Binary collision expansion and partial green's functions of Kadanoff-Baym

A new formula for the binary collision expansion of the unitary operator U (t₂, t₁) is proposed. The formula is applied to the expansion of the partial Green's functions of Kadanoff-Baym in powers of the correct binary scattering amplitude. It is shown that certain linked diagrams of left-multidentate structure should be taken into account. The duration of the binary collision is seen to play an important role in the rigorous formulation. Upon neglecting this duration, a useful approximation is found for the analysis of correlations on a macroscopic time scale.     

Thermodynamic properties of small extended Hubbard rings

We have obtained the exact numerical results of the specific heat, the susceptibility and the correlation functions L₀(T) and L₁(T) for finite extended Hubbard rings at the large U limit. It is shown that the nearest neighbor interactions favor the ferromagnetic ordering. When the number of electrons is less than the number of sites, the electron hopping results in itinerant magnetism and washes out the high temperature peak (around T = U/k_B) in the specific heat. In all cases, the behaviors of L₀(T) and L₁(T) are consistent with the characteristic features of the specific heat and the susceptibility. Thd exact results are used to test the accuracy of the Roth's decoupling scheme.     

Correlated pairs in the attractive Hubbard model

The attractive Hubbard Model is considered in the strong coupling limits (U?t) by treating the hopping integral, t, as a perturbation. A phase diagram emerges with two critical temperatures: itk_BitT_ct²/U and itk_BT_UU/4. For T<T_c, there is regime of strongly correlated pairs reminescent of superconductivity. For T_c<T<T_U, there is a domain of uncorrelated pairs. For T>T_U, one has a normal metal.     

MacDonald's theorem and Milatz's theorem for multivariate stochastic processes

MacDonald's theorem, which expresses the spectral density of a randomly fluctuating variable α(t) in terms of the finite time average of that variable, α_θ(t), is generalized for multivariate processes. For purely random processes, having a white spectrum, this also yields the corresponding generalization of Milatz's theorem.     

K1-Dominance of the Ke3 form factor and Sirlin's relation

We discuss the precise momentum dependence of the K_e3 form factor f₊(t) by studying some of the recent experimental results on K⁰_L → π^± e^? ν decays. The parametrization of f₊(t) based on the assumption of K¹-dominance can considerably improve the agreement of Sirlin's relation with existing data.     

Correction of a misunderstanding about Olbers' paradox

It is sometimes said that, if the universe were not expanding, we all would burn up, (Olbers' paradox). In order to check on this, I have used a solution of Friedmann's equation that seems reasonable, and that predicts a contraction of the universe after it has reached a maximum size. We may then compare the radiation energy density U _n now at age t _n of the universe, with this density (=U ^* ) at a time t ^* during contraction when R(t) takes a value R ^* equal to its present value R _n .We simplify the calculation by choosing 2R _n as maximum of R(t). Then, t _n=(1/2 π?1)R _n/C=6.98 × 10⁹ year for R _n = 1.16× 10²⁸ cm.(The present density would then be ρ_n = 2.4× 10^?29 gram/cm³).We assume the number of galaxies per unit volume = N(t) = η/R(t) ³ with constant η,and we assume a constant average radiative power L per galaxy. Now at t _n we choose N _n L ≈ 10^?31 erg/cm³sec,but our conclusions would be the same for much larger values of this. We split U into three parts: U ₁ is the primordial energy density left over from t ≈ 0.We put U ₁(t _n ) ≈ 6× 10^?13 erg/cm³ corresponding to T ≈ 3°K.U ₂ is the density of the energy flux near the earth emitted by all stars in our own Milky Way. Most of it is the density U _S =L _⊙/4ηr ² c = 4.5 × 10^?5 erg/cm³ in the flux from the sun. Finally, U ₃ is the energy in the radiation emitted by all other galaxies since t ≈ 0, and was going to burn us according to Olbers. Since U ₁ is a function of R(t), we put U ₁(t^*) =U ₁ (t _n ).We shall also assume U ₂ to be unchanged, as it was not the effect of a change of U _s that we were investigating. In calculating U ₃ we shall overestimate it by neglecting the absorption by closer galaxies of some of the light emitted by farther ones.     

Magnetic properties of tetragonal uranium compounds I. the U2N2Z-ternaries

In the present work we report the magnetic behaviour of the tetragonal ternaries of the U₂N₂Z-type (Z=Sb, Bi and Te). Magnetic susceptibility measurements performed in a wide temperature range (4.2–1000 K) have shown, that they are ferromagnetically ordered with Curie temperatures 166, 154 and 71 K for U₂N₂Sb, U₂N₂Bi and U₂N₂Te, respectively. For all the investigated compounds the κ^-1_M(T) function in the temperature range above T_C can be expressed as (A/T + B)^-1 - λ.Magnetization measurements were carried out up to magnetic field strengths of 140 kOe in the temperature range from 4.2 to the respective T_C. It follows from these measurements that σ(T)_H and σ(H)_T for U₂N₂Sb and U₂ N₂Bi are typical as for normal ferromagnets. On the other hand, U₂N₂Te exhibits, unexpectedly, two distinct maxima on the σ(T) curves up to fields of 4.5 kOe; one at 45 K and the other one at 71 K. Previous neutron diffraction studies of this compound have shown that the magnetic moments of uranium atoms at 4.2 K are titled by about 20° from the basal plane.The results obtained are interpreted in terms of the crystal-field interaction of the 5f² electrons of the U⁴ ion. In consequence a γ_5t doublet is expected to be the ground-state crystal field level in the U₂N₂Z-type as well as in many other ternary uranium tetragonal compounds. However, in the case U₂N₂Te, the singlet-singlet-doublet “band” as a ground system is postulated.     

Positivity and monotonicity properties ofC 0-semigroups. II

IfS _t =exp{?tH},T _t =exp{?tK}, are self-adjoint positivity preserving semigroups on a Hilbert space ?=L ²(X; dμ) we write (*) $$T_t \succ 0$$ ifT _t is positivity improving and (**) $$S_t \succ T_t $$ if the differenceS _t ?T _t is positivity improving. We derive a variety of characterizations of (*) and (**). In particular (*) is valid for allt>0 if, and only if,T _t ∪L ^∞ (X; dμ) is irreducible for somet>0. Similarly if the semigroups are ordered the strict order (**) is valid if, and only if, {S _t ?T _t }∪L ^∞(X; dμ) is irreducible for somet>0. These criteria are used to prove that if (*) is valid for allt>0 then $$e^{ - tf(K)} \succ 0,t > 0,$$ and if (**) is valid for allt>0 then $$e^{ - tf(H)} \succ e^{ - tf(K)} ,t > 0$$ for each non-constantf in the class characterized in the preceding paper. We discuss the decomposition of positivity preserving semigroups in terms of positivity improving semigroups on subspaces. Various applications to monotonicity properties of Green's functions are given.     

Neutron study of a displacive phase transition in N-nitrodimethylamine (DMN): High and low frequency vibrational modes; high pressure effect on the transition temperature; principal compressibilities

N-Nitrodimethylamine is known to undergo a displacive structural phase transition at T_t～107 K, (atmospheric pressure) associated with a soft-mode observed in the low temperature phase Raman spectrum.The soft-model has already been assigned to a lattice vibration although crystallographic observations of the symmetry breaking distortion suggest that a coupling with an internal vibration should not be ruled out. To clarify this point neutron inelastic spectra have been recorded. They lead to a better assignment of both the high and low frequency vibrations and to the conclusion that no softening of an intramolecular mode is visible.High pressure (up to 3.5 Kbars) neutron scattering experiments are also described. They give both the directions and magnitudes (k₁=0.33× 10^?2, k_b=1.17 × 10^?2, k₃ = 0.12× 10^?2Kbar^?1) of the isothermal principal compressibilities of DMN and the dependence of T_t on pressure ((dT_t/dP)_P=0 ～ + 4.3 Kbar^?1). Spectroscopic and crystallographic data now available on DMN allow us to discuss the mechanism of the transition. An extension of Samara's rule to molecular crystals is attempted     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Universal Covering Group of U(n) and Projective Representations

Using fiber bundle theory, we construct the universal covering group of U(n),U(n), and show that U(n) is isomorphic to the semidirect product SU(n) ∝.We give a bijection between the set of projective representations of U(n) and theset of equivalence classes of certain unitary representations of SU(n) ∝.Applying Bargmann's theorem, we give explicit expressions for the liftings ofprojective representations of U(n) to unitary representations of SU(n) ∝. Forcompleteness, we discuss the topological and group theoretic relations betweenU(n), SU(n), U(t), and Z _n .     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Spin relaxation of conduction electrons in GaAs

We have used optical spin orientation techniques to measure T₁ of conduction electrons in GaAs (NinA ≈ 10¹⁷ cm^-3) for 4.7 K ? T ? 200 K. From Hall effect measurements we estimated the electron momentum relaxation time τ_p. For 50 K ? T ? 200 K, the product T₁τ_p agrees with our earlier order of magnitude estimate of the D'yakonov-Perel' mechanism, in which band structure induced precession is strongly narrowed by momentum relaxation. The Elliott mechanism is one to two orders of magnitude weaker.     

Operator equivalents in general

We show that recent criticism of a formula for diagonal operator equivalents (OE's) is unfounded. We generalise this formula to derive off-diagonal OE's ^jT_l^m, as a finite polynomial in J_Z, and claim that this is a definitive formula for the ^jT_l^m.     

Time dependence of isothermal magnetization in single-phase B1 MoCy encapsulated in multiwall carbon nanocages

Isothermal magnetization M(t) in nanocrystalline single-phase B1 MoC_y encapsulated in multiwall carbon nanocages is studied within the time window of 100 < t < 5000 s. The current density J exhibits a linear logarithmic time decay. The effective activation energy U_eff increases linearly with increasing temperature T, and decreases linearly with increasing J. The behaviors of J(t), U_eff(T), and U_eff(J) can be described by the Anderson–Kim flux-creep model for thermally activated motion of uncorrelated vortices or vortex bundles over a net potential barrier U_eff. The slower relaxation of current density above the broad peak field in the isothermal magnetization curves suggests that the peak is a result of vortex dynamics.     

Uniqueness Result in the Cauchy Dirichlet Problem via Mehler Kernel

Using the Mehler kernel, a uniqueness theorem in the Cauchy Dirichlet problem for the Hermite heat equation with homogeneous Dirichlet boundary conditions on a class P of bounded functions U(x, t) with certain growth on U _x (x, t) is established.     

Gamma-ray-L-x-ray directional correlations in182W

Directional correlations between gamma radiation andL x-rays in¹⁸²W have been measured. The x-rays are emitted following the internal conversion process of the 100.1 keV 2⁺ → 0⁺ transition. The experimental results for anisotropies involving gamma radiation emitted in the 1189.0 keV transition andL x-rays are A(γ?L _l )=?0.073(27),A(γ?L _α)=?0.0102(45),A(γ?L _β)=?0.0031(35), andA(γ?L _γ)=?0.007(13). The value deduced for the coefficientU ₂(e) pertaining to the converted transition isU ₂(e)=0.52(8) in reasonable agreement with the theoretically expected value 0.410. A note is given on the use of internal conversion radial matrix elements.     

Magnetic relaxation near a fishtail peak of isothermal magnetization in B1 NbCy encapsulated in multiwall carbon nanocages

Isothermal magnetization near a fishtail peak in nanocrystalline B1 NbC_y encapsulated in multiwall carbon nanocages is studied within the time window of 100 < t < 4000 s. The current density J exhibits a linear logarithmic time decay. The effective activation energy U_eff increases linearly with temperature T and is independent of applied magnetic field H. The results of J(t) and U_eff (T, H) are consistent with the Anderson–Kim flux–creep model for thermally activated motion of uncorrelated vortices or vortex bundles over a net potential barrier U_eff. U_eff at a fishtail peak field H_fp evolves quickly above a fishtail peak temperature T_fp, but slowly below that temperature. The result suggests that a decrease of flux viscosity coefficient above T_fp at H_fp is the origin of the fishtail peak in nanocrystalline B1 NbC_y encapsulated in multiwall carbon nanocages.     

The Bose-Einstein condensation in a finite one-dimensional homogeneous system of noninteracting bosons

Condensation of the ideal Bose gas in a closed volume having the shape of a rectangular parallel-epiped of length L with a square base of side length l (L ? l) is theoretically studied within the framework of the Bose-Einstein statistics (grand canonical ensemble) and within the statistics of a canonical ensemble of bosons. Under the condition N(l/L)⁴ ? l, where N is the total number of gas particles, dependence of the average number of particles in the condensate on the temperature T in both statistics is expressed as a function of the ratio t=T/T ₁, where T ₁ is a certain characteristic temperature depending only on the longitudinal size L. Therefore, the condensation process exhibits a one-dimensional (1D) character. In the 1D regime, the average numbers of particles in condensates of the grand canonical and canonical ensembles coincide only in the limiting cases of t → 0 and t → ∞. The distribution function of the number of particles in the condensate of a canonical ensemble of bosons at t ≤1 has a resonance shape and qualitatively differs from the Bose-Einstein distribution. The former distribution begins to change in the region of t ～ 1 and acquires the shape of the Bose-Einstein distribution for t ? 1. This transformation proceeds gradually that is, the 1D condensation process exhibits no features characteristic of the phase transition in a 3D system. For N(l/L)⁴ ? 1, the process acquires a 3D character with respect to the average number of particles in the condensate, but the 1D character of the distribution function of the number of particles in the condensate of a canonical ensemble of bosons is retained at all N values.     

Antiferromagnetic phase of the Hubbard model

Hubbard's alloy analogy is applied to the antiferromagnetic phase of the Hubbard model. At large U/W it is found that kT_N ～ W²/U.