Zero-point Oscillations Research Articles

Sub-barrier heavy-ion fusion/capture: Accurate accounting for zero-point quadrupole shape oscillations with realistic nucleus-nucleus potential

Sub-barrier heavy-ion fusion/capture: Accurate accounting for zero-point quadrupole shape oscillations with realistic nucleus-nucleus potential

A novel approach for taking into account the zero-point oscillations in calculating heavy-ion fusion cross-sections

Earlier in the literature it was shown that accounting for the zero-point oscillations (ZPO) of the shape of colliding atomic nuclei results in significant increasing of the calculated sub-barrier capture (fusion) crosssections. However, calculations of such kind were performed in a simplified way with the schematic nucleus– nucleus potential. The purpose of the present paper is to estimate in an accurate way the sub-barrier capture cross-sections in collisions between oxygen-16 and spherical nuclei with the realistic potential and to compare the calculated cross-sections with the experimental data. Nucleus-nucleus potential is obtained within the doublefolding model with Paris M3Y nucleon–nucleon effective forces. The nucleon densities are taken from the IAEA data base (they are calculated using the Hartree–Fock–Bogoliubov method and approximated by two-parameter Fermi profile). The transmission coefficients are calculated within the WKB approximation below the Coulomb barrier and within parabolic barrier approximation above it. A novel approach for taking into account the ZPO without any fitting parameters is proposed. It is demonstrated that ignoring the ZPO results in underestimating the experimental data whereas accounting for ZPO improves the agreement of the calculated cross-sections with the experimental ones.

A Novel Approach for Taking into Account the Zero-Point Oscillations in Calculating Heavy-Ion Fusion Cross-Sections

A Novel Approach for Taking into Account the Zero-Point Oscillations in Calculating Heavy-Ion Fusion Cross-Sections

The Zero-Point Oscillations in the Planck Vacuum State and Its Coordinate Uncertainty

This short paper argues that the charged quantum oscillators in the quasi-continuum Planck vacuum (PV) state are responsible for the zero-point oscillations in that state. The Planck particle (PP) quantum energy levels for the oscillators are derived from first principles. The PV coordinate uncertainty concerning the PV structure easily follows from these results.

The Zero-Point Oscillations in the Planck Vacuum State and Its Coordinate Uncertainty

This short paper argues that the charged quantum oscillators in the quasi-continuum Planck vacuum (PV) state are responsible for the zero-point oscillations in that state. The Planck particle (PP) quantum energy levels for the oscillators are derived from first principles. The PV coordinate uncertainty concerning the PV structure easily follows from these results.

Parametric broadening of the molecular vibronic band due to zero-point oscillations and thermal fluctuations of interatomic bonds

Numerous computations of the spectra of molecules are performed by mainstream methods based on the fundamental work by Lax [J. Chem. Phys. 20, 1752 (1952)] for smoothing a series of individual transitions represented by delta functions. There is an assumption that the linewidth of an individual rovibronic transition spectrum is many orders of magnitude smaller than the rovibronic bandwidth. However, the presence of rotational–vibrational structure in the molecular spectrum masks the broadening of each individual rovibronic transition. In this work, in the framework of harmonic approximation of potential energy surfaces, a new kind of contribution to homogenous broadening is considered to describe the optical spectrum of any single rovibronic transition. Its origin is in zero-point oscillations and thermal fluctuations around equilibrium positions of nuclei. Franck–Condon diagrams with slanting equidistant vibrational levels are proposed. Expressions of the spectral intensity of a single vibronic transition are derived from the first principles. This theory was used to estimate the broadening magnitude of the vibronic transition due to quantum uncertainty of nuclear coordinates of linear polymethine dyes with an extended π-electron system. It was shown that the calculated magnitude of the broadening is approximately two times smaller than the bandwidth observed in the experiment but it has the same order of magnitude. The value of such broadening depends on the environment that restricts the vibrational and rotational degrees of freedom of the molecule. It was demonstrated that an organic chromophore with an extended π-electron system can be considered to be a molecular optical parametric oscillator.

Interference caused by electromagnetic interactions

We consider interference fluxes of energy, momentum and angular momentum, describing the interaction of electric charges with constant and variable electromagnetic fields. Absorption and stimulated emission of atoms in the field of free and evanescent waves are described. It is shown that in the case of interaction with reactive fields, the momentum of an atom during absorption and stimulated emission does not change. A wave derivation of Planck’s formula based on the interference of the fields of classical thermal radiation and quantum zero-point oscillations is presented.

Quantum versus thermal fluctuations in the fcc antiferromagnet: Alternative routes to order by disorder

In frustrated magnetic systems with competing interactions fluctuations can lift the residual accidental degeneracy. We argue that the state selection may have different outcomes for quantum and thermal order by disorder. As an example, we consider the semiclassical Heisenberg fcc antiferromagnet with only the nearest-neighbor interactions. Zero-point oscillations select the type 3 collinear antiferromagnetic state at T=0. Thermal fluctuations favor instead the type 1 antiferromagnetic structure. The opposite tendencies result in a finite-temperature transition between the two collinear states. Competition between effects of quantum and thermal order by disorder is a general phenomenon and is also realized in the J1-J2 square-lattice antiferromagnet at the critical point J2 = 0.5 J1.

Strictly-correlated-electron approach to excitation energies of dissociating molecules

In this work we consider a numerically solvable model of a two-electron diatomic molecule to study a recently proposed approximation based on the density functional theory of so-called strictly correlated electrons (SCE). We map out the full two-particle wave function for a wide range of bond distances and interaction strengths and obtain analytic results for the two-particle states and eigenenergies in various limits of strong and weak interactions, and in the limit of large bond distance. We then study the so-called Hartree-exchange-correlation (Hxc) kernel of time-dependent density functional theory which is a key ingredient in calculating excitation energies. We study an approximation based on adiabatic SCE (ASCE) theory which was shown to display a particular feature of the exact Hxc kernel, namely, a spatial divergence as function of the bond distance. This makes the ASCE kernel a candidate for correcting a notorious failure of the commonly used adiabatic local density approximation (ALDA) in the calculation of excitation energies of dissociating molecules. Unlike the ALDA, we obtain nonzero excitation energies from the ASCE kernel in the dissociation regime but they do not correspond to those of the true spectrum unless the interaction strength is taken to be very large such that the SCE theory has the right regime of validity, in which case the excitation energies become exact and represent the so-called zero-point oscillations of the strictly correlated electrons. The commonly studied physical dissociation regime, namely, large molecular separation at intermediate interaction strength, therefore remains a challenge for density functional approximations based on SCE theory.

Isotopic exchange between hydrogen from the gas phase and proton-conducting oxides: Theory and experiment

The interaction of hydrogen isotopes from the gas phase with proton-conducting oxides with the perovskite structure La1−x SrxScO3−α (x = 0; 0.04) was studied by means of the hydrogen isotope exchange with gas phase equilibration in the temperature range T = 300–800 °C and in hydrogen pressure range pH2 = 2–20 mbar.A novel kinetic model for the hydrogen isotope exchange experimental data treatment taking into account the isotopic effects was developed. This model was implemented for the obtained experimental results. The heterogeneous exchange rates of hydrogen isotopes with investigated oxides La1−xSrxScO3−α (x = 0; 0.04) were calculated. The mole fractions of hydrogen isotopes were determined for the investigated materials. It was found that deuterium saturation level is higher in comparison with protium, whereas the deuterium surface exchange coefficient for the proton-conducting oxide La0.96Sr0.04ScO3–α is smaller in comparison with the protium surface exchange coefficient. The thermodynamic isotope effect can be caused by the difference of energy of zero-point oscillations between OH- and OD-defects and molecular H2 and D2. The kinetic isotope effect can be explained by the different strength of OH and OD bonds. It is shown that the rate determining stage of hydrogen surface exchange is the process of the exchange between the forms of hydrogen in the gas phase and in the adsorption layer of the proton-conducting oxides (the stage of dissociative adsorption of hydrogen). A new statistical criterion is proposed for the first time allowing dividing the observed surface inhomogeneities caused by not only the natural surface roughness but also the presence of different isotopes of hydrogen (protium and deuterium) with different binding energies on a solid surface.The activity of the investigated proton-conducting oxides with respect to the hydrogen heterogeneous exchange is comparable to the hydrogen heterogeneous exchange activity for the oxides based on cerates and zirconates of alkaline earth metals. High catalytic activity with respect to the process of hydrogen exchange from the gas phase in reducing atmospheres allows us to consider proton-conducting oxides based on the lanthanum scandates as very promising electrolytes for numerous electrochemical applications.

Anomalous zero-temperature magnetopolaronic blockade of resonant electron tunneling in Majorana-resonant-level single-electron transistor

The magnetopolaronic generalization of a Majorana-resonant-level (MRL) model is considered for a single-level vibrating quantum dot coupled to two half-infinite $g=1/2$ Tomonaga-Luttinger liquid (TLL) leads. A qualitatively new non-trivial formula for the effective transmission coefficient and differential conductance for resonant magnetopolaron-assisted tunneling is obtained under the assumption about a fermion-boson factorization of corresponding averages. This approach is valid for the case of weak magnetopolaronic coupling in a system. Surprisingly, it is found that despite a supposed weakness of interaction between fermionic and bosonic subsystems in that case, a strongly correlated electron transport in the system reveals features of strong (and, hence, anomalous) magnetopolaronic blockade at zero temperature if the energy of a vibrational quantum is the smallest (but nonzero) energy parameter in the system. Such an effect should be referred to as magnetic phase-coherent magnetopolaron-assisted resonant tunneling of Andreev type, that originates from a special, Majorana-like, symmetry of magnetopolaron-coupled tunnel Hamiltonian. The effect predicted in this paper can be used as an experimental fingerprint of Majorana-resonant level situation in single-electron transistors as well as for detection of ultra-slow zero-point oscillations of suspended carbon nanotubes in the Majorana-resonant level regime of electron tunneling through corresponding single-electron transistors.

Semi-Harmonic Scaling Enables Calculation of Masses of Elementary Particles of the Standard Model

The underlying rules for a natural system describing cellular automata are simple, but produce highly complex behavior. A mathematical basis for the spectra of discrete coherent and non-coherent electromagnetic (EM) frequencies was derived, in which the algorithm exhibits an information distribution according to ratios of 2:3 in 1:2 at a semi-harmonic manner. This generalized music (GM) model shows that energy both in elementary particles and animate systems is semi-harmonic, quantized and discrete. A support for an ontological basis of the Standard Model was found, and indicates that the GM-model underlies the quantum field theory of subatomic particles. The present theory combines quantum mechanics and classical periodic systems, obeys to locality and solves the “hidden variable theory of Bohm”. The discovered pattern of electromagnetic field eigenvalues, within a broad range of discrete frequencies, points at a de Broglie/Bohm type of causal interpretation of quantum mechanics, implying an integral resonant pilot-wave/particle modality. The model has been substantiated by a meta-analysis of measured discrete energies of: 37 different Elementary Particles, 45 different EPR-measurements, zero-point energies of elements and about 450 electromagnetic wave frequencies of cells with a mean accuracy of 0.58%. It has been shown that the GM-scale is frequency-locked with zero-point oscillations, and thereby evidently implies involvement of entanglement.

Superconductivity, Superfluidity and Zero-Point Oscillations

It is shown that both super phenomena-superconductivity and superfluidity are based on the same mechanism of streamline of zero-point oscillations. Proof of this is the agreement of obtained theoretical estimations with measured data.

ISOTOPIC EXCHANGE BETWEEN HYDROGEN FROM THE GAS PHASE AND PROTON-CONDUCTING OXIDES: THEORY AND EXPERIMENT

The interaction of gaseous hydrogen isotopes from the gas phase with proton-conducting oxides with the perovskite structure La 1−x Sr x ScO 3− α (x = 0; 0.04) was studied by means of the hydrogen isotope exchange with gas phase equilibration in the temperature range T = 300−800 ºC and in hydrogen pressure range pH 2 = 2−20 mbar. A novel kinetic model for the hydrogen isotope exchange experimental data treatment taking into account the isotopic effects was developed. This model was implemented for the obtained experimental results. The heterogeneous exchange rates of hydrogen isotopes with investigated oxides La 1−x Sr x ScO 3− α (x = 0; 0.04) were calculated. The mole fractions of hydrogen isotopes were determined for the investigated materials. It was found that deuterium uptake is higher in comparison with protium, whereas the deuterium surface exchange coefficient for the proton-conducting oxide La 0.96 Sr 0.04 ScO 3– α is smaller in comparison with the protium surface exchange coefficient. The thermodynamic isotope effect can be caused by the difference of energy of zero-point oscillations between OH- and OD-defects and molecular H 2 and D 2 . The kinetic isotope effect can be explained by the different strength of OH and OD bonds. The rate determining stage of hydrogen exchange is shown to be the process of exchange between the forms of hydrogen in the gas phase and in the adsorption layer of the proton-conducting oxide (the stage of dissociative hydrogen adsorption). For the first time, a new statistical criterion is proposed that allows dividing the observed surface inhomogeneities caused by not only the natural surface roughness but also the presence of different isotopes of hydrogen (protium and deuterium) with different binding energies on a solid surface. The activity of the investigated proton-conducting oxides with respect to the hydrogen heterogeneous exchange is comparable to the heterogeneous hydrogen exchange activity for oxides based on cerates and zirconates of alkaline earth metals. High catalytic activity with respect to the process of hydrogen exchange from the gas phase in reducing atmospheres allows us to consider the proton-conducting oxides based on the lanthanum scandates as the very promising electrolytes for numerous electrochemical applications.

The effect of zero Langmuir oscillations of an electromagnetic field on the transverse dielectric permittivity of a degenerate electron–ion plasma

It is shown theoretically that the electromagnetic background of longitudinal zero oscillations of a temperature-degenerate electron–ion plasma in a thermodynamic equilibrium state resonantly distorts the wave functions of its electrons. This gives rise to a characteristic quantum frequency that nonanalytically depends on Planck’s constant ℏ. Vacuum phenomena in plasma attributed to zero oscillations turn out to be anomalously large. Quantum corrections to the transverse dielectric permittivity of a degenerate electron–ion plasma, which are nonanalytic with respect to ℏ and are attributed to the zero-point oscillations of the plasma, are determined.

Scanning Tunneling Microscopy of Atomic Scale Phonon Standing Waves in Quasi-freestanding WSe2 Monolayers

ABSTRACTUsing scanning tunneling microscopy (STM) we observed atomic scale interference patterns on quasi-freestanding WSe2 islands grown on top of graphene. The bias-independent double atomic size periodicity of these patterns and the sharp Brillouin zone edge revealed by 2D STM Fourier analysis indicate formation of optical phonon standing waves due to scattering on intercalating defects supporting these islands. Standing wave patterns of both synchronized and non-synchronized optical phonons, corresponding to resonant and non-resonant phonon scattering regimes, were experimentally observed. We also found the symmetry breaking effect for individual phonon wave packets, one of the unique features distinguishing phonon standing waves. We show that vibrational and electronic anharmonicities are responsible for STM detection of these patterns. A significant contribution to the interference contrast arises from quantum zero-point oscillations.

Chemical and nuclear catalysis driven by localized anharmonic vibrations

In many-body nonlinear systems with sufficient anharmonicity, a special kind of lattice vibrations, namely, Localized Anharmonic Vibrations (LAV) can be excited either thermally or by external triggering, in which the amplitude of atomic oscillations greatly exceeds that of harmonic oscillations (phonons) that determine the system temperature. Coherency and persistence of LAV may have drastic effect on chemical and nuclear reaction rates due to time-periodic modulation of reaction sites. One example is a strong acceleration of chemical reaction rates driven by thermally-activated jumps over the reaction barrier due to the time-periodic modulation of the barrier height in the LAV vicinity. At sufficiently low temperatures, the reaction rate is controlled by quantum tunneling through the barrier rather than by classical jumping over it. A giant increase of sub-barrier transparency was demonstrated for a parabolic potential well with the time-periodic eigenfrequency, when the modulation frequency exceeds the eigenfrequency by a factor of ~2 (parametric regime). Such regime can be realized for a hydrogen or deuterium atom in metal hydrides/deuterides, such as NiH or PdD, in the vicinity of LAV. We present an analytical solution of the Schrodinger equation for a nonstationary harmonic oscillator, analyze the parametric regime in details and discuss its applications to the tunnel effect and to D-D fusion in PdD lattice. We obtain simple analytical expressions for the increase of amplitude and energy of zero-point oscillations (ZPO) induced by the parametric modulation. Based on that, we demonstrate a drastic increase of the D-D fusion rate with in-creasing number of modulation periods evaluated in the framework of Schwinger model, which takes into account suppression of the Coulomb barrier due to lattice vibrations.

Formation of weakly bound molecular complexes: ( $$^3$$ 3 He) $$_2$$ 2

Experimental evidence for low-temperature (exothermic) atom-exchange chemical reactions was recently reported after starting with an optically trapped near-quantum-degenerate gas of polar $$^{40}$$ K $$^{87}$$ Rb (fermionic) molecules prepared in their absolute ground state. Here we demonstrate the similar fermionic ( $$^3$$ He $$^3$$ He) molecules formation via vacancies in quantum $$^4$$ He crystal. A quantum crystal is defined as one in which the energy of the zero-point oscillations of each atom is not small in comparison with the depth of the potential well in which the atom is located (or mathematically $$\Lambda \equiv (\hbar /a\sqrt{m\,E_i})\ge 1$$ ; m is the mass of an atom, $$E_i$$ is the characteristic interaction energy of the atoms, and a is the interatomic distance). Our modified Gross–Pitaevskii approach, based on the extention to Anderson’s adopting Gross–Pitaevskii equation for treating dilute vacancies, supplies in particular the zero-energy limit of the wave function (and the extra energy caused by the curvature of the wave function) for investigations of possible formation of ( $$^3$$ He) $$_2$$ molecules bound by the elastic deformation field around the isotopic impurities as well as bound states (scattering resonances) for a $$^3$$ He-vacancy system in crystalline $$^4$$ He.

Cosmic bubble and domain wall instabilities I: parametric amplification of linear fluctuations

This is the first paper in a series where we study collisions of nucleated bubbles taking into account the effects of small initial (quantum) fluctuations in a fully 3+1-dimensional setting. In this paper, we consider the evolution of linear fluctuations around highly symmetric though inhomogeneous backgrounds. In particular, we demonstrate that a large degree of asymmetry develops over time from tiny initial fluctuations superposed upon planar and SO(2,1) symmetric backgrounds. These fluctuations are inevitable consequences of zero-point vacuum oscillations, so excluding them by enforcing a high degree of spatial symmetry is inconsistent in a quantum treatment. To simplify the analysis we consider the limit of two colliding planar walls, with mode functions for the fluctuations characterized by the wavenumber transverse to the collision direction and a longitudinal shape along the collision direction x, which we solve for. In the linear regime, the fluctuations obey a linear wave equation with a time- and space-dependent mass meff(x,t). In situations where the walls collide multiple times, meff oscillates in time. We use Floquet theory to study the evolution of the fluctuations and generalize the calculations familiar from the preheating literature to the case with many coupled degrees of freedom. The inhomogeneous case has bands of unstable transverse wavenumbers k⊥ whose corresponding mode functions grow exponentially. By examining the detailed spatial structure of the mode functions in x, we identify both broad and narrow parametric resonance generalizations of the homogeneous meff(t) case of preheating. The unstable k⊥ modes are longitudinally localized, yet can be described as quasiparticles in the Bogoliubov sense. We define an effective occupation number and show they are created in bursts for the case of well-defined collisions in the background. The transverse-longitudinal coupling accompanying nonlinearity radically breaks this localized particle description, with nonseparable 3D modes arising that will be studied in subsequent papers.

Raman spectroscopy of hot hydrogen above 200 GPa

It has been theorized that at high pressure the increased energy of the zero-point oscillations in hydrogen would destabilize the lattice and form a ground fluid state at 0 K (ref. 1). Theory has also suggested that this fluid state, representing a new state of matter, might have unusual properties governed by quantum effects, such as superfluidity or superconductivity. Here, by combining Raman spectroscopy and in situ high-temperature, high-pressure techniques, we demonstrate that above 200 GPa a new phase transition occurs as temperature is increased, for example 480 K at 255 GPa. If the transformation is interpreted as melting, it would be the lowest melting temperature of any material at these high pressures. We also find a new triple point between phases I and IV and the new phase, and demonstrate that hydrogen retains its molecular character around this point. These data may require a significant revision of the phase diagram of hydrogen above 200 GPa.