The shape resonance

For a class of Schrödinger operatorsH:=–(²/2m)+V onL ²( ⁿ ), with potentials having minima embedded in the continuum of the spectrum and non-trapping tails, we show the existence of shape resonances exponentially close to the real axis as 0. The resonant energies are given by a convergent perturbation expansion in powers of a parameter exhibiting the expected exponentially small behaviour for tunneling.     

The role of electronic density of states in metallic Lanthanum

Observations of X-ray photoabsorption in metallic Lanthanum in the vicinity of the 3d _5/2-edge are given. Two separated absorption peaks are detected at the quantum energies =830.6eV and =834.0eV. The results are interpreted according to the model given in communication I–IV [1].     

On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential

In this paper, we first construct multi-lump (nonlinear) bound states of the nonlinear Schrödinger equation for sufficiently small >0, in which sense we call them semiclassical bound states. We assume that 1p< forn=1,2 and 1p<1+4/(n–2) forn3, and thatV is in the class(V) _a in the sense of Kato for somea. For any finite collection {x ₁,...,x _N} of nondegenerate critical points ofV, we construct a solution of the forme ^–iEt/v(x) forE<a, wherev is real and it is a small perturbation of a sum of one-lump solutions concentrated nearx ₁,...,x _N respectively. The concentration gets stronger as 0. And we also prove these solutions are positive, and unstable with respect to perturbations of initial conditions for possibly smaller >0. Indeed, for each such collection of critical points we construct 2 ^N–1 distinct unstable bound states which may have nodes in general, and the above positive bound state is just one of them.     

Effects of the blackbody radiation on the harmonically bound electron-energy level shifts and consistency conditions

The influence of the vacuum radiation field on the harmonically bound electron (frequency ₀) is considered. The electron is minimally coupled to the blackbody radiation field. The dynamics of the system is exactly solvable. The high (k _B T₀) and low (k _B T₀) temperature expansions of the kinetic and potential energy are given. In the high temperature regime theT ²-dependent dynamic Stark shift is found whereas in the low temperature regime there is no temperature dependent shift. The position correlation function of the electron shows in the low temperature regime a unclassical algebraic decay (t ^–4,t/k _B T).     

Continuous quantum measurements and the action uncertainty principle

The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral in finite limits). With the help of the measurement amplitude, maximum deviation of measurement outputs from the classical one can be easily determined. The aim of the present paper is to express this variance in a simpler and transparent form of a specific uncertainty principle (called the action uncertainty principle, AUP). The most simple (but weak) form of AUP is S, whereS is the action functional. It can be applied for simple derivation of the Bohr-Rosenfeld inequality for measurability of gravitational field. A stronger (and having wider application) form of AUP (for ideal measurements performed in the quantum regime) is | ^t (S[q]/q(t))q(t)dt|, where the paths [q] and [q] stand correspondingly for the measurement output and for the measurement error. It can also be presented in symbolic form as (Equation) (Path) . This means that deviation of the observed (measured) motion from that obeying the classical equation of motion is reciprocally proportional to the uncertainty in a path (the latter uncertainty resulting from the measurement error). The consequence of AUP is that improving the measurement precision beyond the threshold of the quantum regime leads to decreasing information resulting from the measurement.     

Semiclassical Models for Virtual Antiparticle Pairs, the Unit of Charge e, and the QCD Coupling α s

New semiclassical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields /2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. When the results of the new models and QFT are combined, formulae for e and _s (q) are derived in terms of only and c.     

Large deviations from classical paths. Hamiltonian flows as classical limits of quantum flows

We prove that in the limit0, the probability for the paths of the stochastic jump process associated to the quantum time evolution to be in a tublet around the classical trajectory is of order 1–exp{–A/}. We give some applications of this result to the study of the classical limit of Wigner functions.     

Semiclassical Behaviour of Expectation Values in Time Evolved Lagrangian States for Large Times

We study the behaviour of time evolved quantum mechanical expectation values in Lagrangian states in the limit 0 and t. We show that it depends strongly on the dynamical properties of the corresponding classical system. If the classical system is strongly chaotic, i.e. Anosov, then the expectation values tend to a universal limit. This can be viewed as an analogue of mixing in the classical system. If the classical system is integrable, then the expectation values need not converge, and if they converge their limit depends on the initial state. An additional difference occurs in the timescales for which we can prove this behaviour; in the chaotic case we get up to Ehrenfest time, t ln (1/), whereas for integrable system we have a much larger time range.     

The XPS valence band spectra of NbC

The x-ray photoemission valence band spectra of NbC have been measured and are compared with the x-ray emission spectra and with the results from band structure calculations. This comparison leads to a large enhancement of theC2 _p photoabsorption cross section (at=1,487 eV) compared to the value calculated for the free atom. The effect of the nonmetal vacancy in the valence band can be described very well with vacancy cluster calculations.     

The Euclidean loop expansion for massive λΦ 4 4 : Through one loop

As an application of the theory of solutions of the classical, Euclidean field equation, we prove the existence of solutions to the renormalized functional field equation, for the ⁴ interaction in four Euclidean space dimensions, with non-negative and nonzero mass, through orderc. That is, we prove that the functional derivative of the connected generating functional is in the Schwartz space Re(R ⁴), when evaluated at external sources in Re, through orderc. We also prove the existence of all functional derivatives of the connected generating functional through the same order. All quantities of interest are analytic in the coupling constant at 0<, and continuous in the external source.     

The effect of oxygen on the electric conductivity of a cuprous oxide single crystal

The effect of an excess of oxygen on the electric conductivity of a pre-illuminated and heated single crystal of Cu₂O is investigated. It is found that the influence of illumination on the electric conductivity, together with the concentration of impurities, increases with increasing oxygen pressure during annealing.

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, Cu₂O. , .

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In conclusion the author thanks E. Klier and J. Pastrak for valuable remarks and discussion.     

Anderson localization for the almost Mathieu equation: A nonperturbative proof

We prove that for any diophantine rotation angle and a.e. phase the almost Mathieu operator (H()) _n = _n–1 + _n+1 +cos(2(+n)) _n has pure point spectrum with exponentially decaying eigenfunctions for 15. We also prove the existence of some pure point spectrum for any 5.4.     

Gamma-ray spectroscopy in 110Sn and 111Sn

Excited states in ¹¹⁰Sn and ¹¹¹Sn nuclei have been investigated using in-beam -ray spectroscopic methods. An ¹⁶O beam with an energy of 60-80MeV was used to bombard a ⁹⁸Mo target. On the basis of the relative excitation functions, -ray angular distributions, - and -time distributions, -ray multiplicity and total energy data, the level schemes of ¹¹⁰Sn and ¹¹¹Sn have been studied and extended up to E_exc 11.5MeV, I = 24, and E_exc 11.1MeV and I = (51/2), respectively. An extension of the intruder, g.s. and negative-parity bands, as well as 5 new band-like structures are proposed in ¹¹⁰Sn. The nature of newly introduced collective band 8 as well as 10⁺ states fed in the decay of the collective band is discussed. In the ¹¹¹Sn nucleus an intruder band based on the 23/2^- state has been reinvestigated and the extension of the g.s. band and second negative-parity band is given. Evidence for neutron-core coupling in ¹¹¹Sn is found. The structure and systematics of excited states in light Sn isotopes is discussed.     

Wigner Kirkwood ℏ-expansion of the density matrix in inhomogeneous superfluid Fermi systems

The generalized density matrix of superfluid inhomogeneous Fermi systems is expanded in powers of up to order ². This constitutes the generalisation of the Wigner Kirkwood -expansion of the density matrix of normal fluid systems to the pairing case.One of the authors (P.S.) is very grateful to D. Gogny for contributions in an early stage of this work several years back. He also acknowledges fruitful discussions with M. Centelles and X. Vinas.     

Changes in EPR spectrum of free radical species inγ-irradiated polyformaldehyde

We have found that gamma-irradiated polyformaldehyde does not exhibit the effect of the disappearance of the hyperfine structure of EPR spectrum as a function of the dose or the time passed since the end of irradiation, as was found earlier for a group of polymers having only C-C-C-C-atoms in the polymer chain. This difference in the change in the EPR of the polyformaldehyde (PFA) spectrum compared with the polymers with a -C-C-C-C- chain is explained by the impossibility of forming a conjugate double bond in the -C-O-C-O- chain in PFA.

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, , -, , , atom C-C-C-C-. ( ) C-C-C-C- , C-O-C-O- qu .

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The author thanks K. Vacek for many valuable discussions which helped this work.     

Bremsstrahlung of hot quantum plasma

The classical Debye field is replaced by the respective quantum modification for a hot quantum plasma. The bremsstrahlung spectrum and the total bremsstrahlung intensity are investigated in detail. The results of numerical calculations are tabulatedvs. the characteristic parameter=₀ /kT, where ₀ is the plasma frequency and other symbols have their standard meaning. It is found that the deviations from the bremsstrahlung of a classical plasma become significant for the values10^–2. These modifications are to be taken into consideration in the interpretation of the bremsstrahlung measurements.     

The physics of detecting torsion and placing limits on its effects

We present the essential principles of torsion-detection physics and evaluate several conceivable types of experiments and observations for actually detecting torsion fields, reemphasizing also the evident impossibility of successfully searching for its manifestations among cosmological relics. In particular, a polarized body, with net intrinsic (fundamental-particle) spin, is essential for detecting a torsion field. One which possesses only orbital angular momentum—rotation—or an unpolarized intrinsic spin density will not feel torsion. The fundamental problem in searching for such fields is the extremely small basic unit of the coupling or interaction energy between the torsion field and spin,(8G/c ²)( ²/4). The best way of maximizing the total interaction energy is to increase the spin density of the source _s, and, at the same time the spin numberS _D of the detector.This essay was awarded an honorable mention in 1984 by the Gravity Research Foundation—Ed.     

Probability Backflow for a Dirac Particle

The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is shown that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown that the maximum possible amount of probability that can flow backwards, over a given time interval of duration T, depends on the dimensionless parameter = (4/mc²T)^1/2, where m is the mass of the particle and c is the speed of light. At = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as increases from 0, and show that it depends on the size of m, , and T, unlike the nonrelativistic case.     

Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

The temperature dependence of the methyl rotational potential in methyl iodide under pressure

Inelastic neutron scattering experiments have been performed on CH₃I under pressure. The tunnel splitting of the methyl librational groundstate decreases almost exponentially with increasing hydrostatic pressure: _t (p)=2.48 eV·exp (–0.138·p[kbar]), the librational energy increases asE ₀₁ (p)=13.2 meV (1+0.050p[kbar]). Both relations can be explained by a rotational potentialV which depends on the interatomic distancer asVr ^–9.6 . This large exponent shows the importance of valence forces. The shape of the rotational potential is almost unaffected by pressure. The coupling of the methyl group to phonons via a shaking and a breathing term which was observed at atmospheric pressure is also found at high pressure. The effect appears at higher temperature as expected for the stronger potential.