The correlation function for a quantum oscillator in a low-temperature heat bath

The momentum autocorrelation function c(t) for a quantum oscillator coupled with harmonic forces to a heat bath of oscillators is calculated at low temperatures. It is found that c(t) contains two distinct terms: one, the zero-point contribution c₀(t), is temperature independent, and the other, c₁(t), does depend on temperature. We concentrate our attention on the low-temperature case. An expression for c₁(t) is obtained, which is valid for arbitrary strenghts of the coupling and for arbitrary times. It is shown that c₁(t) is governed by the low-frequency behaviour of F(λ) = A²(λ)ϱ(λ), where ϱ(λ) is the density of normal modes and A(λ) is the central-oscillator component of the λth normal mode; other details of the problem are irrelevant. It is found that c₁(t) decays in time as an inverse-power law, with a relaxation time t_q ≈ ħ/kT.     

Compressible effect algebras

We define a special type of additive map J on an effect algebra E called a compression. We call J(1) the focus of J and if p is the focus of a compression then p is called a projection. The set of projections in E is denoted by P(E). A compression J is direct if J(a) ≤ a for all a ε E. We show that direct compressions are equivalent to projections onto components of cartesian products. An effect algebra E is said to be compressible if every compression on E is uniquely determined by its focus and every compression on E has a supplement. We define and characterize the commutant C(p) of a projection p and show that a compression with focus p is direct if and only if C(p) = E. We show that P(E) is an orthomodular poset. It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressible. We then consider compressible sequential effect algebras, Lüders maps and conditional probabilities.     

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σ_r+iσ_i (where σ_r and σ_i are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σ_rσ_i-plane whose center is at the origin and ²(radius)=RM₁/P_r, where R is the Rayleigh number,M₁ is the magnetic number and P_r is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.     

A discussion of the Barbier plot

At room temperature the constant C in Barbier's relation lg[S_v|_H=Hc]=-C+lgH_c, S_v is the magnetic viscosity parameter and H_c the coercivity, is approximately the same for a wide range of systems. We take into account the frequency dependence of H_c and derive an expression for C which is both system and measurement dependent. At low measurement frequencies and high temperatures, however, the system dependence of C is suppressed. A similar discussion is carried out for the activation volume v|_Hc.     

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures.The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A₁,…,A_r. For every ρ=1,…,r there is prescribed a strict contraction Γ_ρ:A_ρ→M. A random walk (X_m)_m∈N0 on M is then defined as follows. The starting position is X₀=x₀, where x₀∈M is fixed, and if the walk at the m’th step is at position X_m∈M, then one chooses a ρ among the ρ with X_m∈A_ρ (with equal probability, say) and defines X_m+1 as Γ_ρ(X_m). Associated with the walk is a gainφ(X_m) in every round, where φ:M→R is a continuous function.The aim of the present investigations is the study of the expectation G_m of φ(X_m) as a function of m. Our main result states that the sequence (G_m) is “eventually approximately periodic” provided that all A_ρ are not only closed but also open in M: for every ε there is an l₀∈N such that (G_m) is l₀-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain.In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A₁,A₂, the contractions Γ₁,Γ₂ are rather simple, but the expectations of the gains are not even Cesáro convergent.     

Upper critical fields of layered superconducting NbSe2 at low temperature

The upper critical field versus temperature H_c2 (T) is presented for several NbSe₂ samples. H_c2 (T) is above the dirty or clean limit, and at low T is greater than the paramagnetic limiting field. No simple T-dependence is observed. The anisotropy is 3.23 ± 0.03 for 0 ? H_o ? 150 kG and for 1.2 K ? T ? 4.2 K.     

The static potential at large N

In a partial reduced Eguchi-Kawai model with temporal gauge fixing the large N static potential V(R) is determined for R ⩽ 5 and the string tension σ is extracted. Assuming asymptotic scaling, for the continuum value of the deconfinement temperature 0.60±0.13 is found in units of T_c/√σ. This is the first quantitative confirmation that large N is a goodapproximation to N = 3 (where T_c/√σ = 0.61).     

Primordial inflation and present-day cosmological constant from extra dimensions

A semiclassical gravitation model is outlined which makes use of the Casimir energy density of vacuum fluctuations in extra compactified dimensions to produce the present-day cosmological constant as ρ _Λ ∼M ⁸/M _P ⁴, where M _P is the Planck scale and M is the weak interaction scale. The model is based on (4+D)-dimensional gravity, with D=2 extra dimensions with radius b(t) curled up at the ADD length scale b ₀=M _P /M ²∼0.1 mm. Vacuum fluctuations in the compactified space perturb b ₀ very slightly, generating a small present-day cosmological constant.The radius of the compactified dimensions is predicted to be b ₀≈k ^1/40.09 mm (or equivalently M≈2.4 TeV/k ^1/8), where the Casimir energy density is k/b ⁴.Primordial inflation of our three-dimensional space occurs as in the cosmology of the ADD model as the inflaton b(t), which initially is on the order of 1/M∼10⁻¹⁷ cm, rolls down its potential to b ₀.     

Measurement of the surface density of states by field ionization

It is shown that recent measurements of field ion energy distributions from clean tungsten surfaces probe the density of metal states in the vicinity of the surface. We find j(ω) = (2π/kh)Σ_m| ∫ d³rψ_m(r)γ_z|²δ(ω??_m), where j(ω) is the ion current a ω, ψ_mand ?_m are electronic metal eigenfunctions and eigenvalues in the presence of the external electric field used in field ionization and γ(z) is a function which is large near the noble gas atom. An explicit expression for γ(z) is given in the text. It is estimated that tungsten metal states with values of k₆ at least as large as 0.5 Å^?1 make an appreciable contribution to j(ω) where k₆ is the electron momentum parallel to the surface.     

Functional properties of quantum logics

A quantum logic is defined as a setL of functions from the set of all statesS into [0, 1] satisfying the orthogonality postulate: for any sequencea ₁,a ₂, ... of members ofL satisfyinga _i+a _j≤1 fori≠j there isb∈L such thatb+a ₁+a ₂+...=1. Every logicL is in a natural way an orthomodular σ-orthocomplemented partially ordered set (L, ≤, ′) with members ofS inducing a full set of measures onL. It is shown that a logicL is quite full if and only if (L,≤,′) is isomorphic to an orthocomplemented set lattice of subsets ofS. Sufficient conditions are given in order that a quite full logic be representable in the set of projection quadratic formsf(u)=(Pu, u) on a complex Hilbert space, or in the set of trace functionsf(A)=Trace (AP) generated by projectionsP, where the domain off is the set of non-negative self-adjoint trace operators of trace 1 in a complex Hilbert space.     

An approach to radially symmetrical solutions of the sine-Gordon equation

The solution φ(r, t) of the radially symmetric sine-Gordon equation is considered in three and two spatial dimensions for initial curves, analogous to a 2π-kink, in the expanding and in the shrinking phase, for R(t)j? R(0). It is shown that the parameterization φ(r, t) = 4 arcian exp[γ(r?R(0)] + x(r, t), where R(t) describes the exact propagation of the maximum of φ,(r, t), is suitable. Using an appoximate differential equation, recently given for the propagation of the solitary ring wave, a rough analytic approximation for the correction function x(r = R(t), t) is found and tested numerically. A relationship between the fluctuations in x(r = R(t), t) and those in $\text{R}\text{?}\text{(t), t)}\text{and}\text{R(t)}$ explains why the solitary wave is almost stable. From x(r = R(t), t) and the supposition x(1, t) ≈ x(∞, t) ≈ 0 an assymetry in φ_r(r, t) with respect to r = R(t) is predicted. It also exhibits fluctuations corresponding to those in x(r = R(t), t). The condition for validity of this approximation apparently is also a limit for the stability of the solitary ring wave.     

Effect of diffusion on gain saturation in gas lasers

A theoretical model is developed to account for the effect of diffusion on gain saturation in gas lasers. It is shown that the effect can be characterized by the functionK(k ₂ a, k ₂ b), which depends on pressure, temperature, radius of the beama, and the radius of the cylindrical cavityb. It is concluded that diffusion can be very effective whenk ₂ a is small andb is several times larger thana.     

Hybridization and electron interaction in nickel compounds

The bare Coulomb interaction, defined by the reaction 2dⁿ = d^n?1 + d^{n + 1} ? U is determined for some Ni compounds. It is found that U is larger than the 3d bandwidth even for metallic compounds. More relevant to the metal nonmetal transition is the optical gap energy E_G = U ? (E(3d^n?1) ? E(L)) where E(3d^n?1) and E(L) are the d-electron and ligand electron ionization potentials respectively.     

A-dependence of ΛΛ bond energies in double-Λ hypernuclei

The A-dependence of the bond energy ΔB_ΛΛ of the ΛΛ hypernuclear ground states is calculated in a three-body Λ + Λ + ^A Z model and in the Skyrme-Hartree-Fock approach. Various ΛΛ and Λ-nucleus or ΛN potentials are used and the sensitivity of ΔB_ΛΛ to the interactions is discussed. It is shown that in medium and heavy ΛΛ hypernuclei, ΔB_ΛΛ is a linear function of r _Λ ^{? 3} , where r _Λ is rms radius of the hyperon orbital. It looks unlikely that it will be possible to extract ΛΛ interaction from the double-Λ hypernuclear energies only, the additional information about the Λ- core interaction, in particular, on r _Λ is needed.     

Current-voltage dependencies of heterogeneous semiconductor systems

Computed current-voltage (J–V) dependencies of heterogeneous (powder) semiconductor systems reveal an anomalous dependence between the constant-voltage current J and the uncompensated donor (acceptor) concentration N. Over a range of N(N₁ < n < N₂) of approximately one decade, J decreases by as much as four decades with increasing N. For N > N₂, the grain Schottky barrier thickness d is less than the grain half-width l/2, the grain surface potential V_s is almost independent of N and the J–V dependence is superlinear. For N₁ < N < N₂, d > l/2, V_s decreases linearly with N, J increases strongly with decreasing N and the J–V dependence is superlinear. For N < N₁, d > l/2. V_s ? V_th ( = kT/q) and J ∝ NV. The phenomenon is used to account for some observed J–V dependencies with column II-chalcogenide and ZnO powder semiconductor systems (electro-optic displays, electrophotographic receptors and heterogeneous catalysts).     

Low-temperature specific heat study of Ni85.5PxB18.5−x (0 ⩽ x ⩽ 18.5) metallic glasses

The low-temperature specific heat (LTSH) of the melt-quenched Ni_81.5P_x^- B_18.5?x amorphous alloy system, with 0 ? x ? 18.5, is presented. The decomposition of the LTSH into magnetic, lattice and electronic contributions shows that both Debye temperature θ_D and electronic specific heat coefficient decrease when the concentration of P increases.The electronic density of states N(E_F), deduced from γ for various Ni-metalloid alloys, is plotted as a function of the average electronic concentration xZ^M, where x is the metalloid concentration and Z^M is the chemical valence of M. Following Malozemoff et al.'s work, this plot is considered as a representation of the band structure and yields the change of the Fermi level with alloying.     

The inverse problem for the third order equation uxxx + q(x)ux + r(x)u = −iζ3u

The spectral problem u_xxx + q(x)u_x + r(x)u = ?iξ³u is considered. A set of spectral data which is sufficient for the reconstruction of the potentials q(x) and r(x) is found and the problem of this reconstruction, this inverse problem solved.