Creation-annihilation Operators Research Articles

Squeezing characteristics of cavity field in dynamic Casimir effect

The dynamic Casimir effect refers to the phenomenon of photons generated in a cavity with periodically vibrating wall. The Hamiltonian of the dynamic Casimir effect includes the square term of the photon creation (annihilation) operator, which connects to the squeezing light. Here we discuss in detail the squeezing characteristics of the cavity field in the dynamic Casimir effect. When the cavity wall is driven classically, semi classical theory is adopted; When cavity wall vibration needs to be described by phonons, full quantum theory is used. The squeezing properties of the light field are different according to these two theory. In semi classical theory, the squeezing properties depend on the system parameter |B/A|. When |B/A|>1, the squeezing value changes periodically, and the squeezing weakens as |B/A| increases. When |B/A|<1, it is necessary to use optimized squeezing value to measure squeezing, which shows steady value of −0.25. In full quantum theory, we find that the squeezing of the cavity field weakens as the initial average phonon number decreases. This is because the smaller the average phonon number, the more pronounced the quantum properties of cavity wall vibration. During evolution, phonons and photons become entangled, disrupting the squeezing of the cavity field. The quantum properties of phonons have a negative impact on the squeezing of the light field. We also found that in full quantum theory, the optimized squeezing value should be used to better describe the squeezing, and the maximum squeezing can be achieved by controlling the initial average phonon number of the cavity wall without photon divergence. Most studies focus on resonance frequency, so the innovation points of this paper are of the large detuning frequency.. This work has significance for a deeper understanding of the quantum properties of the cavity field in the dynamic Casimir effect, and helps to generate squeezing microwaves using the parameter dynamic Casimir effect.

Quantum walk of two particles on the graphene structure graph with interaction

In this paper, we discuss the quantum walk of two interacting particles on graphene structure graph. Based on the localized graphene structure graph, we get three cases for the position of the two particles, that is ∂(i, j) = 0, ∂(i, j) = 1, and ∂(i, j) = 2. Subsequently, we investigate the quantum walk of two interacting particles from a new perspective, namely, based on the view of quantum probability, a localized quantum decomposition was used to get the corresponding creation operators and annihilation operators for the first time. Finally, we get the Hamiltonian and the time evolution operator of two interacting particles on the graphene structure graph.

Hidden Tensor Structures.

Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and classical signal analysis. Accordingly, systems as simple as a single one-dimensional harmonic oscillator, an infinite potential well, or a classical finite-amplitude signal of finite duration can be decomposed into an arbitrary number of subsystems. The resulting structure is rich enough to enable quantum computation, violation of Bell's inequalities, and formulation of universal quantum gates. Less standard quantum applications involve a distinction between position and hidden position. The hidden position can be accompanied by a hidden spin, even if the particle is spinless. Hidden degrees of freedom are, in many respects, analogous to modular variables. Moreover, it is shown that these hidden structures are at the roots of some well-known theoretical constructions, such as the Brandt-Greenberg multi-boson representation of creation-annihilation operators, intensively investigated in the context of higher-order or fractional-order squeezing. In the context of classical signal analysis, the discussed structures explain why it is possible to emulate a quantum computer by classical analog circuit devices.

Causal perturbative QFT and white noise

In this paper, we present the Bogoliubov’s causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared — and ultraviolet — divergences in the transition to the adiabatic limit for interacting fields. We present here the analysis of the causal axioms for the scattering operator with the Hida operators as the creation-annihilation operators.

Time-symmetric quantization of relativistic fields. 2. Electroweak theory. Observable effects of TSQ

In the method of time-symmetric quantization (TSQ) of relativistic systems, based on the Stückelberg-Feynman interpretation, the creation-annihilation operators of quanta of complex fields and massless gauge fields, are automatically normally ordered, and there is no vacuum energy and charge (Z. Zakir 2023, article 1). In this second article the application of TSQ to massive bosonic fields of electroweak theory and the observational consequences of TSQ are considered. It is shown that the vacuum of these fields is free of zero-point energy and zero-point charge, and thus a contribution of these fields to the cosmological constant is absent. A direct observational consequence of TSQ is crossing symmetry in particle physics. The observable effects, which were attributed to the zero-point energy of the vacuum, are actually generated by the fields of real charges, and there is no evidence of the existence of zero-point energy of fundamental fields. This fact contradicts the prediction of the standard formulation of quantum field theory, but indirectly confirms TSQ.

FDT for fluctuations of a special perturbated harmonic oscillator and its application in q-deformed Harmonic Oscillator

Abstract In this paper, we will use fluctuation dissipation theorem on the harmonic oscillator with time correlation creation annihilation operator as the perturbated term and through calculation, we find that the exact value of the dissipation associated Imχ of this special perturbation harmonic oscillator is exactly equal to π. Next, we give its potential application in the q-deformed harmonic oscillator, which means connect the q-deformed harmonic oscillator with fluctuation dissipation.

On the electron spin and spectrum energy problems within the Fock many temporal and Feynman proper time paradigms

The quantum electron spin structure and the photon dressed electron energy spectrum problem are reanalyzed in the framework of the Fock many-temporal parameter approach. There is analyzed the spin structure and its dependence on the symmetry properties of the related representations of the basic Clifford algebra, generated by creation-annihilation operators. The self-interaction phenomenon is discussed within the quantum renormalized Lorenz constraint on a suitably reduced Fock space. The electron energy spectrum is analyzed within the many-temporal Fock and Feynman proper time paradigms.

Bogoliubov’s causal perturbative QFT with Hida operators

We will present the axioms of Bogoliubov’s causal perturbative QFT in which the creation-annihilation operators are interpreted as Hida operators. We will shortly present the results that can be achieved in this theory: (1) removal of UV and IR infinity in the scattering operator, (2) existence of the adiabatic limit for interacting fields in QED, (3) proof that charged particles have nonzero mass, (4) existence of infrared and ultraviolet asymptotics for QED.

Bogoliubov’s causal perturbative QED and white noise. Interacting fields

We present Bogoliubov’s causal perturbative QFT with a single refinement: the creation–annihilation operators at a point, i.e., for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared and ultraviolet divergences in the transition to the adiabatic limit for interacting fields. We present the existence proof for the adiabatic limit for interacting fields in causal QED with Hida operators. This limit exists if and only if the normalization in the Epstein–Glaser splitting of the causal distributions, in the construction of the scattering operator, is “natural,”, which eliminates the arbitrariness in choosing the splitting that makes the theory definite, with its predictive power considerably strengthened. We present the example of a charge–mass relation that can be proved within this theory and is confirmed experimentally.

A Poisson algebra on the Hida Test functions and a quantization using the Cuntz algebra

In this note, we define one more way of quantization of classical systems. The quantization we consider is an analogue of classical Jordan–Schwinger map which has been known and used for a long time by physicists. The difference, compared to Jordan–Schwinger map, is that we use generators of Cuntz algebra mathcal {O}_{infty } (i.e. countable family of mutually orthogonal partial isometries of separable Hilbert space) as a “building blocks” instead of creation–annihilation operators. The resulting scheme satisfies properties similar to Van Hove prequantization, i.e. exact conservation of Lie brackets and linearity.

Finite dimensional systems of free fermions and diffusion processes on spin groups

In this article, we are concerned with “finite dimensional fermions,” by which we mean vectors in a finite dimensional complex space embedded in the exterior algebra over itself. These fermions are spinless but possess the characterizing anticommutativity property. We associate invariant complex vector fields on the Lie group Spin(2n + 1) to the fermionic creation and annihilation operators. These vector fields are elements of the complexification of the regular representation of the Lie algebra so(2n+1). As such, they do not satisfy the canonical anticommutation relations; however, once they have been projected onto an appropriate subspace of L2(Spin(2n + 1)), these relations are satisfied. We define a free time evolution of this system of fermions in terms of a symmetric positive-definite quadratic form in the creation–annihilation operators. The realization of fermionic creation and annihilation operators brought by the (invariant) vector fields allows us to interpret this time evolution in terms of a positive self-adjoint operator that is the sum of a second order operator, which generates a stochastic diffusion process, and a first order complex operator, which strongly commutes with the second order operator. A probabilistic interpretation is given in terms of a Feynman–Kac-like formula with respect to the diffusion process associated with the second order operator.

The q-analogue of the Higgs algebra

In this paper, the q-generalization of the Higgs algebra is considered. The realization of this algebra is shown in an explicit form using a nonlinear transformation of the creation-annihilation operators of the q-harmonic oscillator. This transformation is the performance of two operations, namely, a “correction” using a function of the original Hamiltonian, and raising to the fourth power the creation and annihilation operators of a q-harmonic oscillator. The choice of the “correcting” function is justified by the standard form of commutation relations for the operators of the metaplectic realization Uq(SU(1,1)). Further possible directions of research are briefly discussed to summarize the results obtained. The first direction is quite obvious. It is the consideration of the problem when the dimension of the operator space increases or for any value N. The second direction can be associated with the analysis of the relationship between q-generalizations of the Higgs and Hahn algebras.

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.

Comparative analysis of properties for amplified coherent state and amplified squeezed vacuum

Two “amplified” quantum states, that is, amplified coherent state (ACS) and amplified squeezed vacuum (ASV), are considered in this paper by applying operator [Formula: see text] on coherent state (CS) and squeezed vacuum (SV), respectively. Here [Formula: see text] [Formula: see text] denotes a amplification factor and [Formula: see text]) denote the creation (annihilation) operator. Along these two lines, we make a comparative analysis of properties for ACS and ASV. The considered properties include density matrix elements, Wigner function, mean photon number, second-order autocorrelation function, and quadrature squeezing. We derive analytical expressions and make numerical simulations for all the properties. The noteworthy results include: (1) the ACS has antibunching and squeezing characters; (2) the ASV will have the bunching and antibunching effect in small initial squeezing.

Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters

Two approaches to the construction of thermodynamics in the framework of the q- and м-formalisms, which correspond to certain deformations of the algebra of the creation–annihilation operators, have been considered. By comparing the obtained results, an approximate, independent of the space dimension, correspondence was revealed between the second virial coefficients for the ideal q- and м-deformed Bose gases. The corresponding discrepancy arises only at the level of the third virial coefficient. A method for emulating the м-deformed Bose gas up to the third virial coefficient inclusive by means of the two-parametric nonadditive Polychronakos statistics is demonstrated.

Charge Oscillations in a Simple Model of Interacting Magnetic Orbits

Exact eigenstates for a set of two or more interacting electronic orbits in a magnetic field are studied for a class of factorized Hamiltonians with coupled Fermi surfaces. We study the condition for the existence of annihilation-creation operators that allows for the construction of eigenstates. For the case of two interacting cyclotronic orbits, we consider the oscillations of the overlap function and the transfer of charge density between the orbits as function of the inverse field. The expressions of the Fourier frequencies are given in the semiclassical regime and they depend on the geometrical structure of the electronic bands. A generalization of this construction is provided for a chain of several interacting orbits with exact eigenfunctions.

ЗАРЯДОВЫЕ КОЛЕБАНИЯ В ПРОСТОЙ МОДЕЛИ ВЗАИМОДЕЙСТВУЮЩИХ МАГНИТНЫХ ОРБИТ

Exact eigenstates for a set of two or more interacting electronic orbits in a magnetic field are studied for a class of factorized Hamiltonians with coupled Fermi surfaces. We study the condition for the existence of annihilation-creation operators that allows for the construction of eigenstates. For the case of two interacting cyclotronic orbits, we consider the oscillations of the overlap function and the transfer of charge density between the orbits as function of the inverse field. The expressions of the Fourier frequencies are given in the semiclassical regime and they depend on the geometrical structure of the electronic bands. A generalization of this construction is provided for a chain of several interacting orbits with exact eigenfunctions.

Remarks on the mean-field theory based on the SO(2N + 1) Lie algebra of the fermion operators

Toward a unified algebraic theory for mean-field Hamiltonian describing paired- and unpaired-mode effects, in this paper, we propose a generalized Hartree–Bogoliubov mean-field Hamiltonian in terms of fermion pair and creation-annihilation operators of the [Formula: see text] Lie algebra. We diagonalize the generalized Hartree–Bogoliubov mean-field Hamiltonian and throughout its diagonalization we can first obtain the unpaired mode amplitudes which are given by the self-consistent field parameters appeared in the Hartree–Bogoliubov theory together with the additional self-consistent field parameter in the generalized Hartree–Bogoliubov mean-field Hamiltonian and by the parameter specifying the property of the [Formula: see text] group. Consequently, it turns out that the magnitudes of these amplitudes are governed by such parameters. Thus, it becomes possible to make clear a new aspect of such results. We construct the Killing potential in the coset space [Formula: see text] on the Kähler symmetric space which is equivalent to the generalized density matrix. We show another approach to the fermion mean-field Hamiltonian based on such a generalized density matrix. We derive an [Formula: see text] generalized Hartree–Bogoliubov mean-field Hamiltonian operator and a modified Hartree–Bogoliubov eigenvalue equation. We discuss on the mean-field theory related to the algebraic mean-field theory based on the generalized density matrix and the coadjoint orbit leading to the nondegenerate symplectic form.

Bose–Einstein condensation for an exponential density of states function and Lerch zeta function

I show how Bose–Einstein condensation (BEC) in a non interacting bosonic system with exponential density of states function yields to a new class of Lerch zeta functions. By looking on the critical temperature, I suggest that a possible strategy to prove the ”Riemann hypothesis” problem. In a theorem and a lemma I suggested that the classical limit ħ→0 of BEC can be used as a tool to find zeros of real part of the Riemann zeta function with complex argument. It reduces the Riemann hypothesis to a softer form. Furthermore I propose a pair of creation–annihilation operators for BEC phenomena. This set of creation–annihilation operators is defined on a complex Hilbert space. They build a set up to interpret this type of BEC as a creation–annihilation phenomenon for a virtual hypothetical particle.

Excitation and depression of coherent state of the simple harmonic oscillator

Othman and Yevick [Int. J. Theor. Phys. 57, 2293 (2018)] introduced a new class of states defined as “near” coherent states attached to the simple harmonic oscillator. Such states can be expressed as superposition of a standard coherent state and a derivative state, which are neither completely quantum nor completely classical. Here, we introduce photon-added (-depleted) near coherent states [PA(D)NCS] through “m” times application of creation (annihilation) operators â†(â) to the near coherent state. A general analysis of nonclassical properties of the PA(D)NCS, such as sub-Poissonian statistics and squeezing effect, is given analytically and numerically in the context of the conventional quantum optics. We also derive the Wigner distribution function of the PA(D)NCS over phase space which may bear negative values, which is a good indication of their nonclassical properties. Finally, an experimental procedure for generating the PA(D)NCSs is established.