Creation And Annihilation Research Articles

Optimization and Prediction Techniques for Self-Healing and Self-Learning Applications in a Trustworthy Cloud Continuum

The current IT market is more and more dominated by the “cloud continuum”. In the “traditional” cloud, computing resources are typically homogeneous in order to facilitate economies of scale. In contrast, in edge computing, computational resources are widely diverse, commonly with scarce capacities and must be managed very efficiently due to battery constraints or other limitations. A combination of resources and services at the edge (edge computing), in the core (cloud computing), and along the data path (fog computing) is needed through a trusted cloud continuum. This requires novel solutions for the creation, optimization, management, and automatic operation of such infrastructure through new approaches such as infrastructure as code (IaC). In this paper, we analyze how artificial intelligence (AI)-based techniques and tools can enhance the operation of complex applications to support the broad and multi-stage heterogeneity of the infrastructural layer in the “computing continuum” through the enhancement of IaC optimization, IaC self-learning, and IaC self-healing. To this extent, the presented work proposes a set of tools, methods, and techniques for applications’ operators to seamlessly select, combine, configure, and adapt computation resources all along the data path and support the complete service lifecycle covering: (1) optimized distributed application deployment over heterogeneous computing resources; (2) monitoring of execution platforms in real time including continuous control and trust of the infrastructural services; (3) application deployment and adaptation while optimizing the execution; and (4) application self-recovery to avoid compromising situations that may lead to an unexpected failure.

Light absorption by interacting atomic gas in quantum optical regime.

Quantum optical theory of absorption properties of interacting atoms is developed. The concept of local absorptance is introduced as a derivative of the logarithm of intensity with respect to the distance in the vicinity of a given spatial point and a moment of time. The intensity is represented by the quantum and statistically averaged normal product of creation and annihilation operators of the electromagnetic field. The development of an analytical method of the estimation for the kinetic and optical parameters for the system is proposed here. The calculation method of the absorption coefficient includes thermal atomic motion, Doppler effect, and the short-range interaction between atoms. The absorption coefficient explicitly takes into account the quantum nature of the optical field. The ability of the system to absorb or emit quanta is quantitatively expressed through the special form of interaction integrals. The specific form of integrals results from the structure of the quantum brackets. The interplay between the collective (virtual photon exchange) and binary (optically induced inter-particle bonding) processes determines the system behavior. The spectral profile of the local absorption coefficient for different atomic densities and time intervals is simulated for realistic parameters.

P†q: a tool for prototyping many-body methods for quantum chemistry

p q is a C++ accelerated Python library designed to generate equations for many-body quantum chemistry methods and to realise proof-of-concept implementations of these equations for rapid prototyping. Central to this library is a simple interface to define strings of second-quantised creation and annihilation operators and to bring these strings to normal order with respect to either the true vacuum state or the Fermi vacuum. Tensor contractions over fully-contracted strings can then be evaluated using standard Python functions (e.g. NumPy's einsum). Given one- and two-electron integrals, these features allow for the rapid implementation and assessment of a wide array of many-body quantum chemistry methods.

Quantization of fractional harmonic oscillator using creation and annihilation operators

Abstract In this article, the Hamiltonian for the conformable harmonic oscillator used in the previous study [Chung WS, Zare S, Hassanabadi H, Maghsoodi E. The effect of fractional calculus on the formation of quantum-mechanical operators. Math Method Appl Sci. 2020;43(11):6950–67.] is written in terms of fractional operators that we called α \alpha -creation and α \alpha -annihilation operators. It is found that these operators have the following influence on the energy states. For a given order α \alpha , the α \alpha -creation operator promotes the state while the α \alpha -annihilation operator demotes the state. The system is then quantized using these creation and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite functions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting α = 1 \alpha =1 .

Bilinear expansion of Schur functions in Schur Q-functions: A fermionic approach

An identity is derived expressing Schur functions as sums over products of pairs of Schur Q Q -functions, generalizing previously known special cases. This is shown to follow from their representations as vacuum expectation values (VEV’s) of products of either charged or neutral fermionic creation and annihilation operators, Wick’s theorem and a factorization identity for VEV’s of products of two mutually anticommuting sets of neutral fermionic operators.

Statistical parameter estimation of multimode multiphoton-subtracted thermal states of light

Thermal states of light are widely used in quantum optics for various quantum phenomena testing. Particularly, they can be utilized for characterization of photon creation and photon annihilation operations. During the last decade the problem of photon subtraction from multimode quantum states become of much significance. Therefore, in this work we present a technique for statistical parameter estimation of multimode multiphoton subtracted thermal states of light, which can be used for multimode photon annihilation test.

Phase squeezing of quantum hypergraph states

Corresponding to a hypergraph G with d vertices, a quantum hypergraph state is defined by , where f is a d-variable Boolean function depending on the hypergraph G, and denotes a binary vector of length 2 d with 1 at the nth position for n = 0, 1, …(2 d − 1). The nonclassical properties of these states are studied. We consider the annihilation and creation operator on the Hilbert space of dimension 2 d acting on the number states . The Hermitian number and phase operators, in finite dimensions, are constructed. The number-phase uncertainty for these states leads to the idea of phase squeezing. We establish that these states are squeezed in the phase quadrature only and satisfy the Agarwal–Tara criterion for nonclassicality, which only depends on the number of vertices of the hypergraphs. We also point out that coherence is observed in the phase quadrature.

Higher-dimensional open quantum walk in environment of quantum Bernoulli noises

Open quantum walks (OQWs) (also known as open quantum random walks) are quantum analogs of classical Markov chains in probability theory, and have potential application in quantum information and quantum computation. Quantum Bernoulli noises (QBNs) are annihilation and creation operators acting on Bernoulli functionals, and can be used as the environment of an open quantum system. In this paper, by using QBNs as the environment, we introduce an OQW on a general higher-dimensional integer lattice. We obtain a quantum channel representation of the walk, which shows that the walk is indeed an OQW. We prove that all the states of the walk are separable provided its initial state is separable. We also prove that, for some initial states, the walk has a limit probability distribution of higher-dimensional Gauss type. Finally, we show links between the walk and a unitary quantum walk recently introduced in terms of QBNs.

Quantum spatial dynamics of high-gain parametric down-conversion accompanied by cascaded up-conversion

Quantum cascaded up-conversion (CUpC) of parametric down conversion (PDC) in a finite nonlinear ${\ensuremath{\chi}}^{(2)}$ crystal is studied theoretically within parametric approximation. The exact solution for creation and annihilation operators presented in the form of Bogoliubov transformation is valid for the high-gain regime and explicitly includes the nonzero wave-vector mismatch both for PDC and CUpC. Characteristic equation is used to analyze parametric amplification and oscillating regimes for degenerate, three- and four-mode cases. We show that the parametric amplification exists under the fulfillment of the cascaded phase-matching conditions while both the PDC and CUpC processes are separately non-phase-matched. The influence of CUpC on quadrature squeezing of degenerate PDC is estimated.

Accelerated impurity solver for DMFT and its diagrammatic extensions

We present ComCTQMC, a GPU accelerated quantum impurity solver. It uses the continuous-time quantum Monte Carlo (CTQMC) algorithm wherein the partition function is expanded in terms of the hybridisation function (CT-HYB). ComCTQMC supports both partition and worm-space measurements, and it uses improved estimators and the reduced density matrix to improve observable measurements whenever possible. ComCTQMC efficiently measures all one and two-particle Green's functions, all static observables which commute with the local Hamiltonian, and the occupation of each impurity orbital. ComCTQMC can solve complex-valued impurities with crystal fields that are hybridized to both fermionic and bosonic baths. Most importantly, ComCTQMC utilizes graphical processing units (GPUs), if available, to dramatically accelerate the CTQMC algorithm when the Hilbert space is sufficiently large. We demonstrate acceleration by a factor of over 600 (100) in a simulation of δ-Pu at 600 K with (without) crystal fields. In easier problems, the GPU offers less impressive acceleration or even decelerates the CTQMC. Here we describe the theory, algorithms, and structure used by ComCTQMC in order to achieve this set of features and level of acceleration. Program summaryProgram Title: ComCTQMCCPC Library link to program files:https://doi.org/10.17632/x2gzgm8njh.1Licensing provisions: GPLv3Programming language: C++/CUDANature of problem: In dynamical mean-field theory (DMFT), the computational bottleneck is the repeated solution of a quantum impurity problem [1]. The continuous-time quantum Monte-Carlo (CTQMC) algorithm has emerged as one of the most efficient methods for solving multiorbital impurity problems at moderate-to-high temperatures [2]. However, the low-temperature regime remains inaccessible, particularly for f-shell systems, and the measurement of two-particle correlation functions on an impurity adds a substantial computational burden. The bottleneck of the CTQMC solver is itself the computation of the local trace which includes the multiplication of many moderate-to-large sized matrices. The efficient solution of the impurity, measurement of the two-particle correlation functions, and acceleration of the trace computation are therefore critical.Solution method: ComCTQMC uses the hybridisation expansion of the impurity action to explore partition space [3]. It uses the worm algorithm [4] to explore the union of the partition space with observables spaces, e.g., the two-particle correlation functions. It uses improved estimators to more accurately measure the one- and two-particle Green's functions [5]. Identical impurities are solved across all MPI ranks (for ideal weak scaling) and the trace computations of these impurities are distributed to and accelerated by GPUs (when available). The lazy-trace algorithm [6] is used to further reduce the burden of the local trace calculation.Additional comments including restrictions and unusual features: ComCTQMC solves nearly arbitrary impurities, including those with complex valued and time-dependent interactions. However, there are two restrictions: (1) The retarded part of the interaction is described by a set of bilinears (a paired creation and annihilation operator), and these bilinears must commute with the local Hamiltonian and have real quantum numbers; (2) If a local Green's function vanishes, then the corresponding hybridisation function also vanishes.

Locally acting mirror Hamiltonians

Photons, i.e. the basic energy quanta of monochromatic waves, are highly non-localized and occupy all available space in one dimension. This non-local property can complicate the modelling of the quantized electromagnetic field in the presence of optical elements that are local objects. Therefore, in this paper, we take an alternative approach and quantize the electromagnetic field in position space. Taking into account the negative- and the positive-frequency solutions of Maxwell's equations, we construct annihilation operators for highly localized field excitations with bosonic commutator relations. These provide natural building blocks of wave packets of light and enable us to construct locally acting interaction Hamiltonians for two-sided semi-transparent mirrors.

Boundary and Rigidity of Nonsingular Bernoulli Actions

Let $ G $ be a countable discrete group and consider a nonsingular Bernoulli shift action $ G \curvearrowright \prod_{g\in G }(\{0,1\},\mu_g)$ with two base points. When $ G $ is exact, under a certain finiteness assumption on the measures $\{\mu_g\}_{g\in G }$, we construct a boundary for the Bernoulli crossed product C$^*$-algebra that admits some commutativity and amenability in the sense of Ozawa's bi-exactness. As a consequence, we obtain that any such Bernoulli action is solid. This generalizes solidity of measure preserving Bernoulli actions by Ozawa and Chifan--Ioana, and is the first rigidity result in the non measure preserving case. For the proof, we use anti-symmetric Fock spaces and left creation operators to construct the boundary and therefore the assumption of having two base points is crucial.

Importance of meson-meson and of diquark-antidiquark creation operators for a b¯b¯ud tetraquark

In recent years, the existence of a hadronically stable $\bar{b} \bar{b} u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$ was confirmed by first principles lattice QCD computations. In this work we use lattice QCD to compare two frequently discussed competing structures for this tetraquark by considering meson-meson as well as diquark-antidiquark creation operators. We use the static-light approximation, where the two $\bar{b}$ quarks are assumed to be infinitely heavy with frozen positions, while the light $u$ and $d$ quarks are fully relativistic. By minimizing effective energies and by solving generalized eigenvalue problems we determine the importance of the meson-meson and the diquark-antidiquark creation operators with respect to the ground state. It turns out, that the diquark-antidiquark structure dominates for $\bar{b} \bar{b}$ separations $r < 0.25 \, \text{fm}$, whereas it becomes increasingly more irrelevant for larger separations, where the $I(J^P) = 0(1^+)$ tetraquark is mostly a meson-meson state. We also estimate the meson-meson to diquark-antidiquark ratio of this tetraquark and find around $60\% / 40\%$.

Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundary

We present a comprehensive treatment of the non-periodic trigonometric sℓ(2) Gaudin model with triangular boundary, with an emphasis on specific freedom found in the local realization of the generators, as well as in the creation operators used in the algebraic Bethe ansatz. First, we give Bethe vectors of the non-periodic trigonometric sℓ(2) Gaudin model both through a recurrence relation and in a closed form. Next, the off-shell action of the generating function of the trigonometric Gaudin Hamiltonians with general boundary terms on an arbitrary Bethe vector is shown, together with the corresponding proof based on mathematical induction. The action of the Gaudin Hamiltonians is given explicitly. Furthermore, by careful choice of the arbitrary functions appearing in our more general formulation, we additionally obtain: i) the solutions to the Knizhnik-Zamolodchikov equations (each corresponding to one of the Bethe states); ii) compact formulas for the on-shell norms of Bethe states; and iii) closed-form expressions for the off-shell scalar products of Bethe states.

On an alternative quantization of R-NS strings

We investigate an alternative quantization of R-NS string theory. In the alternative quantization, we define the distinct vacuum for the left-moving mode and the right-moving mode by exchanging the role of creation operators and annihilation operators in the left-moving sector. The resulting string theory has only a finite number of propagating degrees of freedom. We show that an appropriate choice of the GSO projection makes the theory tachyon free. The spectrum coincides with the massless sector of type IIA or type IIB superstring theory without any massive excitations.

Sub-bosonic (deformed) ladder operators

The canonical operator \({\hat{a}}^{\dagger }\) (\({\hat{a}}\)) represents the ideal process of adding (subtracting) an exact amount of energy E to (from) a physical system in both elementary quantum mechanics and quantum field theory. This is a “sharp” notion in the sense that no variability around E is possible at the operator level. In this work, we present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.

Hamiltonian matrix representation of harmonic oscillator system with Linear-Cubic-Quartic (LCQ) perturbation

In this paper, we analyze the matrix representation of the energy operator (Hamiltonian) of the harmonic oscillator system when this system is perturbed by an LCQ perturbation. The LCQ perturbation is simultaneously acted on this system, so the total Hamiltonian is a summation of the pure oscillator harmonic operator term (in the annihilation and creation operator statement) and the three perturbation terms. In this work, we use three different small parameters for each term of the perturbation for keeping the generality. We use the simple algebraic method by using the Dirac notation and the well-known base vector of harmonic oscillator to analyze this problem. Next, we present every term of this operator in matrix representation and then adding them for finding matrix representation for the total Hamiltonian.

Rotational bands beyond the Elliott model

Rotational bands are commonplace in the spectra of atomic nuclei. Inspired by early descriptions of these bands by quadrupole deformations of a liquid drop, Elliott constructed discrete nucleon representations of SU(3) from fermionic creation and annihilation operators. Ever since, Elliott’s model has been foundational to descriptions of rotation in nuclei. Later work, however, suggested the symplectic extension Sp(3, R) provides a more unified picture. We decompose no-core shell-model nuclear wave functions into symmetry-defined subspaces for several beryllium isotopes, as well as 20Ne, using the quadratic Casimirs of both Elliott’s SU(3) and Sp(3, R). The band structure, delineated by strong B(E2) values, has a more consistent description in Sp(3, R) rather than SU(3). In particular, we confirm previous work finding in some nuclides strongly connected upper and lower bands with the same underlying symplectic structure.

Translational symmetries of quadratic Lagrangians

In this paper, we show that a quadratic Lagrangian, with no constraints, containing ordinary time derivatives up to the order [Formula: see text] of [Formula: see text] dynamical variables, has [Formula: see text] symmetries consisting in the translation of the variables with solutions of the equations of motion. We construct explicitly the generators of these transformations and prove that they satisfy the Heisenberg algebra. We also analyze other specific cases which are not included in our previous statement: the Klein–Gordon Lagrangian, [Formula: see text] Fermi oscillators and the Dirac Lagrangian. In the first case, the system is described by an equation involving partial derivatives, the second case is described by Grassmann variables and the third shows both features. Furthermore, the Fermi oscillator and the Dirac field Lagrangians lead to second class constraints. We prove that also in these last two cases there are translational symmetries and we construct the algebra of the generators. For the Klein–Gordon case we find a continuum version of the Heisenberg algebra, whereas in the other cases, the Grassmann generators satisfy, after quantization, the algebra of the Fermi creation and annihilation operators.

Electric–magnetic duality as a quantum operator and more symmetries of U(1) gauge theory

We promote the Noether charge of the electric-magnetic duality symmetry of $U(1)$ gauge theory, "$G$" to a quantum operator. We construct ladder operators, $D_{(\pm)a}^\dagger(k)$ and $D_{(\pm)a}(k)$ which create and annihilate the simultaneous quantum eigen states of the quantum Hamiltonian(or number) and the electric-magnetic duality operators respectively. Therefore all the quantum states of the $U(1)$ gauge fields can be expressed by a form of $|E,g\rangle$, where $E$ is the energy of the state, the $g$ is the eigen value of the quantum operator $G$, where the $g$ is quantized in the unit of 1. We also show that 10 independent bilinears comprised of the creation and annihilation operators can form $SO(2,3)$ which is as demonstrated in the Dirac's paper published in 1962. The number operator and the electric-magnetic duality operator are the members of the $SO(2,3)$ generators. We note that there are two more generators which commute with the number operator(or Hamiltonian). We prove that these generators are indeed symmetries of the $U(1)$ gauge field theory action.