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At present, there are many methods of quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of the Schrodinger equation. There is a need for new methods for obtaining quantum-entangled particles and mathemat...
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We investigate a spin-1/2 Ising-XYZ diamond chain with Ising-like interaction between nodal and interstitial sites and Heisenberg-like interaction between interstitial sites, subjected to an external magnetic field applied along the $z$-direction. This model presents exact analytical solution and can be solved using the transfer matrix technique. H...
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... The Schmidt decomposition is a convenient mathematical tool for measuring the nature of quantum entanglement (Ekert & Knight, 1995). One can use the value of the Schmidt modes to calculate the measure of the quantum entanglement of the system (Makarov, 2018b). ...
We wrote this paper to study in detail the mathematical methods used in deriving the parameters 𝑝𝑝′1, 𝑝𝑝′2, 𝑥𝑥′1, 𝑥𝑥′2, 𝑀𝑀, 𝐾𝐾 and 𝑒𝑒2𝜂𝜂 in the research papers by Han et al. (1999), Makarov (2018a), Han et al. (1993), and Han et al. (1995) to find the Schmidt modes 𝛬𝛬𝑘𝑘 in quantum entanglement. Here, we have analysed and developed a thorough calculation in exploring the rationales behind the existence of these parameters in two and three-coupled harmonic oscillators. Various mathematical approaches were applied in the study, ranging from polynomials and linear algebra to trigonometry and the Pythagorean theorem. We found the parameters 𝐾𝐾 and 𝑒𝑒2𝜂𝜂 using the matrices’ determinants and eigenvalues. With these rationales in deriving the parameters 𝐾𝐾 and 𝑒𝑒2𝜂𝜂 in the research papers for the two-coupled harmonic oscillators, we have formulated similar parameters for three-coupled harmonic oscillators as the conclusion of our study.
... File S1: Quantum theory of scattering of nonclassical fields by free electrons. References [7,[15][16][17][18][23][24][25][26][27] are cited in the Supplementary Materials. ...
At present, there is no non-perturbative theory of scattering of nonclassical electromagnetic waves by free electrons that describes the scattering process completely with the help of quantum physics. In this paper, such a theory is presented, which takes into account the statistics and the number of scattered photons. This theory is completely analytical for an arbitrary number of electrons in the system and, in a particular case, is equivalent to the previous theory of scattering as the number of incident photons tends to infinity. It is shown that this theory can differ greatly from the previously known theory of Thomson scattering in the non-perturbative case and at relatively small numbers of incident photons. In addition, this theory is applicable to the scattering of ultrashort pulses by free electrons.
... In this frequency distribution pattern decoherent wave frequencies could not be established , probably, since the particular scientists only reported positive effects on degree of entanglement. Recently, the influence of electromagnetic fields on quantum entanglement of harmonic oscillator was demonstrated (Makarov, 2018). ...
This study was initiated to establish whether spatio-spectral Eigen-modes of EEG brain waves can be described by an Acoustic Quantum Code of Resonant Coherence, as found by us earlier in a spectrum of animate and inanimate systems. Presently available EEG-and MEG recordings were analyzed as to their peak frequencies in relation to our Quantum Code coherence values. Both the EEG-and MEG studies of healthy persons exhibited quantum coherence of EEG peaks with mean quantum coherence of 0.95 (an average of 90-100% showed coherent peak values), while in patient groups with various mental disorders, a significant decrease of coherence correlation was found. ADHD subjects show a moderate change in peak coherence, being in the range of 1.0 to 0.83, while during epileptic seizures the degree of peak coherence is reduced to a range of 0.94 to 0.75. Depressed patients have EEG peaks with a consistently lower coherence values than healthy persons: 0.77-0.88, while autistic persons show an even lower coherence of 0.50 till 0.75. Patients with severe psychiatric disorders, such as depression, show a coherence of only 0.49-0.61. The importance of EEG brain coherence for conscious states was demonstrated in patients under anaesthesia that exhibited a very low coherence level of about 0.25. The graded loss of brain EEG coherence combined with alterations in Phi based EEG wave separation, can therefore be of value for differentiation in severity and nature of neurological disorders. The value of our frequency algorithm was also shown for trans-cranial therapy: the presently chosen frequencies of rTMS therapy in clinical practice correspond very well with the values of our algorithm. Of interest, the Acoustic Quantum Code pattern was also shown to describe neuronal microtubular (MT) wave frequencies, as measured in vitro by others. MT oscillations were claimed by Hameroff and Penrose to be instrumental in the creation of brain consciousness through alignment with gravity fluctuation at the Planck scale. Our results on brain EEG coherence are therefore discussed in relation to the current models for understanding the nature of (self)-consciousness. We regard the potential relation between neuronal coherence/decoherence balance and conscious states as a central mechanism for producing quantum entanglement in the brain as related to long-distance neuro-communication and brain binding. As postulated earlier, consciousness can be modelled by a 5D brain-associated, toroidal workspace, that provides quality control and monitoring of integral brain function, according to holographic principles and was earlier framed as the "Event Horizon Brain". Consciousness, in this concept, requires photon/phonon mediated and resonant communication with this field-receptive holographic workspace, seen as associated with but not reducible to the human brain. The related brain supervening role of the event horizon workspace requires the collective conscious and unconscious states and realizes a total holographic modality of consciousness that enables effective predictive coding. This 5D, scale invariant, memory workspace, therefore, can be instrumental in the manifestation of Psi phenomena and experiences of cosmic consciousness. At the sub-atomic level, gravity guided quantum tunnelling and coherence of micro-tubular oscillations may produce neuronal entanglement. The latter represents a dominant factor in long distance neural information transfer and functional brain binding. The resulting synchronization of neural network frequencies is likely reflected in the abovementioned brain coherency of EEG peaks, as well as in various mental states that promote feelings of mental wholeness in meditation and psycho-mimetic drug therapy. 2
... We specify a harmonic oscillator in interaction with a single-mode electromagnetic field and the transmission of an entangled photon. The system is solved exactly as two harmonic oscillators in [16]. The time dependence of the system is linked to its interaction, namely the atomic system (harmonic oscillator behaves as an electron in an atom) by changing the direction of its magnetic field, because a magnetic field has an undetermined duration. ...
... , and the system of linear equations, [16,20] ...
We exploit the dynamics of entangled system between a harmonic oscillator and a single mode electromagnetic field as two harmonic oscillators, to examine quantum entanglement in coherent states. Through the Schrödinger cat state, we compute analytically its distribution function. Then, we check graphically the evolution of entanglement and the distribution function for two particular cases: the first is defined by two harmonic oscillators in quantum motion in a Paul trap; here whatever the quantum state, the system is at most entangled. The second case is visualised by two harmonic oscillators with a perturbative force, in that case, by varying the displacement numbers of the coherent states, the quantum entanglement and the distribution function present a similar evolution and they reach very large values. Comparing the two models: in the first, the dynamics of quantum entanglement exhibits a multi-frequency lines behaviour while in the second model, it shows an exponential behaviour.
... This is quite natural because they can be created and assisted via linear optics. Recently, it was shown that the entanglement can be assisted via temperature [5], magnetic field [17] and both [18], but most of works dealt with time independent potential. ...
We investigate the dynamics of entanglement, uncertainty and mixedness by solving time-dependent Schrödinger equation for two-dimensional harmonic oscillator with time-dependent frequency and coupling parameter subject to a static magnetic field. We compute the purities (global/marginal) and then calculate explicitly the linear entropy [Formula: see text] as well as logarithmic negativity [Formula: see text] using the symplectic parametrization of vacuum state. We introduce the spectral decomposition to diagonalize the marginal state and get the expression of von Neumann entropy [Formula: see text] and establish its link with [Formula: see text]. We use the Wigner formalism to derive the Heisenberg uncertainties and show their dependencies on both [Formula: see text] and the coupling parameters [Formula: see text] [Formula: see text] of the quadrature term [Formula: see text]. We graphically study the dynamics of the three features (entanglement, uncertainty, mixedness) and present a similar topology with respect to time. We show the effects of the magnetic field and quenched values of [Formula: see text] and [Formula: see text] on these three dynamics, which lead eventually to control and handle them.
... In Equation (3),Ĥ int is the Hamiltonian responsible for the interaction of bound oscillators with two particles. It should be added that this type of interaction H int is primarily defined in possible application cases [1,19,20], as well as the possibility to further obtain an analytical solution. This type of interaction can be implemented, for example, in a two-port lossy waveguide beam splitter. ...
... Each mode of the electromagnetic field interacts with the environment (Hamiltonian H 2 ) through the electromagnetic interaction H 3 , which leads to an interaction operator with a charged particle in the well-known form (p − e/cA) 2 /(2m), where p is the momentum operator of a particle of mass m and charge e, and A is the electromagnetic field potential vector. In this case, the interaction of two modes with particles of mass m 3 and m 4 will be described by the Hamiltonian equationĤ, similar to References [1,19,20] (of course, considering m 1 and m 2 as just some constants, not masses). ...
... From Equation (19) follows an interesting property: when α = β → 0, it turns out that D i,l = C i,n 0 +m 0 −i n 0 ,m 0 (it turns out that l = m 0 + n 0 − i). As a result, with α = β → 0, it turns out that Ψ = ∑ n 0 +m 0 i=0 C i,n 0 +m 0 −i n 0 ,m 0 |i |n 0 + m 0 − i . ...
The coupled quantum harmonic oscillator is one of the most researched and important model systems in quantum optics and quantum informatics. This system is often investigated for quantum entanglement in the environment. As a result, such studies are complex and can only be carried out using numerical methods that do not reveal the general pattern of such systems. In this work, the external environment is considered to be two independent particles interacting with coupled harmonic oscillators. It is shown that such a system has an exact analytical solution to the dynamic Schrödinger equation. The analysis of this solution is carried out, and the main parameters of this system are revealed. The solutions obtained can be used to study more complex systems and their quantum entanglement.
... From the simulation results, it can be seen that under the condition of internal oil cooling and heat dissipation, the temperature of each part of the motor increases with the increase of rotating speed, which is within the safe operation range, and can ensure the stable operation of the motor. However, the stable temperature of all parts above the rated speed increased significantly, mainly because the iron consumption is proportional to the power of frequency, and the larger the speed is, the greater the iron consumption is [17]. Therefore, long-term high-speed operation should be avoided. ...
Due to the insulation aging, demagnetization and other problems of the permanent magnet and insulating material in the permanent magnet synchronous hub motor under high temperature, the numerical simulation of the heat dissipation of surface mounted permanent magnet synchronous hub motor is proposed. According to the heat transfer of hub motor, the effect degree of heat conduction, heat convection and heat radiation is obtained, the heat transfer coefficient of each part is calculated, and the influence of motor insulation material on temperature rise is analyzed. The experimental results show that the heat dissipation of hub motor under natural cooling condition is poor, and the internal oil cooling method can effectively improve the heat dissipation of hub motor and reduce the temperature difference. When operating at high speed, this reduces the potential safety hazard.
... This type of connection can occur when we consider the interaction of a charged oscillator with a quantized mode of the electromagnetic field, see, e.g., [35,36]. The constant α determines the value of the connection and can be different, depending on the problems under consideration. ...
... Next, we will use the same initial states as above, i.e., |s 1 , s 2 [the system was not connected, i.e., for t = 0 in Eq. (11), the constant α = 0]. In [35], a solution and Schmidt mode of the nonstationary Schrodinger equation with a Hamiltonian (11) ...
Quantum entanglement of a system of two coupled quantum harmonic oscillators with a Hamiltonian Ĥ=121m1p̂12+1m2p̂22+Ax12+Bx22+Cx1x2 can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. Despite this, the quantum entanglement of such a system is still a problem under study. This is primarily due to the fact that the system is multiparametric and the quantum entanglement of such a system is not defined in a simple analytical form. This paper solves this problem and shows that quantum entanglement depends on only one parameter that has a simple physical meaning: the reflection coefficient R∈(0,1). The reflection coefficient R has a simple analytical form and includes all the parameters of the system under consideration. It is shown that for certain values of the coefficient R, the quantum entanglement can be large. The developed theory can be used not only for calculating quantum entanglement, but also for many other applications in physics, chemistry, and biophysics, where coupled harmonic oscillators are considered.
... It should be added that the dipole approximation gives correct results at photon wavelengths ≫ 1 i.e. much larger than atomic sizes. Furthermore Eq. (2) is more convenient to consider in the form of a differential equation (which was the approach taken in [21][22][23], going from the operators â = 1 ...
Hong-Ou-Mandel (HOM) effect is known to be one of the main phenomena in quantum optics. It is believed that the effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the photons are identical, they will extinguish each other. In this work, it is shown that these fundamental provisions of the HOM interference may not always be fulfilled. One of the main elements of the HOM interferometer is the beam splitter, which has its own coefficients of reflection R=1/2 and transmission T=1/2. Here we consider the general mechanism of the interaction of two photons in a beam splitter, which shows that in the HOM theory of the effect it is necessary to know (including when planning the experiment) not only R=1/2 and T=1/2, but also their root-mean-square fluctuations ΔR2,ΔT2, which arise due to the dependence of R=R(ω1,ω2) and T=T(ω1,ω2) on the frequencies where ω1,ω2 are the frequencies of the first and second photons, respectively. Under certain conditions, specifically when the dependence of the fluctuations ΔR2 and ΔT2 can be neglected and R=T=1/2 is chosen, the developed theory coincides with previously known results.
... Using BS in the form of a coupled waveguide proved to be very convenient, since such BSs are small in size and have many other technical advantages [12]. As a result, such BSs are used widely in quantum technologies (e.g., [15][16][17]). Despite this, there is an unsolved problem of finding the coefficients R, T and the phase shift φ, in the general case, i.e., when photons can be different and not monochromatic. ...
... (Further, the atomic system of units to be used is: = 1; |e | = 1; m e = 1). Equation (2) is more convenient to consider in the form of a differential equation (which was the approach taken in [17,18]), going from the operatorsâ = 1 √ 2 (q + ∂ ∂q ),â + = 1 √ 2 (q − ∂ ∂q ) to the electromagnetic field variables q [6,7]. As a result, the Hamiltonian of Eq. (2) iŝ ...
It is well known that the Hong–Ou–Mandel (HOM) effect can be realized on beam splitters (BSs) in the form of coupled waveguides. It is believed that in this case, the theory is similar to HOM interference on conventional BSs. In this work, it is shown that if a BS is used in the form of a coupled waveguide, the theory of HOM interference can differ significantly from the known one. It is shown that even in the case of completely identical photons, the visibility of ${\cal V}$ V can essentially differ from unity. The developed theory must be taken into account in quantum optical schemes, where BSs are represented mainly as coupled waveguides.
