Creation And Annihilation Research Articles

АНАЛІЗ МОЖЛИВОСТЕЙ РЕАЛІЗАЦІЇ МОДУЛЬНОГО ПРИНЦИПУ СТВОРЕННЯ МОДИФІКАЦІЙ ПОВІТРЯНИХ СУДЕН ТА ЇХ ЕФЕКТИВНОЇ ЕКСПЛУАТАЦІЇ В СИСТЕМІ ВІТЧИЗНЯНИХ АВІАПЕРЕВЕЗЕНЬ

It is known that an aircraft generates income for the operating airline only when it is in the air. Being on the ground, at the airport, airlines incur high costs for aerodrome maintenance of the aircraft. The longer the aircraft is stationary on the ground, the shorter the actual flight time of the aircraft. In this regard, the possibility of implementing one of the promising principles for the creation and effective operation of modifications of aircraft of the transport category - the modular principle - has been analyzed. The prospects for the implementation of modular modifications in domestic airlines in the context of further development of the market economy are considered. Modifications based on the implementation of the modular principle are classified into two types - created in the form of autonomous modules placed in the fuselage during aircraft operation and in the form of a removable modular compartment of the aircraft fuselage. A review and analysis of existing projects of these types of modular constructive and technological solutions, a comparison of their advantages and disadvantages in the technical and economic aspects of the prospects for their feasibility are carried out. The possibility of effective implementation of the modular principle of modifications of aircraft of the transport category was assessed, for which a generalized analysis of domestic and foreign information related to the state of the problem under discussion was carried out, on the basis of which an enlarged block diagram of a comprehensive methodology for analyzing the efficiency of operation of modular modifications in the air transportation system was synthesized in comparison with traditional (existing). The key aspects of the content of the main blocks of the scheme are revealed, including the main provisions of the maintenance and repair of aircraft in modern conditions of their operation, based on foreign experience, as well as the main aspects of the content of the blocks for accounting for weight losses in the design and implementation of traditional and modular modifications of aircraft. The generalized information related to the implementation of the synthesized block diagram, focused on subsequent addition, should form the basis of compliance methods and regulatory documentation in the design and implementation of promising domestic modifications of aircraft of the transport category.

Weak- and strong-expansions of coherent states eigenfunctions for the generalized q-deformed harmonic oscillator and their completeness relations

The explicit expressions for generalized q-deformed harmonic oscillator coherent states (q-DHO CS) obtained in terms of a weak- and strong-behavior expansions are investigated. We first employ the weak-deformed version () of q-boson annihilation operator to solve Barut-Girardello’s eigenvalues coherent states equation for generalized q-deformed harmonic oscillator, using for this some lemmas directly related to the resolution of Riccati differential equation. The similarity with the perturbation theory is established. In strong-behavior limit, (), the previous results are resumed using the variational perturbation theory, and the corresponding q-DHO CS are deduced. We also construct, in both limits, their associated completeness relations which turns out to be the elliptic Jacobi -function.

The Generalized Tavis—Cummings Model with Cavity Damping

In this Communication, we consider a generalised Tavis–Cummings model when the damping process is taken into account. We show that the quantum dynamics governed by a non-Hermitian Hamiltonian is exactly solvable using the Quantum Inverse Scattering Method, and the Algebraic Bethe Ansatz. The leakage of photons is described by a Lindblad-type master equation. The non-Hermitian Hamiltonian is diagonalised by state vectors, which are elementary symmetric functions parametrised by the solutions of the Bethe equations. The time evolution of the photon annihilation operator is defined via a corresponding determinant representation.

From Ising Model to Kitaev Chain

In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev's one-dimensional p-wave superconductor, which has its application in fault-tolerant topological quantum computing. Mapping Pauli's spin operators of transverse Ising chain to spinless fermionic creation and annihilation operators by Inverse Jordan-Wigner transformation leads to a Hamiltonian form closely related to Kitaev Chain, which exhibits topological phase transition where phases are characterized by different topological invariant that changes discontinuously at the transition point. Kitaev Chain supports two Majorana zero modes (MZMs) in the non-trivial topological phase, while none is in the trivial phase. The doubly degenerate ground state of the transverse Ising in ferromagnetic phase corresponds to non-local free fermion degree made from MZMs. The quasi-particle excitations of Ising chain, viz., domain wall formation in the ferromagnetic phase and spin-flip in paramagnetic phase maps to Bogoliubon excitations. The mapping suggests that a non-local order parameter can be defined for Kitaev Chain to work with the usual paradigm of Landau's theory.

Multiparticle quantum interference in Bogoliubov bosonic transformations

We explore the multiparticle transition probabilities in Gaussian unitaries effected by a two-mode Bogoliubov bosonic transformation on the mode annihilation and creation operators. We show that the transition probabilities can be characterized by remarkably simple, yet unsuspected recurrence equations involving a linear combination of probabilities. The recurrence exhibits an interferometric suppression term - a negative probability - which generalizes the seminal Hong-Ou-Mandel effect to more than two indistinguishable photons impinging on a beam splitter of rational transmittance. Unexpectedly, interferences thus originate in this description from the cancellation of probabilities instead of amplitudes. Our framework, which builds on the generating function of the non-Gaussian matrix elements of Gaussian unitaries in Fock basis, is illustrated here for the most common passive and active linear coupling between two optical modes driven by a beam splitter or a parametric amplifier. Hence, it also allows us to predict unsuspected multiphoton interference effects in an optical amplifier of rational gain. In particular, we confirm the newly found two-photon interferometric suppression effect in an amplifier of gain 2 originating from timelike indistinguishability (arXiv:2012.15165 [quant-ph]). Overall, going beyond standard two-mode optical components, we expect our method will prove valuable for describing general quantum circuits involving Bogoliubov bosonic transformations.

Quantum groups and polymer quantum mechanics

In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Quantum Gravity, position and momentum operators cannot be both well defined on the Hilbert space [Formula: see text]. It is henceforth deemed impossible to define standard creation and annihilation operators. In this paper, we show that a [Formula: see text]-oscillator structure, and hence [Formula: see text]-deformed creation/annihilation operators, can be naturally defined on [Formula: see text], which is then mapped into the sum of many copies of the [Formula: see text]-oscillator Hilbert space. This shows that the [Formula: see text]-calculus is a natural calculus for Polymer Quantum Mechanics. Moreover, we show that the inequivalence of different superselected sectors of [Formula: see text] is of topological nature.

Calculation of the creation and annihilation operators of a free particle in the light cone coordinate formalism

This work didactically presents the mathematical procedures required for the construction of the creation and annihilation operators for a free quantum particle considering the coordinates of the light cone. For that, the relationships between the aforementioned coordinates and the coordinates (ct, x, y, z) are listed, in addition to the use of the Klein-Gordon-Fock equation in the formalism of the light cone coordinates. Finally, the temporal evolution operator and the quantum operators of creation and annihilation of the integral type of motion are obtained.

Completely positive maps for imprimitive complex reflection groups

In 1994, M. Bożejko and R. Speicher proved the existence of completely positive quasimultiplicative maps from the group algebra of Coxeter groups to the set of bounded operators. They used some of them to define an inner product associated to creation and annihilation operators on a direct sum of Hilbert space tensor powers called full Fock space. Afterwards, A. Mathas and R. Orellana defined in 2008 a length function on imprimitive complex reflection groups that allowed them to introduce an analogue to the descent algebra of Coxeter groups. In this article, we use the length function defined by A. Mathas and R. Orellana to extend the result of M. Bożejko and R. Speicher to imprimitive complex reflection groups, in other words to prove the existence of completely positive quasimultiplicative maps from the group algebra of imprimitive complex reflection groups to the set of bounded operators. Some of those maps are then used to define a more general inner product associated to creation and annihilation operators on the full Fock space. Recall that in quantum mechanics, the state of a physical system is represented by a vector in a Hilbert space, and the creation and annihilation operators act on a Fock state by respectively adding and removing a particle in the ascribed quantum state.

Quantum doubles of Fock type and bosonization

We introduce analogs of creation and annihilation operators, related to involutive and Hecke symmetries R, and perform bosonic and fermionic realization of the modified Reflection Equation algebras in terms of the so-called Quantum Doubles of Fock type. Also, we introduce Quantum Doubles of Fock type, associated with Birman-Murakami-Wenzl symmetries coming from orthogonal or simplectic Quantum Groups and exhibit the algebras obtained by means of the corresponding bosonization (fermionization). Besides, we apply this scheme to current braidings arising from Hecke symmetries R via the Baxterization procedure.

Lower- versus higher-order nonclassicalities for a coherent superposed quantum state

A coherent state is defined conventionally in different ways such as a displaced vacuum state, an eigenket of an annihilation operator, or as an infinite dimensional Poissonian superposition of Fock states. In this work, we describe a superposition ( t a + r a † ) of field annihilation and creation operators acting on a continuous variable coherent state | α ⟩ and specify it by | ψ ⟩ . We analyze the lower- as well as higher-order nonclassical properties of | ψ ⟩ . The comparison is performed by using a set of nonclassicality witnesses (e.g., higher-order photon statistics, higher-order antibunching, higher-order sub-Poissonian statistics, higher-order squeezing, Agarwal–Tara parameter, Klyshko’s condition, and a relatively new concept, matrix of phase-space distribution). It is found that the higher-order criteria are much more efficient to detect the presence of nonclassicality as compared to lower-order conditions except squeezing, where the lower-order one is more competent than its higher-order counterpart.

Quantum fields in the future Rindler wedge

We consider interacting massive scalar quantum field theory in the future Rindler wedge. This is a model example of quantum field theory in curved space--time. On this simple example we show how dynamics of correlation functions depends on the choice of initial Cauchy surface, basis of modes and on the choice of initial state build with the use of the corresponding creation and annihilation operators. We show which choice of modes in the future Rindler wedge respects Poincare symmetry. But we do not restrict our attention only to these modes and the corresponding state.

Structuring tasks of control over driverless vehicles within intelligent transport systems

The relevance of the research topic is defined by the global level of significance of the problem of creation and safe operation of driverless transport on public roads. The research objective was to develop a mathematical model of the problem that allows forming a scientifically grounded strategy for driverless transport progress. The Zwicky Morphological Box method was used as a research method, which allowed building a structured set of intelligent transport system variants. Variables corresponding to the hard-surfaced road types, the level of informational support in the form of digital road models and the level of control tasks with increasing complexity were used as structural variables. A complex of tasks required to control traffic or driving in closed territories, on highways, suburban motorways passing through human settlements, urban streets, and yards has been defined. The control task complexes of each consecutive level include the task complexes of all the previous levels, and the digital road models of a higher level contain the digital models of all the previous levels. The analysis of the obtained results allowed building a trajectory of progressive development of the driverless vehicle focus area within the field of control task levels, road types, and their digital models.

Mean Field Derivation of DNLS from the Bose\u2013Hubbard Model

We prove that the flow of the discrete nonlinear Schrödinger equation (DNLS) is the mean field limit of the quantum dynamics of the Bose–Hubbard model for N interacting particles. In particular, we show that the Wick symbol of the annihilation operators evolved in the Heisenberg picture converges, as N becomes large, to the solution of the DNLS. A quantitative L^p-estimate, for any p ge 1, is obtained with a linear dependence on time due to a Gaussian measure on initial data coherent states.

Missing Understanding of the Phase Factor between Valence-Electron and Hole Operators

This paper provides the long-missing foundation to connect semiconductor and atomic notations and to support results incorrectly obtained by doing as if semiconductor electrons possessed an orbital angular momentum. We here show that the phase factor between valence-electron destruction operator and hole creation operator is the same as the one between particle and antiparticle in quantum relativity, namely $\hat{a}_{m}=(-1)^{j-m} \hat{b}^\dag_{-m}$ provided that $m=(j,j-1\cdots,-j)$ labels the degenerate states of the $(2j+1)$-fold electron level at hand. This result is remarkable because $(i)$ the hole is definitely not a naive antiparticle due to the remaining valence electrons; $(ii)$ unlike atomic electrons in a central potential, semiconductor electrons in a periodic crystal do not have orbital angular momentum $\textbf{L}=\textbf{r}\wedge\textbf{p}$ nor angular momentum $\textbf{J}=\textbf{L}+\textbf{S}$. Consequently, $(j,m)$ for semiconductor electrons merely are convenient notations to label the states of a degenerate level. To illustrate the physical implications, we discuss the interband couplings between photons and semiconductor, in terms of valence electrons and of holes: the phase factor is crucial to establish that bright excitons are in a spin-singlet state.

How squeezed states both maximize and minimize the same notion of quantumness

Beam splitters are routinely used for generating entanglement between modes in the optical and microwave domains, requiring input states that are not convex combinations of coherent states. This leads to the ability to generate entanglement at a beam splitter as a notion of quantumness. A similar, yet distinct, notion of quantumness is the amount of entanglement generated by two-mode squeezers (i.e., four-wave mixers). We show that squeezed-vacuum states, paradoxically, both minimize and maximize these notions of quantumness, with the crucial resolution of the paradox hinging upon the relative phases between the input states and the devices. Our notion of quantumness is intrinsically related to eigenvalue equations involving creation and annihilation operators, governed by a set of inequalities that leads to generalized cat and squeezed-vacuum states.

On the Q operator and the spectrum of the XXZ model at root of unity

The spin-\frac{1}{2}12 Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We construct Baxter’s Q operator at arbitrary anisotropy from a two-parameter transfer matrix associated to a complex-spin auxiliary space. A decomposition of this transfer matrix provides a simple proof of the transfer matrix fusion and Wronskian relations. At root of unity a truncation allows us to construct the Q operator explicitly in terms of finite-dimensional matrices. From its decomposition we derive truncated fusion and Wronskian relations as well as an interpolation-type formula that has been conjectured previously. We elucidate the Fabricius–McCoy (FM) strings and exponential degeneracies in the spectrum of the six-vertex transfer matrix at root of unity. Using a semicyclic auxiliary representation we give a conjecture for creation and annihilation operators of FM strings for all roots of unity. We connect our findings with the `string-charge duality’ in the thermodynamic limit, leading to a conjecture for the imaginary part of the FM string centres with potential applications to out-of-equilibrium physics.

Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer

We present explicit expressions for the central piece of a variational method developed by Shi et al (2018 Ann. Phys. 390 245) which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian states. In particular, we derive iterative analytical expressions for the evaluation of expectation values of products of fermionic creation and annihilation operators in a Grassmann variable-free representation. Using this result we find a closed expression for the energy functional and its gradient of a general fermionic quantum many-body Hamiltonian. We present a simple gradient-descent-based algorithm that can be used as an optimization subroutine in combination with imaginary time evolution, which by construction guarantees a monotonic decrease of the energy in each iteration step. Due to the simplicity of the quantum circuit implementing the variational state ansatz, the results of the algorithms discussed here and in Shi et al’s work could serve as an improved, beyond mean-field initial state in quantum computation.

Quantization of Foster mesoscopic circuit and DC–pumped Josephson parametric amplifier from fractal measure arguments

A quantum theory of the mesoscopic LC-circuit based on the product-like fractal measure which was introduced by Li and Ostoja-Starzewski is proposed. On the basis of the theory, the Schrödinger equation and the energy spectrum for the quantum LC circuit were derived. By introducing special forms of position-dependent LC-electric components, the associated creation and annihilation operators were obtained and analyzed. The quantization of the DC-driven Josephson circuit and its parametric amplifier were studied in details. The main outcome of this study concerns the finite form of the energy expectation value at very high temperature in contrast to the results obtained in literature which is time-dependent. Further details were analyzed and discussed. • The mesoscopic circuit and its quantum structure were explored using the concept of fractal product measure. • The theory is characterized by position-dependent electronic circuit's components. • The quantization of the DC-driven Josephson circuit and its parametric amplifier were constructed. • At very high temperature, a finite value of the energy expectation value was obtained.

Bulk reconstruction and Bogoliubov transformations in AdS2

In the bulk reconstruction program, one constructs boundary representations of bulk fields. We investigate the relation between the global/Poincare and AdS-Rindler representations for AdS2. We obtain the AdS-Rindler smearing function for massive and massless fields and show that the global and AdS-Rindler boundary representations are related by conformal transformations. We also use the boundary representations of creation and annihilation operators to compute the Bogoliubov transformation relating global modes to AdS-Rindler modes for both massive and massless particles.

Mott-insulator-like Bose-Einstein condensation in a tight-binding system of interacting bosons with a flat band

We propose a new class of tight-binding systems of interacting bosons with a flat band, which are exactly solvable in the sense that one can explicitly write down the unique ground state. The ground state is expressed in terms of local creation operators, and apparently resembles that of a Mott insulator. Based on an exact representation in terms of a classical loop-gas model, we conjecture that the ground state may exhibit quasi Bose-Einstein condensation (BEC) or genuine BEC in dimensions two and three or higher, respectively, still keeping Mott insulator-like character. Our Monte Carlo simulation of the loop-gas model strongly supports this conjecture, i.e., the ground state undergoes a Kosterlitz-Thouless transition and exhibits quasi BEC in two dimensions.