Phase transition and phonon-drag conductivity in quasi-unidimensional systems

We investigate the properties of a quasi-unidimensional system which exhibits Peierls instability at T_c(μ), where μ is the Fermi energy as measured from the middle of the conduction band. T_c(μ) decreases as 6μ6 increases. The phonon-drag diagrams contribute to fluctuation conductivity, which is proportional to $\text{(T ? T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, if |μ| > 1.056 T_c(0). The Kohn Anomalies do not occur at 2k_F unless μ = 0 or |μ| ? T.     

A Landau theory of the Peierls-BCS transition

We introduce a Landau type theory of the Peierls instability-superconductor transition involving two complex order parameters. Under a particular inequality condition among expansion parameters, the theory predicts that the superfluid conductivity should vary as $\text{(T?T}{}_{\mathrm{<mtext>c</mtext>}}\text{)}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ above the critical region and as $\text{(T}{}^1{}_{\mathrm{<mtext>c</mtext>}}\text{?T)}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ below the critical region.     

Functional derivative δTc/δα2 (Ω)F(Ω) for weak coupling superconductors

We present approximate analytic calculation of the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω)}$, where T_c is the superconducting critical temperature and $\text{α}{}^2\text{(Ω)F(Ω)}$ is the electron-phonon spectral function, within the “square-well model” for the phonon mediated electron-electron interaction and weak coupling limit $\text{ω}{}_{\mathrm{D}}\text{(2πT}{}_{\mathrm{c}}\text{)? 1 (ω}{}_{\mathrm{D}}$ is the Debye energy). It is found that $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω) = (1 + λ)}{}^{-1}\text{G(Ω)}$ where λ is the familiar electron-phonon coupling parameter and $\text{G(Ω)}$ is a universal function of the reduced frequency $\text{Ω}\text{=}\text{Ω}\text{T}{}_{\mathrm{c}}$. We compare this formula with accurate numerical results for several weak coupling superconductors. The overall agreement is good     

Softening of acoustic and optical modes in ferroelastic phase in Hg2Br2

The softening of an acoustic and an optical phonons in Hg₂Br₂ has been investigated by means of the light scattering technique.It has been observed that the cube of the frequency of the soft optical phonon varies proportionally with the temperature below T_c.An expression for the relation of the elastic constant C₆₆ to the temperature has been derived from the phenomenological thermodynamic potential function. The observed temperature dependence of the elastic constant and the optical phonon frequency is described when we assume that the order parameter Q varies as $\text{Q ∝ [T ? T}{}_0\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>6</mtext>}}$.     

Depinning by thermal fluctuations of the charge density wave in Peierls Fröhlich state

It is shown that the thermal fluctuations depin the charge density wave of the Peierls Fröhlich state pinned by impurities at absolute zero temperature. The critical temperature, T_d, of this depinning is estimated as $\text{T}{}_{\mathrm{d}}\text{= 0.55√}\text{m}{}^1\text{mγ}{}_0$ where m¹ and γ₀ are the mass of the collective mode and the pinning frequency at T = 0.     

Deuteron optical model calculations including a Tp tensor interaction

Deuteron-nucleus optical model calculations which include two types of tensor spin-orbit interactions are compared. The interactions considered are of the forms $\text{V}{}_{\mathrm{<mtext>T</mtext><mtext>R</mtext>}}\text{(r)T}{}_{\mathrm{r}}\text{and}\text{1}\text{2}\text{[V}{}_{\mathrm{<mtext>T</mtext><mtext>P</mtext>}}\text{(r)T}{}_{\mathrm{p}}\text{+ T}{}_{\mathrm{p}}\text{V}{}_{\mathrm{<mtext>T</mtext><mtext>P</mtext>}}\text{(r)]}$ where the operators T_r and T_p are defined as $\text{T}{}_{\mathrm{r}}\text{ (}\text{s}\text{·}\text{r}\text{?}\text{)}{}^2\text{?}\text{2}\text{3}\text{and}\text{T}{}_{\mathrm{p}}\text{ (}\text{s}\text{·}\text{p}\text{)}{}^2\text{?}\text{2}\text{3}\text{p}{}^2$. Here, $\text{s}\text{,}\text{r}\text{and}\text{p}$ are the deuteron spin, position, and momentum operators, respectively. If a physically reasonable radial dependence V_TP(r) is used, the S-matrix elements (and hence all observables) calculated using a T_p tensor potential are found to be similar to those calculated using a suitably chosen T_r potential, provided that the incident deuteron energy is small compared to the real central potential. At higher deuteron energies, the differences between the effects of T_r and T_p potentials are more pronounced.     

The law of corresponding states for metals

Using the similarity of the effective potentials seen by ions in metals a reduced phonon equation of state is derived. It is shown that the melting point T_m(0) and the atomic volume Ω₀ at T = 0 K and at p = 0 are suitable macroscopic parameters for scaling ? and σ characterizing the interatomic potentials of metals having similar structures. The temperature and pressure dependence of thermodynamical quantities reduced with the above parameters are discussed and the results are compared with the experiment. It is shown that the pressure dependence of the reduced thermodynamic quantities can be described by the pressure dependence of the scaling parameters T_m(p) and Ω₀(p).The general form of the reduced equation of state (containing the electronic contributions as well) obtained gives that the reduced pressure is a universal function of the following reduced variables: the volume, temperature, de Broglie wavelength, Gibbs free energy of electrons $\text{3}\text{5}\text{zE}{}_{\mathrm{fo}}\text{?}$ (E_fo is the Fermi energy at T = 0 K) and depe of the valence z as well. It is shown that $\text{E}{}_{\mathrm{fo}}\text{?}$ is a function of $\text{Ω}{}_{\mathrm{o}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ and $\text{(}\text{E}{}_{\mathrm{fo}}\text{/?}\text{)Ω}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is approximately constant within the same sub-group of the periodic table.     

Brillouin study of acoustic phonon softening and optical absorption coefficients of ultraheavily doped n-Si

The self-energies of acoustic phonons in ion implanted and laser annealed ultraheavily doped n-type Si have been measured by Brillouin scattering. The corresponding softening of the elastic constants has been estimated from the observed phonon softening and compared it with theory. At high doping levels ($\text{N}{}_{\mathrm{e}}\text{≧ 10}{}^{21}\text{cm}{}^{-3}$) the effect of the increase in atomic mass on the phonon frequency is observed in the case of doping with As. From the increase in the linewidths of the Brillouin lines with doping, the optical absorption coefficients for $\text{λ = 5145}\text{A}\text{?}$ as a function of doping are determined.     

Magnetic circular dichroism of transition metal ions in solids—II K2NaGaF6: Cr3+

The absorption and MCD spectra of the ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{a}}$ and ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{b}}$ spin-allowed transitions of Cr³⁺ in K₂NaGaF₆ are reported. It is shown that transitions to the ${}^4\text{T}{}_{\mathrm{1g}}$. states are induced by T_1u vibratio the other spin-allowed transition, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, there are three competing intensity mechanisms: electric dipole induced by T_1u vibrations, electric dipole induced by T_2u vibrations and magnetic dipole, and an estimate is made of the relative importance of these. The magnetic dipole ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^2\text{E}{}_{\mathrm{g}}$ zero-phonon line is observed to be accompanied by a vibrational sideband for which the coupling is predominantly with T_2u vibrations. Other weak transitions are observed in MCD spectra and their origin briefly discussed.     

Theory of hopping conduction in two-dimensional impurity band under strong magnetic field

It is shown that the low-temperature conductivity in two-dimensional impurity band of n-type inversion layer under strong magnetic field is $\text{σ}{}_{\mathrm{xx}}\text{(}\text{min}\text{)=σ}{}_0\text{exp}\text{[?(}\text{T}{}_0\text{T}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{]}$. Therefore the effective conductivity of inversion layer $\text{σ}{}_{\mathrm{<mtext>eff</mtext>}}\text{=}\text{σ}{}^2{}_{\mathrm{xy}}\text{σ}{}_{\mathrm{xx}}\text{(}\text{min}\text{)}$ at Shubnikov-de Haas conductivity minima may be very high at low temperature.     

Pressure dependence of superconductivity in the pseudo-one-dimensional compound Tl2Mo6Se6

Measurements of the temperature and pressure dependences of the resistivity of the pseudo-one-dimensional ternary compound Tl₂Mo₆Se₆ are presented. We find that the conductivity parallel to the highly conducting c-axis is enhanced by pressure and the superconducting transition temperature T_c is suppressed by pressure at a rate $\text{?T}{}_{\mathrm{c}}\text{?P}\text{=?7.6×10}{}^{\mathrm{?5}}$ kbar^?1. These results are discussed in relation to the current models of transport in one-dimensional conductors.     

Electron-phonon interaction in superconducting Nb

Acoustic phonon damping in Nb due to superconductivity is accurately measured by the inelastic neutron scattering technique. The phonon line widths can be characterized by the reduced parameters $\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{/2Δ(0)}$ and T/T_c, and are in good qualitative agreement with the calculation by Bobetic based on the BCS theory.     

The measurement of the rotational relaxation times of OCS from the nutation signals

The time dependence of microwave absorption was measured for the J = 2-1 and J = 3-2 transitions of OCS under on- and off-resonant conditions utilizing Stark and source modulation, respectively. The two effective pressure parameters obtained under the two conditions, which correspond to $\text{(T}{}_2{}^{\mathrm{?1}}\text{+ T}{}_1{}^{\mathrm{?1}}\text{)}\text{4πP}$ and $\text{(2πT}{}_2\text{P)}{}^{\mathrm{?1}}$, respectively, according to the Bloch equation, are different beyond experimental error; the difference $\text{(T}{}_2{}^{\mathrm{?1}}\text{? T}{}_1{}^{\mathrm{?1}}\text{)}\text{2πP}$ is 0.94 ± 0.38 (2.5σ) MHz/Torr for J = 2?1. This difference was also determined to be 1.19 ± 0.30 MHz/Torr from the dependence of the nutation frequency on the microwave power.     

Self-adjointness of the minimal Schrödinger operator with potential belonging to L1, loc

Let $\text{0 ?q(x) ∈L}{}_{\mathrm{1,loc}}\text{(}\text{R}{}^{\mathrm{m}}\text{)}$,m? 1.Consider the operatorT₀ = ?Δ+q with domain consisting of all bounded measurable functions $\text{u(x), x ∈}\text{R}{}^{\mathrm{m}}$, having bounded support, for which the distribution ?Δu+qu belongs to $\text{L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The main result of the paper is essential self-adjointness of $\text{T}{}_0\text{in L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The proof is independent of a method due to Kato who recently established the self-adjointness of a maximal Schrödinger operator corresponding to such potential.     

Features of dynamically broken gauge theories

We discuss several features of dynamical symmetry breaking in gauge theories of strong, weak and electromagnetic interactions. We speculate that in some such theories the fine structure constant calculable. A possible solution of the strong P and T violation problem in QCD by dynamical symmetry breaking is indicated. Self-energy divergences are absent in such models and we compute the finite electromagnetic self-energy of a quark in QCD. The mass hierarchy problem is examined. We find models in which the fermion-gauge boson mass ratio is $\text{M}{}_{\mathrm{<mtext>F</mtext>}}{}^2\text{M}{}_{\mathrm{<mtext>B</mtext>}}{}^2\text{～}\text{exp}$ ($\text{?1}\text{g}{}^2$), where g is a gauge boson coupling, which could account for the origin of weak interactions.     

Hard core phonon frequency at transition temperature

A simple theoretical derivation is given to show that one may expect a hard core for the phonon frequency at the transition temperature. This approach implies that the frequency of the phonon will follow $\text{ω ∝ {[1 + γ(T ? T}{}_{\mathrm{<mtext>C</mtext>}}\text{)] V}{}_0\text{}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ instead of that predicted by soft mode theory. Our expression should be valid whenever a Brownian sublattice exists in the crystal.     

The particle-hole spectra of 16O and 16N as observed in pick-up reactions from 17O

The reactions ¹⁷O(d, t) ¹⁶O and ¹⁷O(d, τ)¹⁶N have been investigated at E_d = 52 MeV. Energy spectra of tritons and τ-particles have been measured simultaneously up to excitation energies of 22 MeV in ¹⁶O and 10 MeV in ¹⁶N, respectively. Spectroscopic factors have been obtained by a DWBA analysis of the measured angular distributions. From the comparison of the t- and τ-spectra analog (T = 1) states in ¹⁶O could be identified and the distribution of T = 0 and T = 1 spectroscopic strengths could be deduced. Nearly the total $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ hole strengths have been found and the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{and}\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ particle-hole multiplets could be located both for T = 0 and T = 1. The average residual interactions in both shell-model configurations turned out to be strikingly different.     

Semi-inclusive scaling for largepT events

We consider semi-inclusive reactions of the type p + p → (particle with large p_T) + n charged particles + neutrals, and propose the following scaling law

$\text{E}\text{d}{}^3\text{σ}{}_{\mathrm{n}}\text{d}{}^3\text{p}\text{=}\text{1}\text{(}\text{s}\text{)}{}^{\mathrm{k+1}}\text{H}{}^{\mathrm{2p}}\text{T}\text{s}\text{,}\text{n}\text{s}$

for the distribution function of the large-p_T particle produced in association with n charged particles. This scaling rule is shown to be consistent with present information on single-particle spectra and average associated multiplicities at large p_T. Also, we show that if the associated multiplicity were to continue to increase linearly with p_T, then moments of the multiplicity distribution would increase like powers of s.     

Central peak in polaronic crystals

A possibility of the central peak appearance in crystals with low concentration of small-radius polarons is pointed out. The intensity of the central peak increases sharply with the softening of the phonon mode $\text{(ω}{}_{\mathrm{<mtext>K</mtext><mtext>0</mtext>}}\text{→ 0)}$ in the vicinity of the structural phase transition . The peak width γ₀ is determined by the probability W of the polaron hopping between the sites γ₀ = K₀²a²W.