Theory of transient two-photon resonant up-conversion with non-synchronized excitation

The theory of the two-photon resonant up-conversion process (ω_a + ω_a) + ω_c ? ω_d is developed for short pulse excitation. Prominence is given to the case where the pulse at frequency ω_c is not time-synchronized with the pulse ω_a but travels immediately behind it. Not only is the conversion efficiency thereby maximized, but the associated theoretical simplification enables several analytical formulae to be derived which provide new insight into the mechanism of resonant non- linear interactions. In particular, an expression is derived for the maximum useful energy per unit area of the pulse at ω_c. Exceeding this value is of little or no advantage in the non-synchronized case and is positively detrimental when the a- and c-pulses are coincident. The results are supported by computer solutions.     

Lattice hydrodynamic model with bidirectional pedestrian flow

The two-dimensional lattice hydrodynamic model of traffic is extended to the two-dimensional bidirectional pedestrian flow via taking four types of pedestrians into account. The stability condition and the mKdV equation to describe the density wave of pedestrian congestion are obtained by linear stability and nonlinear analysis, respectively. In addition, there exist three phase transitions among the freely moving phase, the coexisting phase and the uniformly congested phase in the phase diagram. It can also be found that the critical point a_c refers to not only the fraction c₁ of the eastbound and westbound pedestrians, but also the fraction c₂ of the northbound and southbound pedestrians. However, the critical point a_c could not appear in the phase diagram and congested crowd at any time when two fractions are equal to same value of 0.5 (c₁=c₂=0.5). Furthermore, numerical simulation is carried out to examine the performance of such a model and the results show coincidence with the theory analysis results.     

Elastic constants of 2H-MoS2 and 2H-NbSe2 extracted from measured dispersion curves and linear compressibilities

Recent neutron data on the dispersion curves and X-ray measurements of the linear compressibilities of the 2H polytypes of MoS₂ and NbSe₂ have been used to obtain approximate values of the five independent elastic constants of these materials. In the case of NbSe₂ sufficient information is available to over-determine the elastic constants and the results are self consistent within estimated uncertainties, although the uncertainties are especially large for c₃₃ and c₁₁. Additional related considerations such as Debye temperatures and model calculations of c₃₃, and c₄₄ are also made. It is found that there is significant and unexplained disagreement between the value of the low temperature specific heat Debye temperature of NbSe₂ and the value determined on the basis of the elastic constants, but that the model predictions of c₃₃ and c₄₄ are in satisfactory agreement with the values extracted from the neutron data for both MoS₂, and NbSe₂.     

Interacting Frenkel defects at high concentration and the superionic transition in fluorite crystals

A spherical cell model is proposed to account for the explicit concentration dependence of Frenkel defects in an ionic system. In the model, the linearized Debye-Hückel equation is soluble exactly, subject to the boundary condition that the electric field is zero at the cell boundary R, related to the concentration c of defects by $\text{R ∝ c}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$This screened field is used to calculate the chemical potential, which in turn leads to a condition for the instability of the interacting defect assembly. This condition allows one to calculate the enhancement of the concentration of defects above its Arrhenius value at the point of instability in terms of (a) the critical concentration c₀, (b) $\text{a}\text{R}$, where a is the radius of defect and (c) the Debye-Hückel screening length k_c.It is clear from the cell model that this enhancement factor is reduced somewhat in the relevant range of parameters in some of the fluorites from its value in extended Debye-Hückel theory. It is anticipated that the instability discussed here should afford an upper bound to c_v, at the superionic transition, within the range of validity of the model. The excess heat capacity c_p is also discussed briefly.     

Coulomb repulsion-induced hyperbolic pairing as a mechanism of high-T c superconductivity

The hyperbolic metric of the dispersion law (the effective mass tensor components of carriers are opposite in sign) in the vicinity of the Fermi contour in high-T _c superconducting cuprates in the case of repulsive interaction gives rise to a superconducting state characterized by the condensate of pairs with a large total momentum (hyperbolic pairing). The gain in the energy of the superconducting state over the normal state is due to the fact that a change in the kinetic energy of pairs (because of the negative light component of the effective mass) dominates over the change in the potential energy (corresponding to energy loss). The shift of the chemical potential upon the transition to the superconducting phase is substantial in this case. With increasing repulsive interaction, the superconducting gap δ_K increases and the resulting gain in energy changes to an energy loss at a certain critical value of the repulsive potential. The low temperature T _c of the superconducting transition and the large value of δ _K in this region of potential values are the reasons for the high value of the 2δ_K/T _c ratio and for the developed quantum fluctuations that are observed in underdoped cuprate superconductors.     

New determination of the neutron-proton scattering amplitude and precise measurements of the scattering amplitudes on carbon,chlorine, fluorine and bromine

After an improvement on the theory of the neutron-gravity-refractometer and after refinements of the experimental procedure we have performed new measurements of the absolute value of the neutron-proton scattering amplitude at low neutron energies. In order to obtain and to confirm a very high accuracy we carried out neutron-reflection experiments on 18 various liquids of 11 different organic substances containing the elements carbon, hydrogen and/or chlorine. Compounds with fluorine and bromine were used to measure the scattering amplitudes of these elements. We found the coherent scattering amplitudes of the bound atoms to be:a _H=?3.7409(1l)fm,a _c=6.6484(13)fm,a _c1=9.5792(8)fm,a _F=5.66(2)fm anda _Br=6.79(2)fm. The low energy (n, p)-parametersa _t anda _s were calculated with the presenta _H and a new value of the (n, p) scattering cross-sectionσ ₀. By comparing the measureda _C with values obtained from precise transmission experiments we could determine the gravitational accelerationg _f of the free neutron in terms of the local value g. We found the two values to be equal:g _f =0.9996(7)g.     

Elastic properties and phonon dispersions of rhenium in hexagonal-close-packed structure under pressure from first principles

The elastic properties of the hexagonal-close-packed (hcp) structure rhenium (Re) and their behavior under pressure are investigated using the local density approximation (LDA) and the generalized gradient approximation (GGA). The obtained high pressure elastic constants are well consistent with previous theoretical date, while large discrepancies are found between theory and the high pressure experiments. The calculated isothermal bulk modulus B₀ (376 GPa for GGA and 389 GPa for LDA) and its initial pressure derivative (4.52 for LDA and 4.58 for GGA) compare favorably with the experimental values. Moreover, it is found that the value of c/a, B/G, Poisson's ratio, and B_c/B_a are virtually independent of pressure. We also performed calculation for phonon dispersions at high pressure. GGA in our calculation exhibits a same trend as the high pressure experimental curve.     

Macroscopic behaviour of ferromagnets with random and statistically vanishing anisotropy

A model is defined in which the anisotropy tensor is a random function of space point characterised by its mean square value σ and a correlation lenght a_c, and the exchange density A is uniform. If the magnetic moment density is M, it is shown that two dimensionless numbers can be defined a_c/a_p, where a_p is a typical Bloch wall width$\text{(}\text{A}\text{δ}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and 4πM²/σ they define four types of macroscopic behaviour. For 4πM²/σ<1, the pole fields are a perturbation; if a_c<a_p, as in rare earth amorphous alloys, there is some frustration in the ground state and if a_p <a_c, as in inhomogeneous weak ferromagnets the magnetization direction is mainly fixed by the local anisotropy. For 4πM²/σ#62; 1, as in iron alloys, if a_p#62;a_c one has the case of soft alloys, the shape anisotropy is the dominant effect and if a_p<a_c the usual domain theory applies.     

Entanglement Teleportation Via Two-Qubit Channel Under the Non-Markovian Environment

Entanglement teleportation via a two-qubit quantum channel under the non-Markovian environment is investigated in detail. We mainly concentrate on the effects about the channel initial states and decoherence environment on the entanglement of the output state C _out and the average fidelity F _a. It is shown that for different channel initial states with increasing noise environment parameters the teleportated entanglement is initially decreased from the maximum value to a minimum value and then undergoes a increasing tendency finally to be one constant nonzero value. The average fidelity is strongly dependent on the channel initial states and the Non-Markovian environment, tuning these parameters can make the average fidelity larger than the maximum value of classical communication 2/3. Moreover, there is a threshold time t _c , when t<t _c the average fidelity is always superior to 2/3, tuning the environment parameters and channel initial states not only can make F _a superior to 2/3 but also can broaden the region where F _a is larger than 2/3. We also obtain the analytic solution values of t _c in the limit case of γ→∞ where the non-Markovian environment reduced to the Markovian one.     

Quantum phase transition in the anisotropic one-dimensional XY model with long-range interactions

In this paper we study the one-dimensional XY model with single ion anisotropy and long-range interaction that decay as a power law. The model has a quantum phase transition, at zero temperature, at a critical value D_c of the anisotropy parameter D. For values of D below D_c we use a self-consistent harmonic approximation. We have found that the critical temperature increases with D for small values of this parameter. For values of D above D_c we use the bond operator technique and calculate the gap as a function of D, at zero temperature.     

Diffusion cooling in neon,argon, and krypton afterglow plasmas

Measurements are reported of ambipolar diffusion coefficients as determined from ion density loss rates, and of electron temperatures determined using the single Langmuir probe technique, in afterglow plasmas of spectroscopically pure neon, argon and krypton. In each gas there was a critical pressure,p _{0 c} , above which the product of the ambipolar diffusion coefficient,D _a , and the reduced gas pressure,p ₀, was pressure independent and above which the electron temperature was found to cool asymptotically to the gas temperature. For pressures belowp _{0 c} ,D _a p ₀ decreased with decreasing pressure, and the electron temperature cooled asymptotically to a steady equilibrium value,T _eq, below the gas temperature, this equilibrium value itself decreasing with decreasing gas pressure. These results clearly show that diffusion cooling of electrons was taking place at these low gas pressures. A detailed study of the krypton afterglow showed that the values ofD _a p ₀ andT _eq for a given gas pressure were related in a manner predicted by simple diffusion theory. During the course of these measurements values for the zero field mobilities of Ne⁺, Ar⁺ and Kr⁺ ions in their parent gases were obtained and are also reported.     

Some parameters of superconductors with an extreme singularity in the density of state: (s+d) model

We study some parameters of superconductors with δ-function type singularities in the electronic density of states (DOS), exhibiting (s+d)-wave symmetry of the order parameter. Starting with a pure s-wave pairing potential V_s, the critical temperature T_c at first slightly increases with increasing the d-wave interaction potential V_d, being determined by this interaction only for stronger V_d values. The ratio R=2|Δ(0)|/k_BT_c of the mean value of the zero temperature energy gap |Δ(0)| to T_c increases with increasing V_d, reaching a maximum which depends on the mixing interaction term. The maximum values of R are comparable with very high values obtained in some gap measurements. The jump in the specific heat at critical temperature is by a factor 2.4 higher for the extreme singularity of pure s-wave symmetry, as compared with the BCS theory with constant DOS. Such higher values of the jump are in agreement with the experimentally observed values, as well as with the calculations determined by extended saddle points in the electronic bands. By switching the d-wave channel, the value of the jump decreases. The results show the usefulness of calculations with δ-type singularities as a limiting case of very strong singularities in the DOS.     

Relationship between superconducting transition temperature and number of CuO2 layers in mercury-based superconductors

The nonmonotonic dependence of the superconducting transition temperature on the number of CuO₂ layers (n) per unit cell for mercury-based cuprate systems is investigated with the framework of the electrostatic model and the Ginsburg-Landau theory. It is found that the largest value of the normalized density of states is 1.8 when n = 3, which corresponds to the highest T_c in this series. Using reasonable parameters we predict an upper limit of T_c of 160 K.     

Head-on and head-off collisions of discrete breathers in two-dimensional anharmonic crystal lattices

The ground-state phase diagram of the extended Falicov-Kimball model with f-f electron hopping is studied numerically in the one-dimensional case. To identify the nature of ground states three complementary numerical methods are used, and namely, (i) the small-cluster exact-diagonalization method, (ii) the density-matrix-renormalization-group method (DMRG) and (iii) an approximate, but very accurate, numerical method based on the reduction of the Hilbert space. It is found that the physics of the Falicov-Kimball model found for the zero value of the f-electron hopping integral t _f (including the existence of the devil’s staircase structure) persists also at finite values of t _f . The critical values of t ^c _f below which the physics of the Falicov-Kimball model dominates are calculated numerically and it is shown that they depend very strongly on the f-electron concentration n _f and only very weakly on the Coulomb interaction. In particular, we have found that for strong Coulomb interactions the value of t ^c _f rapidly increases from t ^c _f ~ 0.003 found for n _f = 1 / 4 up to relatively large t ^c _f ~ 0.4 found for n _f near the half-filled band case n _f = 1 / 2. In addition, the complete picture of valence transitions is presented for non-zero t _f and strong Coulomb interactions.     

Anomaly in the nuclear curvature energy

By use of semiclassical mean-field methods, we study the dependence of the curvature-energy coefficient and other surface properties of nuclear matter upon the energy-density functional. This is done both by solving the Euler-Lagrange equation with a simplified phenomenological functional and by obtaining a variational solution with a fourth-order extended Thomas-Fermi functional. The calculated curvature-energy coefficient a_c decreases with increasing value of the bulk nuclear incompressibility coefficient K for physically relevant values of K, but always remains larger than 3 MeV in either approach when the volume-energy coefficient, saturation density, surface-energy coefficient and surface diffuseness are constrained to their experimental values. The calculated values of the curvature-energy coefficient a_c are significantly larger than experimental values obtained from analyses of fission-barrier heights and ground-state masses of nuclei throughout the periodic table. Among possible resolutions of this anomaly, we suggest that relativistic effects or correlations may play a significant role in the nuclear surface, or that the leptodermous expansion may break down in regions of large curvature, such as occurs for highly deformed shapes and for light nuclei.     

Quantum critical phenomena, entanglement entropy and Hubbard model in 1d with the boundary site with a negative chemical potential −p and the Hubbard coupling U positive

Recently the ground state and some excited states of the half-filled case of the 1d Hubbard model were discussed exactly for an open chain with L sites. The case when the boundary site has the chemical potential −p and the Hubbard coupling U is positive was considered. We model CeAl₂ nanoparticles, in which a valence of 4f electron number changes on surface Ce atoms, by this Hubbard model. A surface phase transition exists at some critical value pc3 of chemical potential (its absolute value) p in the model; when p<pc3 all the charge excitations have the gap, while there exists a massless charge mode when p>pc3. The aim of this Letter is to find whether this surface phase transition is of the first order or of the second order. We have found that the entanglement entropy and its derivative has a discontinuity at pc3 in general and thus this transition is of the first order (with exception of two points for the probability w₂ of occurrence of two electrons with opposites spins on the same site). There is a divergence in the difference of entanglement entropy for points w₂=0 and . The first point w₂=0 corresponds to ferro- (antiferro-) magnetic state at half-filled case. The second point does not correspond to any state for halffilled case. In the first case there is present the surface phase transition of the second order type.     

The contribution of color-octet current color-octet current toD decays

Bauer and Stech pointed out that inD decaysa ₁ anda ₂ are approximately equal toc ₁ andc ₂ obtained from the renormalization group equation. This means that the non-leading 1/N _c term in the formulation vanishes. Many authors conjecture that there is a cancellation between the 1/N _c term and an extra <λ ^a λ λ ^a > term emerging from the analysis of non-factorizable matrix elements. We employ the hybrid MIT bag model to estimate the cancellation effects and find that the ratio of <λ ^a λ λ ^a > over the 1/N _c term is about ?0.16～?0.24 which is 2～3 times smaller than the value from data fitting.     

Two-dimensional and layered structures in the discrete φ4 model

The properties of phase transitions in two-dimensional and layered systems are investigated on the basis of a discrete φ⁴ model by numerical and analytical methods. The only parameter a of the discrete φ⁴ model determines the behavior of the system and makes it possible to investigate phase transitions ranging from transitions of the displacement type (a → +0) to order-disorder type (a → +∞). The behavior of a two-dimensional system is investigated in a wide range of values of the parameter a. The temperature dependences of the squared order parameter η²(T) and the phase transition temperature T _c as a function of the thickness N of the system are obtained for three characteristic values of the parameter a using the Monte Carlo method. The properties of phase transitions in the discrete φ⁴ model are investigated on the basis of the mean-field approximation and the independent-mode approximation. The results obtained in the numerical experiments are compared with the analytical approximations. It is shown that the mean-field approximation qualitatively describes the behavior of the phase-transition temperature T _c as a function of the thickness N of the system for a wide range of values of the parameter a, and the independent-mode approximation describes quantitatively, to within 5%, the results of the numerical simulation for small values of a.     

Metal insulator transition due to surface roughness scattering in a quantum well

We calculate the critical width a_c for a quantum well structure as function of the two-dimensional electron density. For a > a_c the electron gas has a finite dc conductivity at temperature zero, and for a < a_c the dc conductivity is zero. Homogeneous background doping, remote doping, and surface roughness scattering are considered. Due to surface roughness we find a strong increase of a_c at high electron concentration, in novel contrast to heterostructures. Explicit results are presented for GaAs and InAs quantum wells and compared with experimental results. Experiments are suggested to test the predictions of the localization theory.     

Third-order elastic constants for 2:2 chalcide crystals possessing the sodium chloride structure

Third-order elastic constants of 45 chalcide crystals having the sodium chloride structure are reported using Born-Mayer potential model. We have considered repulsive interaction up to second nearest neighbours. The temperature coefficients of the third-order elastic constants have also been computed for these crystals. As is the case for NaCl-type alkali halides we find that C₁₁₁, C₁₁₂, C₁₆₆ are negative and C₁₄₄ are positive for 2:2 chalcide crystals possessing the NaCl-type structure. We have found that a₁₂₃, a₄₅₆ and a₁₄₄ are negative whereas a₁₁₂ and a₁₆₆ are positive, once again in agreement with the situation found for the alkali halides a₁₁₁ values are positive for alkali halides whereas they are both positive and negative depending upon the interionic distance for the chalcide crystals. We have found that the nature of the variation of C⁰_αβγ with interionic separation is similar for alkali halides and for the 2:2 chalcides having the NaCl-structure. We have also computed the values of the pressure derivatives of second-order elastic constants for MgO, CaO, and SrO which agree well with the experimental values indicating the satisfactory nature of our computed data for C_αβγ.