED system where two qubits are strongly coupled to a single-mode cavity. In the regime of ultrastrong coupling (USC), the rotating-wave approximation is not valid, and the Rabi Hamiltonian contains counter-rotating wave terms, leading to level crossing and avoided crossings in the energy spectrum. We further analyze the intensity-amplitude correlation of the output field in these two novel scenarios. In the USC regime, the creation and annihilation operators in the correlation function are replaced, allowing for the identification of non-Gaussian features in the output field. Our findings reveal that despite the absence of squeezing effects in the output light, significant non-Gaussian characteristics are present. Additionally, we demonstrate that as the driving or coupling strength increases, the non-Gaussian features of the output field become more pronounced. This suggests that USC systems hold broad potential applications in the realms of nonlinear optics and the generation of non-Gaussian states.

The Effect of Innovation on the Performance of SMEs in Zimbabwe: A Case Study of Manufacturing Companies in Harare

Technological Innovation has become an indispensable tool for organizations to gain competitive advantage, increase performance, venture into new markets and survive in such a competitive atmosphere. A plethora of research has found that technological innovation is a critical factor that improves organizational performance. The study focused on investigating the effects of technological innovation on the performance of SMEs in the manufacturing industry. The study objectives were to establish the factors that influence technological innovativeness among manufacturing SMEs in Zimbabwe, determine the effect of product innovation on the performance of manufacturing SMEs, to ascertain the effect of process innovation on the performance of manufacturing SMEs in Zimbabwe and to establish the challenges faced by SMEs in the manufacturing sector adopting technological innovation in Zimbabwe. A quantitative research approach was adopted. The researcher used simple random sampling in this study and every member in the sample size has an equal opportunity to be selected. A total sample size of 66 respondents was selected randomly. A structured questionnaire was distributed to respondents and the response rate was approximately 76%. Data was processed on excel which was later uploaded on the SPSS and SmartPLS version 3.2.1 softwares. Cronbach Alpha of 0.886 was obtained and this indicated the strong reliability and validity of the study results. Composite and Average variance extracted was also used to assessed the validity of the study. It was discovered that experienced human capital, leadership, access to funding, competition, and organisation mission and culture are important in influencing innovation in SMEs. In addition, the study revealed that product and process innovation had an impact on manufacturing SMEs’ organizational performance that was statistically significant. It emerged that product and process innovation improves a number of financial performance indicators for a business, including sales growth, market expansion, rising customer happiness, and rising profit margins. Therefore, in line with the findings, the study recommends that the government must develop and implement a wide range of innovation policies that encourage best practices and support company growth and should support the creation and ongoing operation of innovative businesses through partnerships. Future studies should expand the study’s scope and sample size and other factors related to product and process innovations. In addition, future research has to take into account the creation of national and regional government policies that encourage innovation among SMEs.

Covariance-analytic performance criteria, Hardy-Schatten norms and Wick-like ordering of cascaded systems

This paper is concerned with robust performance analysis of linear stochastic systems acting as an integral operator on a standard Wiener process at the input and producing a stationary Gaussian random process at the output. We propose a performance criterion which uses the trace of an analytic function of the spectral density of the output process. This class of “covariance-analytic” cost functionals includes the usual mean square and risk-sensitive criteria as particular cases. Due to the “cost-shaping” analytic function, the covariance-analytic performance criterion depends on higher-order Hardy-Schatten norms of the system transfer function. We discuss the links of these norms with the asymptotic behaviour of cumulants of finite-horizon quadratic functionals of the system output and their variational properties pertaining to system robustness to statistically uncertain inputs which differ from the standard Wiener process. In the case of strictly proper finite-dimensional systems, governed in state space by linear stochastic differential equations, we develop a method for recursively computing the Hardy-Schatten norms through a recently proposed technique of rearranging cascaded linear systems, which resembles the Wick ordering of mixed products of noncommuting annihilation and creation operators in quantum mechanics. This computational procedure, which is one of the main results of the paper, involves a recurrence sequence of solutions to algebraic Lyapunov equations and represents the covariance-analytic cost as the squared H2-norm of an auxiliary cascaded system. These results are also compared with an alternative approach, which uses higher-order derivatives of stabilising solutions of parameter-dependent algebraic Riccati equations, and illustrated by a numerical example.

More on symmetry resolved operator entanglement

The ‘operator entanglement’ of a quantum operator O is a useful indicator of its complexity, and, in one-dimension, of its approximability by matrix product operators. Here we focus on spin chains with a global U(1) conservation law, and on operators O with a well-defined U(1) charge, for which it is possible to resolve the operator entanglement of O according to the U(1) symmetry. We employ the notion of symmetry resolved operator entanglement (SROE) introduced in Rath et al (2023 PRX Quantum 4 010318) and extend the results of the latter paper in several directions. Using a combination of conformal field theory and of exact analytical and numerical calculations in critical free fermionic chains, we study the SROE of the thermal density matrix ρβ=e−βH and of charged local operators evolving in Heisenberg picture O=eitHOe−itH . Our main results are: i) the SROE of ρβ obeys the operator area law; ii) for free fermions, local operators in Heisenberg picture can have a SROE that grows logarithmically in time or saturates to a constant value; iii) there is equipartition of the entanglement among all the charge sectors except for a pair of fermionic creation and annihilation operators.

Platform labour on the margins and beyond the digital realm: Mapping the landscape of “platform-generated labour” in the digitally mediated short-term rental market.

This paper explores the landscape of labour in the platform economy and, more specifically, the ways local economic activities and actors are exposed to pressures of platformisation, building on the case of the Airbnb platform and the digitally-mediated short-term rental (STR) market in Athens. Conceptualising STR networks as infrastructural assemblages and through a qualitative study building on 27 semi-structured interviews with relevant actors, I focus on: tracing the wide range of workers who undertake essential tasks, the employment statuses, compensations and modes of engagement of workers, restrictions and gender-dimensions, as well as the content and attributes of STR-related work. My main argument is built around the notion of ‘platform worker’ and the need to expand it beyond workers that are directly related to the platforms, in order to include the on-site labour force upon which the creation and everyday operation of broader platform ecosystems and related infrastructure are depended.

Combinatorial aspects of weighted free Poisson random variables

This paper will be devoted to the study of weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will be defined in a sense by the sum of weighted (deformed) free creation, annihilation, scalar, and intermediate operators with certain parameters on a weighted (deformed) free Fock space together with the vacuum expectation. We shall provide a combinatorial moment formula of non-commutative Poisson random variables. This formula gives us a very nice combinatorial interpretation to two parameters of weights. One can see that the deformation treated in this paper interpolates free and boolean Poisson random variables, their distributions and moments, and yields some conditionally free Poisson distribution by taking limit of the parameter.

Generalization of Gisin’s theorem to quantum fields

We generalize Gisin’s theorem on the relation between the entanglement of pure states and Bell non-classicality to the case of mode entanglement of separated groups of modes of quantum fields extending the theorem to cover also states with undefined particle number. We show that any pure state of the field which contains entanglement between two groups of separated modes violates some Clauser–Horne (CH) inequality. In order to construct the observables leading to a violation in the first step, we show an isomorphism between the Fock space built from a single-particle space involving two separated groups of modes and a tensor product of two abstract separable Hilbert spaces spanned by formal monomials of creation operators. In the second step, we perform a Schmidt decomposition of a given entangled state mapped to this tensor product space and then we map back the obtained Schmidt decomposition to the original Fock space of the system under consideration. Such obtained Schmidt decomposition in Fock space allows for construction of observables leading to a violation of the CH inequality. We also show that our generalization of Gisin’s theorem holds for the case of states on non-separable Hilbert spaces, which physically represent states with actually infinite number of particles. Such states emerge, for example, in the discussion of quantum phase transitions. Finally, we discuss the experimental feasibility of constructed Bell test and provide a necessary condition for realizability of this test within the realm of passive linear optics.

Algebraic Solution of the Quantum Harmonic Oscillator

The Wave-particle duality and the Schrodinger cat paradox pose important notions on quantum mechanical systems, in which a quantum system can exist in two physically opposite or distinct states. This motivates scientists from the days of Louis de Broglie to confidently look at matter as having a dual nature, which is a physical particle that can also be visualized as a wave entity. This paper seeks to provide an elegant method of solving the time-independent Schrodinger Equation (TISE) for a quantum simple harmonic oscillator (QSHO). A fully algebraic method is presented, the paper explains in detail how simple algebra, coupled with basic quantum mechanical operator commutation algebra can be employed to solve the TISE without resorting to complicated mathematical methods of solving second-order differential equations. The construction of the Hamiltonian is explained and an analogy between the classical simple harmonic oscillator (CSHO) and the QSHO is drawn to develop the solution method. The action of creation and annihilation operators on wave functions is exploited to generate states with higher and lower energies respectively and to generate a Hamiltonian that can act on a system and generate required quantum states. The aim is to generate the ground state of the QSHO and its associated energy value. From this state, other higher energy states can be generated by the action of the creation operator. The use of algebraic methods has been seen to be versatile as it does not explicitly rely on any particular basis or coordinate system. The method allows operators to be manipulated in different bases for example the momentum operator can be given as P ̂ x=-iℏ (∂/∂x) in a spatial coordinate basis or as a pure number p ̂ =p in the momentum basis.

Polar coherent states in bilayer graphene under a constant uniform magnetic field

In this work, the interaction of the electrons in bilayer graphene with a constant, homogeneous magnetic field perpendicular to its surface is analyzed. A symmetric gauge is used for the electromagnetic vector potential, which leads to the use of polar coordinates. The symmetries associated with the Hamiltonian that describes this system are applied to explain some fundamental properties, such as the spectrum and the integer pseudo-spin character of the eigenfunctions. The current densities associated with the bilayer Hamiltonian have been calculated in both Cartesian and polar coordinates showing that they are gauge invariant. Additionally, the appropriate coherent states of this system have been derived as eigenstates of a suitable annihilation operator with complex eigenvalues. The local current densities of these coherent states have been calculated, revealing a type of radial component interference effect that has been overlooked until now. Some of these newly presented results are illustrated graphically.

Numerical quantization of interfering photons using liquid crystal retarder

Numerical quantization of interfering small photons using a liquid crystal (LC) retarder is investigated. A beam splitter can be considered a four-port device with the input-output relations in the Heisenberg picture using the creation and annihilation operator. We introduce the phase shift in one of the annihilation operators using the LC device, where, the amplitude of these operations is ultimately reduced. The alignment of an LC director is homogeneous and the director profile is calculated by solving the Euler–Lagrange equation. A total number of retardations can be calculated using the effective refractive index of the LC molecule integrating through cell thickness direction. As a result, a detail of the quantization operation is clarified.

ALGORITHMS FOR OBTAINING A RESIDENCE PERMIT AND PURCHASING REAL ESTATE FOR UKRAINIANS UNDER SPECIAL MARTIAL LAW CONDITIONS

Approximately a quarter of the surveyed Ukrainian refugees and IDPs said that they plan to stay in their new places of residence, in the countries of their choice, obtain a residence permit, and purchase real estate. The legislation of Ukraine, like that of other countries, provides that ownership and other real rights to real estate, encumbrances, as well as their creation, transfer and termination, are subject to state registration. Rights to real estate subject to state registration arise from the moment of such registration. In essence, state registration is the fact of public recognition by the state of a person's right to real estate by entering information about it into the State Register of Real Property Rights. However, each country has its own regulatory requirements. Therefore, research into real estate registration procedures and algorithms for obtaining a residence permit is relevant. The study is aimed at identifying the peculiarities and algorithms for obtaining a permanent or temporary residence permit by investing in real estate or business in the country of study. real estate registration for Ukrainian citizens who went abroad during the military operations and intend not to return home but to integrate into other countries. The research objects are 9 countries of the world, namely: Turkey, Greece, Montenegro, the United Kingdom, Cyprus, the United Arab Emirates, the United States, Portugal, and Hungary. These countries are characterized by: attractiveness in terms of residence, democratic development, improvement of the quality of service provision and strengthening of trust in the government by the population, the public and the private sector. The information base of the study was based on collections of scientific papers, periodicals, and Internet resources. Summarizing the results of the study, we have constructed a diagram of the cost of investment real estate for permanent residence for the selected countries. The largest investment is required in the UK, while Montenegro has no requirements for real estate investment at all. 
 It is determined that the procedure for obtaining the right to temporary or permanent residence through investment and registration of real estate may vary, and the package of documents required for registration also differs depending on the specific object and the circumstances of the rights to it. However, there are simple general recommendations that can help protect real estate rights and save time and money: compliance with the country's legislation; creation and proper operation of a unified registration system. This analysis will help to identify ways to implement foreign experience in Ukraine's activities in the future. The practical content is indicated by the target orientation of this study for Ukrainian citizens who are forced to stay abroad, urban planning and cadastre specialists.

Wave function of the sexaquark or compact H-dibaryon

We derive and explicitly display the internal wave function of a color-, flavor- and spin- singlet dibaryon composed of uuddss quarks in a spatially symmetric state, in the approximation of exact SU(3) flavor symmetry. This wavefunction shows that the often-used superposition of ΛΛ, NΞ and ΣΣ baryons, relevant for di-baryon molecules, accounts for only 1/5 of a spatially symmetric six-quark color-flavor-spin-singlet state, with the remaining 4/5 consisting of products of color-octet baryons. Using the correct wavefunction has important implications for calculations of the mass of the lowest-lying flavor-singlet dibaryon, as we illustrate using the Cornell potential. We also provide a compact representation of the state in terms of creation operators, and comment on the impact of not using the optimal operator in lattice studies of this system.

Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States.

The Jordan-Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 su(2)-group states) and even and odd Schrödinger cat states related to the other representation of su(2)-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan-Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the su(2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C2 and C3. Also, their use in quantum information and computing is mentioned.

On infinite symmetry algebras in Yang-Mills theory

Similar to gravity, an infinite tower of symmetries generated by higher-spin charges has been identified in Yang-Mills theory by studying collinear limits or celestial operator products of gluons. This work aims to recover this loop symmetry in terms of charge aspects constructed on the gluonic Fock space. We propose an explicit construction for these higher spin charge aspects as operators which are polynomial in the gluonic annihilation and creation operators. The core of the paper consists of a proof that the charges we propose form a closed loop algebra to quadratic order. This closure involves using the commutator of the cubic order expansion of the charges with the linear (soft) charge. Quite remarkably, this shows that this infinite-dimensional symmetry constrains the non-linear structure of Yang-Mills theory. We provide a similar all spin proof in gravity for the so-called global quadratic (hard) charges which form the loop wedge subalgebra of w1+∞.

Asymmetric particle-antiparticle Dirac equation: second quantization

We build the fully relativistic quantum field theory related to the asymmetric Dirac fields first presented in a prequel to this work. These fields are solutions of the asymmetric Dirac equation, a Lorentz covariant Dirac-like equation whose positive and ‘negative’ frequency plane wave solutions’ dispersion relations are no longer degenerate. At the second quantization level, we show that this implies that particles and antiparticles sharing the same wave number have different energies and momenta. In spite of that, we prove that by properly fixing the values of the relativistic invariants that define the asymmetric Dirac free field Lagrangian density, we can build a consistent, fully relativistic, and renormalizable quantum electrodynamics (QED) that is empirically equivalent to the standard QED. We discuss the reasons and implications of this non-trivial equivalence, exploring qualitatively other scenarios in which the asymmetric Dirac fields may lead to beyond the standard model predictions. We give a complete account of how the asymmetric Dirac fields and the corresponding annihilation and creation operators transform under improper Lorentz transformations (parity and time reversal operations) and under the charge conjugation operation. We also prove that the present theory respects the CPT theorem.

Separation of metric in Wick's theorem.

In quantum chemistry, Wick's theorem is an important tool to reduce products of fermionic creation and annihilation operators. It is especially useful in computations employing reference states. The original theorem has been generalized to tackle multiconfigurational wave functions or nonorthogonal orbitals. One particular issue of the resulting structure is that the metric and density matrices are intertwined despite their different origin. Here, an alternative, rather general tensorial formulation of Wick's theorem is proposed. The main difference is the separation of the metric-the coefficients at normal-ordered operators become products of an n-electron density matrix element and the Pfaffian of a matrix formed by orbital overlaps. Different properties of the formalism are discussed, including the use of density cumulants, the particle-hole symmetry, and applications to transition density matrices, i.e., the case of different bra and ket reference states. The metric-separated version of Wick's theorem provides a platform for the derivation of various quantum chemical methods, especially those complicated by non-trivial reference states and nonorthogonality issues.

Quantum second harmonic generation in terms of elementary processes

We address the quantum dynamics of second harmonic generation with a perturbative approach. By inspecting the Taylor expansion of the unitary evolution, we identify the subsequent application of annihilation and creation operators as elementary processes and find out how the expansion of the second-harmonic photon-number probability distribution can be expressed in terms of the interplay of these processes. We show that overlaps between the output states of different elementary processes contribute to the expansion of the probability distribution and provide a diagrammatic technique to analytically retrieve terms of the distribution expansion at any order.

Quantum Robust Optimal Control for Linear Complex Quantum Systems With Uncertainties

The aim of this note is to study quantum robust optimal control problem for a class of linear quantum systems with uncertainties. It is shown that such problem can be converted into a mixed linear quadratic Gaussian (LQG) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H^{\infty }$</tex-math></inline-formula> quantum control problem. A physical model described by complex quantum stochastic differential equations (CQSDEs) is presented for the quantum system with uncertainties. The quantum system described by CQSDEs is called a complex quantum system in terms of annihilation and creation operators [1]. For an uncertain quantum system, we build a connection with a scaled linear system without uncertainty. The desired quantum robust optimal control results are derived based on the connection. We provide one numerical procedure for quantum robust optimal controller synthesis and then provide an example. The resulting controller presents robustness and optimal performance.