The formation of correlated states and the increase in barrier transparency at a low particle energy in nonstationary systems with damping and fluctuations

We consider peculiarities in the formation of a coherent correlated state (CCS) of a particle in a periodically modulated harmonic oscillator with damping for various types of stochastic perturbation. It is shown that in the absence of stochastic perturbation, an optimal relation exists between the damping parameter (damping coefficient) and the modulation depth, for which the ??extrinsic?? characteristics of the oscillator (amplitudes of ??classical?? oscillation and the momentum of a particle) remain unchanged, while the correlation coefficient rapidly increases from |r| = 0 to |r|_max ?? 1; this corresponds to a completely correlated coherent state. Under nonoptimal conditions, the formation of the CCS with a simultaneous increase in is accompanied by damping or excitation of the oscillator. It is shown that for a certain relation between the damping coefficient and the modulation depth, the presence of a stochastic external force acting on the nonstationary oscillator does not prevent the formation of a CCS with |r|_max ?? 1. A fundamentally different effect is observed under a stochastic influence on the nonstationary frequency of the oscillator; this effect always limits the value of |r| at a level |r|_max < 1; a CCR cannot be formed with an unlimited increase in its intensity, and |r|_max ?? 0. The influence of the CCS formation on the averaged probability ??D?? of the tunnel effect (transparency of the potential barrier) is considered for a particle in an oscillator with damping both in the absence and in the presence of a stochastic force. It is shown using a specific example that complete clearing of the potential barrier and the increase in the barrier transparency from the initial value ??D _r=0?? = 10^?80 to ??D?? ?? 1 can occur over a comparatively short time interval in both these cases. These effects can be used to obtain highly efficient nuclear fusion at a low energy of interacting particles.     

Correlated states and transparency of a barrier for low-energy particles at monotonic deformation of a potential well with dissipation and a stochastic force

The features of the formation of correlated coherent states of a particle in a parabolic potential well at its monotonic deformation (expansion or compression) in finite limits have been considered in the presence of dissipation and a stochastic force. It has been shown that, in both deformation regimes, a correlated coherent state is rapidly formed with a large correlation coefficient |r| → 1, which corresponds at a low energy of the particle to a very significant (by a factor of 10⁵⁰–10¹⁰⁰ or larger) increase in the transparency of the potential barrier at its interaction with atoms (nuclei) forming the “walls” of the potential well or other atoms located in the same well. The efficiency of the formation of correlated coherent states, as well as |r|, increases with an increase in the deformation interval and with a decrease in the deformation time. The presence of the stochastic force acting on the particle can significantly reduce the maximum |r| value and result in the fast relaxation of correlated coherent states with |r| → 0. The effect of dissipation in real systems is weaker than the action of the stochastic force. It has been shown that the formation of correlated coherent states at the fast expansion of the well can underlie the mechanism of nuclear reactions at a low energy, e.g., in microcracks developing in the bulk of metal hydrides loaded with hydrogen or deuterium, as well as in a low-pressure plasma in a variable magnetic field in which the motion of ions is similar to a harmonic oscillator with a variable frequency.     

Anomalies in orientation interaction of slow neutrons with nuclei and the problem of neutron molecule existence

Based on the Dirac equation, the features of long-range electromagnetic orientational interaction of slow neutrons with even-even and even-odd nuclei are considered. This interaction is controlled by a narrow potential barrier arranged beyond the nucleus. The barrier height is U _tot = 20–40 eV and depends on Z, A, and the nucleus magnetic moment μ_nucl. The barrier formation is associated with the ponderomotive nonlinear interaction of the anomalous neutron moment with the nucleus electric field. The barrier transparency for thermal neutrons is D(E) ≈ 0.8–0.95. For cold neutrons, the barrier transparency and their reaction cross sections with nuclei sharply decrease and, at E → 0, their cross sections tend toward zero. It was shown that the combined effect of the magnetic dipole-dipole and ponderomotive interaction of the neutron and even-odd nucleus results in the formation of removed symmetrically positioned potential wells for neutrons beyond the nucleus. The presence of these wells results in the possible existence of short-lived or virtual nucleus-neutron molecules and the “neutron halo” effect beyond the nucleus.     

Correlated states of interacting particles and problems of the Coulomb barrier transparency at low energies in nonstationary systems

Premises for the formation of a correlated coherent state of particles in nonstationary quantum systems are considered. The relation between the correlation factor of particles and the probability of their passage through the potential barrier (including that in nuclear reactions) is analyzed. The optimal regime for parametric excitation of a harmonic oscillator is found, in which the asymptotic formation of the correlated state of particles takes place, the dispersion of their coordinates increases manifold, and the barrier transparency becomes many orders of magnitude higher at a low energy of interacting particles.     

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ ₀, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ ₀ r ², we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ ₀, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.     

The Controlled Teleportation of an Arbitrary Two-Atom Entangled State in Driven Cavity QED

In this paper, we propose a scheme for the controlled teleportation of an arbitrary two-atom entangled state |φ〉₁₂=a|gg〉₁₂+b|ge〉₁₂+c|eg〉₁₂+d|ee〉₁₂ in driven cavity QED. An arbitrary two-atom entangled state can be teleported perfectly with the help of the cooperation of the third side by constructing a three-atom GHZ entangled state as the controlled channel. This scheme does not involve apparent (or direct) Bell-state measurement and is insensitive to the cavity decay and the thermal field. The probability of the success in our scheme is 1.0.     

Equation of state of fluid helium at high temperatures and densities

Helium, hydrogen, and their isotopes are the simplest monoatomic and diatomic molecules. It is relatively easy to describe their properties using the basic principles of quantum mechanics. In condensed matter physics, hydrogen and helium serve as the models for the condensed matter properties at extreme conditions so that both experi- mental and theoretical physicists pay much attention to the study of their properties[1], especially the insulator-metal transition of hydrogen[2]. The aim to st…     

Equation of state of fluid helium at high temperatures and densities

Hugoniot curves and shock temperatures of gas helium with initial temperature 293 K and three initial pressures 0.6, 1.2, and 5.0 MPa were measured up to 15000 K using a two-stage light-gas gun and transient radiation pyrometer. It was found that the calculated Hugoniot EOS of gas helium at the same initial pressure using Saha equation with Debye-Hückel correction was in good agreement with the experimental data. The curve of the calculated shock wave velocity with the particle velocity of gas helium which is shocked from the initial pressure 5 MPa and temperature 293 K, i.e., theD ≈u relation,D=C ₀+λu (u<10 km/s, λ=1.32) in a low pressure region, is approximately parallel with the fittedD ≈u (λ=1.36) of liquid helium from the experimental data of Nellis et al. Our calculations show that the Hugoniot parameter λ is independent of the initial density p{in0}. TheD≈u curves of gas helium will transfer to another one and approach a limiting value of compression when their temperature elevates to about 18000 K and the ionization degree of the shocked gas helium reaches 10⁻³.     

Elastic model of protein-protein interaction

Summary The elastic distortions of a model membrane are discussed, by taking into account those due to incorporated proteins. Two types of distortions exist: i) membrane compression and ii) displacement at constant thickness. The first mode decays on a very-short-length scale (≈nm). The second one is important since the characteristic lengh is of the order of the μm. This last distortion is characterized by a multipole expansion, in a way similar to electrostatics. The interaction of different elastic distortions is described in the context of their multipole expansion: for example, i) the monopole-monopole interaction is attractive (repulsive) in the case of opposite (equal) signs of the monopoles. The interaction energy behaves asW _AB≈Inr _AB (r _AB distance between the monopoles A and B) and may be even at large distance much higher thankT. ii) The dipole-dipole interaction is always attractive if the elastic dipole can rotate (fluid membrane). iii) The interaction energy varies asW _AB≈r _AB ⁻² (r _AB distance between the dipoles) and so on. This multipole concept may be used for the understanding of the recognition of different proteins. In addition, the particles which creaste the distortion may be polarizable. This means that shape changes of the particle could be induced by an external elastic field. We expect for a large particle a large polarizability. As a consequence, two static monopoles which reped each other may attract if they become polarizable. This feature is reminiscent of the Van der Waals interaction in electrostatics. Paper presented at the “Meeting on Lyotropics and Related Fields?, held in Rende, Cosenza, September 13–18, 1982.     

Collision broadening of spectral lines corresponding to transitions between excited levels of the cesium atom

The constants of pressure self-broadening of cesium have been measured for the transitions 6P _1/2−8D _3/2, 6P _3/2−10S _1/2, and 5D _5/2−nF(n=14−19). The constants of the resonance broadening of the 6P _1/2 and 6P _3/2 cesium levels, the constants of electron collisional broadening of thenF levels at a temperature ofT≈1500 K, and the oscillator strengths of the 5D _5/2−nF(n=14−18) transitions have been determined. Translated from Trudy Fizicheskogo Instituta im. P. N. Lebedeva, Lebedev Physics Institute, Russian Academy of Sciences, Moscow, Vol. 195, pp. 217–233, 1989.     

Selective excitation of the 62 D 3/2 state of the atomic thallium beam

The absorption of the tunable narrow-band laser radiation with λ = 276.9 nm at the 6² P _1/2 → 62 D _3/2 transition in the atomic thallium beam is experimentally studied. The isotopic selectivity and efficiency of the excitation of the 6² D _3/2 state is investigated. The splittings between the ²⁰³Tl and ²⁰⁵Tl isotopes were found to be Δv = 0.98 and 1.25 GHz for the transitions with the nuclear momenta F = 1 → F = 1, 2 and F = 0 → F = 1, respectively, which is sufficient for a relatively high isotopic selectivity of the 6² D _3/2 state excitation with the subsequent ionization for the laser separation of the thallium isotopes. The effects that lead to the broadening of the resonance and a decrease in the selectivity are analyzed. The main contribution is related to the field broadening by the laser radiation, which limits the mean laser power density.     

Formation of correlated states and tunneling for a low energy and controlled pulsed action on particles

We consider a method for optimizing the tunnel effect for low-energy particles by using coherent correlated states formed under controllable pulsed action on these particles. Typical examples of such actions are the effect of a pulsed magnetic field on charged particles in a gas or plasma. Coherent correlated states are characterized most comprehensively by the correlation coefficient r(t); an increase of this factor elevates the probability of particle tunneling through a high potential barrier by several orders of magnitude without an appreciable increase in their energy. It is shown for the first time that the formation of coherent correlated states, as well as maximal |r(t)|_max and time-averaged 〈|r(t)|〉 amplitudes of the correlation coefficient and the corresponding tunneling probability are characterized by a nonmonotonic (oscillating) dependence on the forming pulse duration and amplitude. This result makes it possible to optimize experiments on the realization of low-energy nuclear fusion and demonstrates the incorrectness of the intuitive idea that the tunneling probability always increases with the amplitude of an external action on a particle. Our conclusions can be used, in particular, for explaining random (unpredictable and low-repeatability) experimental results on optimization of energy release from nuclear reactions occurring under a pulsed action with fluctuations of the amplitude and duration. We also consider physical premises for the observed dependences and obtain optimal relations between the aforementioned parameters, which ensure the formation of an optimal coherent correlated state and optimal low-energy tunneling in various physical systems with allowance for the dephasing action of a random force. The results of theoretical analysis are compared with the data of successful experiments on the generation of neutrons and alpha particles in an electric discharge in air and gaseous deuterium.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

Molecular dynamics investigation of the size effect upon the β → α transformation in Zr nanocrystals

The stability of the β phase in cubic zirconium nanoparticles has been calculated as a function of the size r (r varies in the range from 2.5 to 11.5 nm) by the molecular dynamics method with the many-body interatomic interaction potential obtained within the embedded-atom model. It has been demonstrated that the temperature T _k at which the cubic cluster of body-centered cubic zirconium becomes structurally unstable depends nonlinearly on the particle size. The curve T _k (r) exhibits a pronounced maximum in the range r ≈ 4.3−4.7 nm. It has been established that the mechanism of the structural transition from the body-centered cubic phase to the hexagonal close-packed phase depends substantially on the particle size. For particles with sizes in the range from 2.5 to 5.0 nm, there exists a temperature range in which the transition from the body-centered cubic phase to the hexagonal close-packed phase remains incomplete for a long time. In this case, two phases coexist and the initial particle undergoes a strong deformation along the habit plane.     

Suppression of hole doping in fine-grained HTSC YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> due to structural disordering

It was proven experimentally that the structural disordering inherent to fine-grained high-temper- ature YBa₂Cu₃O _y superconductors (with an average grain size of 〈D〉 < 2 μm) leads to a reduction of the level of hole doping and the creation of features inherent to the pseudogap state (antiferromagnetic correlations and the lowered density of states at the Fermi level) even in samples with optimum oxygen content y ≈ 6.92.     

The Current Distribution of the Multiparticle Hopping Asymmetric Diffusion Model

In this paper we treat the multiparticle hopping asymmetric diffusion model (MADM) on ℤ introduced by Sasamoto and Wadati in 1998. The transition probability of the MADM with N particles is provided by using the Bethe ansatz. The transition probability is expressed as the sum of N-dimensional contour integrals of which contours are circles centered at the origin with restrictions on their radii. By using the transition probability we find ℙ(x _m (t)=x), the probability that the mth particle from the left is at x at time t. The probability ℙ(x _m (t)=x) is expressed as the sum of |S|-dimensional contour integrals over all S⊂{1,…,N} with |S|≥m, and is used to give the current distribution of the system. The mapping between the MADM and the pushing asymmetric simple exclusion process (PushASEP) is discussed.     

Nuclear charge radii and electromagnetic moments of scandium isotopes and isomers in the f7/2 shell

Collinear laser spectroscopy experiments on the ScII transition 3d4s ³D₂→3d4p ³F₃ at λ ≈ 363.1 nm were performed on the ^42–46Sc isotopic chain using an ion guide isotope separator with a cooler–buncher. Isotope and isomer shifts and hyperfine structures of five ground states and two isomers were measured. Preliminary results on the nuclear moments and charge radii changes deduced from these measurements are reported.     

Large Deviations for the Fermion Point Process Associated with the Exponential Kernel

For the fermion point process on the whole complex plane associated with the exponential kernel , we show the central limit theorem for the random variable ξ(D _r , the number of points inside the ball D _r of radius r, as r → ∞ and we establish the large deviation principle for the random variables {r ⁻²ξ (D _r ), r > 0}.     

Fredholm Modules on P.C.F. Self-Similar Fractals and Their Conformal Geometry

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct non-trivial Fredholm modules on post critically finite fractals by regular harmonic structures (D, r). The modules are (d _S , ∞)–summable, the summability exponent d _S coinciding with the spectral dimension of the generalized Laplacian operator associated with (D, r). The characteristic tools of the noncommutative infinitesimal calculus allow to define a d _S -energy functional which is shown to be a self-similar conformal invariant. Thiswork has been supported by the project “Teoria ellittica e forme di Dirichlet su spazi frattali” G.N.A.M.P.A. 2008 and by the G.R.E.F.I.-G.E.N.C.O. French-Italian Research Group.     

Photophoresis of coarse aerosol particles with nonuniform thermal conductivity

The photophoresis of a coarse solid spherical aerosol particle in a one-component gas of nonuniform temperature is examined with consideration of the inertial effects in the hydrodynamic equations and the temperature jump in the Knudsen layer. The problem is solved in the spherical coordinates r, Θ, and ϕ. The photophoresis of a homogeneous particle is considered first. Then the results are generalized to an inhomogeneous particle. A particle whose thermal conductivity χ _i varies as a function of r is chosen as a model which describes a broad class of natural and artificially produced aerosol particles. It is shown that the error can be significant if the variable internal thermal conductivity χ _i =χ _i (r) of the particle is ignored and only the value of the thermal conductivity on its surface χ _i (a) is considered, on the assumption that the particle is homogeneous. It is also shown that a particle with a variable internal thermal conductivity χ _i =χ _i (r) and a density of heat sources within it q _i (r,Θ) can be regarded as a homogeneous particle with a thermal conductivity γχ _i (a) and a heat-source density m(r)q _i (r,Θ). Recurrence formulas for gand m(r) in the general case are presented. Analytical expressions for γ and m(r) are found for a model particle with pronounced inhomogeneity. Zh. Tekh. Fiz. 68, 1–6 (April 1998)