Unconventional superconductivity in two-dimensional electron systems with long-range correlations

Properties of superfluid states of two-dimensional electron systems with critical antiferromagnetic fluctuations are investigated. These correlations are found to result in the emergence of rapid variation in the momentum space terms in all components of the mass operator, including the gap function Δ(p). It is shown that the domain where these terms reside shrinks with temperature, leading to a significant difference between the temperature T _c , at which superconductivity is terminated, and the temperature T*, where the gap in the single-particle spectrum vanishes.     

Bloch electron dynamics

New equations of motion for a Bloch electron [momentum p=h k,energy ε _n(p),zone number n, charge -e]: $$m_j \frac{{dv_j }}{{dt}} = - e(E + v \times B)_j $$ are proposed, where v≡?ε_n(p)/?p is the velocity, and {m_j}are the principal masses m _j ^? 1=?²ε_n/?p _j ² along the normal and the two principal axes of curvatures at each point of the constant-energy surface represented by ε=ε_n(p).Their advantages over the prevalent equations of motion where the left-hand-side is replaced by hk _j are demonstrated by examining de Haas-van Alphen oscillations and orientation-dependent cyclotron resonance peaks.     

Bound fermion states in the field of a soliton of the nonlinear O(3) σ model

The (2 + 1)-dimensional nonlinear O(3) σ model whose n field is coupled to the fermion field by the Yukawa interaction has been examined. The cases of the isosinglet and isodoublet fermion fields with respect to the internal symmetry group have been considered. It has been shown that bound states of the fermion in the n field of a soliton of the nonlinear O(3) σ model exist for some variants of the Yukawa interaction. The absence of zeroth fermion modes in the n field of the soliton has been established. The properties of the ground state of the fermion have been numerically studied. In particular, it has been shown that an increase in the spatial size of the soliton results in a decrease in the energy of the ground state. This leads to the instability of the soliton in a certain region of the parameters of the model.     

On the Maximal Excess Charge of the Chandrasekhar–Coulomb Hamiltonian in Two Dimension

We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom – or the corresponding magnetic quantum dot – the maximal number of electrons does not exceed twice the nuclear charge. The result is then generalized to the presence of external magnetic fields and atomic Hamiltonians. This is based on the positivity of $$|{\bf x}| T({\bf p}) + T({\bf p} ) |{\bf x}|$$ which – in two dimensions – is false for the non-relativistic case T(p) = p ²/2, but is proven in this paper for T(p) = |p|, i.e., the ultra-relativistic kinetic energy.     

The mass-shell and gauge-fixing conditions for the free relativistic massive quantum particle

Working in the context of the Weyl group, which describes off-mass-shell relativistic particles, we impose “gauge-fixing” constraints involvingR ⁰,R ⁺, andD as matrix element conditions to be satisfied by the on-mass-shell states of a massive particle. We evaluate the matrix elements inp-space using five sets of co-ordinates: (p ²,p), (p ²,p ⁺,p _T ), (p ²,p ^?,p _T ), (p ²,π), and (p ²,π ⁺,π _T ) where \(\pi ^\mu \equiv p^\mu /(p^2 )^{\tfrac{1}{2}} \) . We find that, only in the case ofR ⁰ with (p ²,p) coordinates,R ⁺ with (p ²,p ⁺,p _T ) coordinates, andD with (p ², π) or (p ²,π ⁺,π _T ) coordinates, can the condition be satisfied by arbitrary on-mass-shell states. In all other cases, the condition can be satisfied only by states belonging to a subset of subspaces of the on-mass-shell Hilbert space, i.e it forces a violation of the superposition principle. These results constitute thep-space quantum version of Shanmugadhasan's theorem for constrained classical systems which states that there exists, at least locally in phase space, a canonical transformation to a set of variables in which the second-class constraints become canonical pairs equal to zero with the other canonical coordinates independent of the second-class constraints.     

Integrable structure of conformal field theory,quantum KdV theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as “T-operators,” act in highest weight Virasoro modules. TheT-operators depend on the spectral parameter λ and their expansion around λ=∞ generates an infinite set of commuting Hamiltonians of the quantum KdV system. TheT-operators can be viewed as the continuous field theory versions of the commuting transfermatrices of integrable lattice theory. In particular, we show that for the values $c = 1 - 3\frac{{3(2n + 1)^2 }}{{2n + 3}}$ ,n=1,2,3 .... of the Virasoro central charge the eigenvalues of theT-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of the massless Thermodynamic Bethe Ansatz for the minimal conformal field theoryM _2,2n+3; in general they provide a way to generalize the technique of the Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator Φ_1,3. The relation of theseT-operators to the boundary states is also briefly described.     

Perpendicularev mass fromW decay

We point out properties of the “perpendicularev mass”, defined in terms of transverse momentap _t byM _T ² (ev)=2|p _eT | |p _vT |?2p _eT ·p _vT , that make it particularly well suited toW mass and width determinations. We give an analytic expression for its distribution inW production and subsequentW→ev decay a \(\bar pp\) colliders, accurate to order 〈p _WT ² /M _W ² 〉≈1%. A maximum likelihood fit of this formula to the five UA1 events givesM _W=80.3 _?3 ⁺⁶ GeV.     

Dislocation structure of intermetallic Ti3Al subjected to high-temperature deformation

Transmission electron microscopy was used to examine the dislocation structure of intermetallic Ti₃Al subjected to deformation at tempertures T = 1073–1273 K. The microstructure of samples subjected to high-temperature deformation is established to contain mobile superdislocations of a and 2c + a types, and single dislocations with Burgers vector [0001] are also observed on the prismatic planes. Possible models of destruction of barriers associated with 2c + a superdislocations on the pyramidal planes are discussed using the results of computer simulations of the structure of a superdislocation core in in Ti₃Al.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Fast calculation of HELAS amplitudes using graphics processing unit (GPU)

We use the graphics processing unit (GPU) for fast calculations of helicity amplitudes of physics processes. As our first attempt, we compute $u\overline{u}\rightarrow n\gamma$ (n=2 to 8) processes in pp collisions at $\sqrt{s}=14$  TeV by transferring the MadGraph generated HELAS amplitudes (FORTRAN) into newly developed HEGET (HELAS Evaluation with GPU Enhanced Technology) codes written in CUDA, a C-platform developed by NVIDIA for general purpose computing on the GPU. Compared with the usual CPU programs, we obtain a 40–150 times better performance on the GPU.     

Spatial representation of groups of automorphisms of von Neumann algebras with properly infinite commutant

Theorem. Let a topological groupG be represented (a→φ _a ) by *-automorphisms of a von Neumann algebraR acting on a separable Hilbert spaceH. Suppose that

1. G is locally compact and separable,
2. R′ is properly infinite,
3. for anyT∈R,x,y∈H the function

$$a \to \left\langle {\phi _a (T)x,y} \right\rangle _H $$ is measurable onG. Then there exists a strongly continuous unitary representation ofG onH,a→U _a , such that forT∈R,a∈G, $$\phi _\alpha (T) = U_a TU_a *.$$ .     

Dynamical aspects of intermediate-energy nucleus-nucleus collisions

Central collisions of heavy nuclei are investigated within the limit of selfconsistent independent single-particle motion in terms of the Wigner transform of the one-body density matrix in space and time. The energy regime considered extends from roughly 15 MeV/u to 150 MeV/u. Special attention is devoted to the relation between energy and momentum of the nucleons in the collision zone of the two nuclei. An initial average energy-momentum distributionf(k;E) is determined within the fully quantal approach which proves to be vital for our understanding of energetic particle production in the very early stage of the heavy-ion reaction. A comparison with related classical quantities shows the peculiar features of quantum dynamics for finite size fermion systems far from equilibrium.     

Experimental and numerical modelling of the fluid flow in the continuous casting of steel

This article gives an overview of recent research activities with respect to the mold flow in the continuous casting of steel in presence of DC magnetic fields. The magnetic fields appear to be an attractive tool for controlling the melt flow in a contactless way. Various kinds of magnetic systems are already in operation in industrial steel casting, but the actual impact on the melt flow has not been sufficiently verified by experimental studies. The rapid development of innovative diagnostic techniques in low-melting liquid metals over the last two decades enables new possibilities for systematic flow measurements in liquid metal model experiments. A new research program was initiated at HZDR comprising three experimental facilities providing a LIquid Metal Model for continuous CASTing of steel (LIMMCAST). The facilities operate in a temperature range from room temperature up to 400^°C using the low-melting alloys GaInSn and SnBi, respectively. The experimental program is focused on quantitative flow measurements in the mold, the submerged entry nozzle and the tundish. Local potential probes, Ultrasonic Doppler Velocimetry (UDV) and Contactless Inductive Flow Tomography (CIFT) are employed to measure the melt flow. The behavior of two-phase flows in case of argon injection is investigated by means of the Mutual Inductance Tomography (MIT) and X-ray radioscopy. The experimental results provide a substantial data basis for the validation of related numerical simulations. Numerical calculations were performed with the software package ANSYS-CFX with an implemented RANS-SST turbulence model. The non-isotropic nature of MHD turbulence was taken into account by specific modifications of the turbulence model. First results of the LIMMCAST program reveal important findings such as the peculiar, unexpected phenomenon that the application of a DC magnetic field may excite non-steady, non-isotropic large-scale flow oscillations in the mold. Another important result of our study is that electrical boundary conditions, namely the wall conductivity ratio, have a serious influence on the mold flow while it is exposed to an external magnetic field.     

Study on spin configuration in photoresponsive iron mixed-valence complexes by Mössbauer spectroscopy

We have investigated magnetic properties in a series of photoresponsive dithiooxalato (dto)-bridged iron mixed-valence complexes, (SP-R)[Fe^IIFe^III(dto)₃] (SP-R = R-substituted pyridospiropyran cation; R = Me, Et, and Pr; abbreviated as 1 ^Me, 1 ^Et, and 1 ^Pr, respectively). As for our previous reports, 1 ^Me and 1 ^Et show two-step succeeding ferromagnetic transitions at T _C?=?25 & 8 K and 22 & 5 K, respectively. However, 1 ^Et has no hysteresis in the magnetic susceptibility, while 1 ^Me undergoes the charge transfer phase transition with thermal hysteresis around 75 K. To elucidate the two-step transitions of them, we measured ⁵⁷Fe Mössbauer spectra of 1 ^Et. The spectra of Fe^II (S?=?2) and Fe^III (S?=?1/2) in the HTP were observed in the magnetically ordered state as well as the paramagnetic state, and revealed that only HTP exists in a temperature range up to 5 K. The result is consistent with that of 1 ^Pr, where one ferromagnetic phase transition occurs at T _C?=?10 K. ⁵⁷Fe Mössbauer spectroscopy is useful to clarify the origin of the succeeding magnetic transition for these systems.     

Substituent Dependent Optical Properties of <Emphasis Type="Italic">p</Emphasis>-phenyl Substituted ethenyl-<Emphasis Type="Italic">E</Emphasis>-thiophenes

Various electron donor and acceptor substituted (NO₂, CN, Cl, H, OCH₃, NH₂) p-phenyl ethenyl-E- thiophenes (1–6) were synthesized and substituent dependent optical properties (dipole moment, transition dipole moment, oscillator strength, optical band gap, hyperpolarizability) were studied using Solvatochromism and Density functional theory. It is shown that thiophene acts as a weak electron donor in presence of an electron withdrawing p-phenyl substituent (NO₂, CN, Cl), whereas thiophene acts as a weak electron acceptor in presence of an electron donating p-phenyl substituent (OCH₃, NH₂). In comparison to ethenyl thiophene 4, the HOMO-LUMO energy band gap is decreased upon increasing the electron donating or electron withdrawing capacity of p-phenyl substituent. From the excited state dipole moment calculation, it is shown that the excited state is highly dipolar for nitro and amino compounds 1 and 6, whereas compounds 2–5 show a non-polar excited state. As compared to the ethenyl thiophene 4, the first hyperpolarizability (β) increases upon substitution either with a strong electron withdrawing or strong electron donating p-phenyl substituent. A large β value is found for p-nitro phenyl ethenyl-E-thiophene and p-amino phenyl ethenyl-E- thiophene. Overall, these studies provide useful information in understanding the optical properties of phenyl and heterocyclic based ethenyl systems.     

Magnetic nesting and coexistence of ferromagnetism and superconductivity

If the condition ε_σ(p)=ε_?σ(?p+nI/v_F) for magnetic nesting is fulfilled for the electron dispersion law with spin σ along a certain preferential direction n, ferromagnetism and the inhomogeneous superconducting state can coexist up to a very high magnetization I. This fact was used to explain the coexistence of ferromagnetism and superconductivity for layered cuprates of the RuSr₂GdCu₂O₈ type, which possess a finite, though rather high, critical magnetization, because the conditions for magnetic nesting are fulfilled only approximately.     

Types of defect ordering in undoped and lanthanum-doped Bi2201 single crystals

Undoped and lanthanum-doped Bi2201 single crystals having a perfect average structure have been comparatively studied by x-ray diffraction. The undoped Bi2201 single crystals exhibit very narrow satellite reflections; their half-width is five to six times smaller than that of Bi2212 single crystals grown by the same technique. This narrowness indicates three-dimensional defect ordering in the former crystals. The lanthanumdoped Bi2201 single crystals with x = 0.7 and T _c = 8–10 K exhibit very broad satellite reflections consisting of two systems (modulations) misoriented with respect to each other. The modulation-vector components of these two modulations are found to be q ₁ = 0.237b* + 0.277c* and q ₂ = 0.238b* + 0.037c*. The single crystals having a perfect average structure and a homogeneous average distribution of doping lanthanum consist of 70-to 80-Å-thick layers that alternate along the c axis and have two different types of modulated superlattice. The crystals having a less perfect average structure also consist of alternating layers, but they have different lanthanum concentrations. The low value of T _c in the undoped Bi2201 single crystals (9.5 K) correlates with three-dimensional defect ordering in them, and an increase in T _c to 33 K upon lanthanum doping can be related to a thin-layer structure of these crystals and to partial substitution of lanthanum for the bismuth positions.     

First-order phase transition from an antiferromagnetic ferroelectric to a cycloidal multiferroic with weak ferromagnetism during the joint action of applied magnetic and electric fields

The thermodynamics of the phase transition in a perovskite-like multiferroic, in which an antiferromagnetic ferroelectric transforms into a new magnetic state where a spiral spin structure and weak ferromagnetism can coexist in applied magnetic field H, is described. This state forms as a result of a first-order phase transition at a certain temperature (below Néel temperature T _N ), where a helicoidal magnetic structure appears due to the Dzyaloshinskii-Moriya effect. In this case, the axes of electric polarization and the helicoid of magnetic moments are mutually perpendicular and lie in the ab plane, which is normal to principal axis c. Additional electric polarization p, which decreases the total polarization of the ferroelectric P, appears in the ab plane. The effect of applied magnetic and electric fields on the properties of a multiferroic with a helicoidal magnetic structure is described. An alternating electric field is shown to cause a field-linear change in magnetic moment m, whose sign is opposite to the sign of the change of electric field E. The detected hysteretic phenomena that determine the temperature ranges of overheating and supercooling of each phase are explained. A comparison with the experimental data is performed.     

Exact solution of the Boltzmann equation in the relaxation approximation,existence of negative differential conductivity for certain types of energy bands and its implication for the fluctuation spectrum and the noise temperature

The Boltzmann equation for the distributionf _k of a system of charged particles obeying classical statistics in a uniform fieldF, $$\frac{{\partial f_k }}{{\partial t}} + F\frac{{\partial f_k }}{{\partial k}} = \smallint d^3 k'(W_{kk'} f_{k'} - W_{k'k} f_k ),$$ will be solved analytically for a special class of transition ratesW _kk′=const·h _k ·ν _k ·ν _k′ for any initial distribution.h _k is the Maxwell distribution andν _k >0 can be interpreted as ak-dependent relaxation frequency. The constant relaxation approximation (ν _k =ν) will be used to discuss the drift velocitiesu for all the fields and temperaturesT for certain types of band structuresE(k). Bands with lineark-dependence for largek give rise to drift velocities saturating for large fields. For bands with the periodicity of the reciprocal lattice, the zero drift-theorem has been proved. It states that $$\mathop {\lim }\limits_{F \to \infty } u (F,T) = \mathop {\lim }\limits_{T \to \infty } u (F,T) = 0$$ for all the periodic band structures. This theorem is even correct for a generalW _kk′ if certain restrictions are made. Finally, making use of the Markov character of the conditional probability (Green's function) solution of the Boltzmann equation, the velocity fluctuation spectrumS is calculated forE(k)=A(1?cosa k). It will be shown thatS(F, T, 0) remains positive for the critical field and all temperatures, and therefore the noise temperature diverges on approaching the critical field.