Charmonium states in quark-gluon plasma

We discuss how the spectral changes of quarkonia at T _c can reflect the ‘critical’ behaviour of QCD phase transition. Starting from the temperature dependencies of the energy density and pressure from lattice QCD calculation, we extract the temperature dependencies of the scalar and spin-2 gluon condensates near T _c. We also parametrize these changes into the electric and magnetic condensate near T _c. While the magnetic condensate hardly changes across T _c, we find that the electric condensate increases abruptly above T _c. Similar abrupt change is also seen in the scalar condensate. Using the QCD second-order Stark effect and QCD sum rules, we show that these sudden changes induce equally abrupt changes in the mass and width of J/ψ, both of which are larger than 100 MeV at slightly above T _c.      

Dynamics of uniform quantum gases, I: Density and current correlations

A unified approach valid for any wavenumber q, frequency ω, and temperature T is presented for uniform ideal quantum gases allowing for a comprehensive study of number density and particle-current density response functions. Exact analytical expressions are obtained for spectral functions in terms of polylogarithms. Also, particle-number and particle-current static susceptibilities are presented which, for fugacity less than unity, additionally involve Kummer functions. The q- and T-dependent transverse-current static susceptibility is used to show explicitly that current correlations are of long range in a Bose-condensed uniform ideal gas but for bosons at T>T_c and for Fermi and Boltzmann gases at all temperatures these correlations are of short range. Contact repulsive interactions for systems of neutral quantum particles are considered within the random phase approximation. The expressions for particle-number and transverse-current susceptibilities are utilized to discuss the existence or nonexistence of superfluidity in the systems under consideration.     

Microscopic theory of a strongly correlated two-dimensional electron gas

The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T _⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T _*, appears through a crossover at temperatures T ∼ T _* > T _⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T ^−α with the exponent α }~ 2/3.     

Multiply connected Fermi sphere and fermion condensation

We examine the structure of the ground state of a homogeneous Fermi liquid beyond the instability point of the Fermi-like quasiparticle momentum distribution in the effective-functional method with a strong repulsive effective interaction. A numerical study of the initial stage of rearrangement of the ground state, based on a simple effective functional, showed that there exists a temperature T ₀, above which the behavior of the system is the same as in the theory of fermion condensation, and for T<T ₀ the scenario of rearrangement of the ground state is different. At low temperatures an intermediate structure arises, with a multiply connected quasiparticle momentum distribution. The transition of this structure with growth of the coupling constant to a state with a fermion condensate is discussed. Zh. éksp. Teor. Fiz. 114, 2078–2088 (December 1998)     

Specific heat jump in non-Fermi superconductors

We derive the jump in the specific heat at T=T _c for a superconductor in a non-Fermi liquid model. We took into consideration the two possible limits in this problem: the spin-charge separation model for a Fermi liquid and the usual non-Fermi liquid model which satisfies the homogeneity relation for the spectral function , ). We also derive the order parameter behavior for these two cases in the vecinity of the critical temperature. Received: 25 January 1998 / Revised: 25 March 1998 / Accepted: 25 March 1998     

Electron spectrum in high-temperature cuprate superconductors

A microscopic theory for the electron spectrum of the CuO₂ plane within an effective p-d Hubbard model is proposed. The Dyson equation for the single-electron Green’s function in terms of the Hubbard operators is derived and solved self-consistently for the self-energy evaluated in the noncrossing approximation. Electron scattering on spin fluctuations induced by the kinematic interaction is described by a dynamical spin susceptibility with a continuous spectrum. The doping and temperature dependence of electron dispersions, spectral functions, the Fermi surface, and the coupling constant λ are studied in the hole-doped case. At low doping, an arc-type Fermi surface and a pseudogap in the spectral function close to the Brillouin zone boundary are observed. The text was submitted by the authors in English.     

Magnetic impurities in gapless Fermi systems: perturbation theory

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, with r>0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U>0case: it exhibits both strong coupling (SC) states (for r<1) and local moment states (for r>1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U>0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon familiar in the normal r=0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for and r>1 but not for . Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength. Received 26 August 1999     

Electronic structure of p-type La1 ? xM x2+ MnO3 manganites in the ferromagnetic and paramagnetic phases in the LDA + GTB approach

The band structure, spectral intensity, and position of the Fermi level in doped p-type La_{1 − x} M _x/2+MnO₃ manganites (M = Sr, Ca, Ba) is analyzed using the LDA + GBT method for calculating the electronic structure of systems with strong electron correlations, taking into account antiferro-orbital ordering and using the Kugel-Khomskii ideas and real spin S = 2. The results of the ferromagnetic phase reproduce the state of a spin half-metal with 100% spin polarization at T = 0, when the spectrum is of the metal type for a quasiparticle with one spin projection and of the dielectric type for the other. It is found that the valence band becomes approximately three times narrower upon a transition to the paramagnetic phase. For the paramagnetic phase, metal properties are observed because the Fermi level is located in the valence band for any nonzero x. The dielectrization effect at the Curie temperature is possible and must be accompanied by filling of d _x orbitals upon doping. The effect itself is associated with strong electron correlations, and a complex structure of the top of the valence band is due to the Jahn-Teller effect in cubic materials.     

Theory of substitutional alloys of intermediate valence systems: Concentration and temperature dependence of the static magnetic susceptibility

The effect of alloying in intermediate valence compounds is studied within an extended version of the Anderson model which takes into account substitutional disorder of the rare earth ions. In particular, we concentrate on modifications of the conduction band, describe them by an effective shift in the Fermi energy, and consider its influence on the mixed valence behaviour. By applying the alloy analog approximation to the manyparticle Hamiltonian describing the local magnetic 4f shells, the complete effective Hamiltonian is that of a ternary alloy. This problem is solved within the coherent potential approximation and the static magnetic susceptibility is calculated as a function of temperature and disorder. Depending on the shift of the Fermi energy with respect to the 4f levels, qualitatively different behaviour is obtained which corresponds very well with magnetic measurements on different Yb alloys. The model yields an inverse proportionality between the susceptibility atT=0 and the temperatureT _M of the susceptibility maximum as functions of the disorder.Work performed within the research program of the Sonderfor-schungsbereich 125 Aachen-Jülich-Köln     

Microscopic Theory of Pinning of Multiquantum Vortex in Cylindrical Cavity

We have proposed and developed a microscopic model of depinning (escape) of a multiquantum vortex in a superconductor with a cylindrical nonconducting cavity with the transverse size smaller than or on the order of the superconducting coherence length ξ₀ at zero temperature. The spectrum of subgap quasiparticle excitations in two- and three-quantum vortices trapped by a cylindrical cavity has been calculated in the quasiclassical approximation. It is shown that the transformation of the spectrum is accompanied by break of anomalous spectral branches due to normal reflection of quasiparticles from the surface of a defect. A microscopic (spectral) criterion for multiquantum vortex pinning has been proposed; according to this criterion, the multiquantum vortex can be trapped in the cavity during the formation of a minigap in the elementary excitation spectrum near the Fermi level. Self-consistent calculations of density of states N(r, ε) for two- and three-quantum vortices trapped by a cylindrical cavity of radius on the order of ξ₀ have been performed using quasiclassical Eilenberger equations. In the pure limit and for low temperatures T ? T _c , peculiarities observed in the N(r, ε) distribution reflect the presence of M anomalous spectral branches in the M-quantum vortex and confirm the correctness of the spectral criterion of pinning (depinning) of a multiquantum vortex.     

QCD at finite temperature

Quantum chromodynamics is studied at finite temperatures and densities using the temperature Green functions method. For the Green functions the renormalized Schwinger-Dyson equations are obtained and their qualitative properties are discussed. The equality of the renormalization constants for the equations obtained at T, μ ≠ 0 with those for quantum field theory is pointed out. General properties of the gluon polarization tensor are investigated at T, μ ≠ 0. The temperature Green functions are calculated within the one-loop approximation using both relativistic and axial gauges. The fulfilment of the Slavnov-Taylor identities is verified. The asymptotic behaviour of the polarization tensor at T, μ ≠ 0 is established and the excitation spectrum of quark-gluon plasma is found. Both Fermi and Bose excitations are considered and the gauge invariance of the spectra is demonstrated. The renormalization group extension of the dispersion laws into the regions of high temperatures and densities is presented. The exact representation of the thermodynamical potential in QCD is found in terms of the temperature Green functions. For the quark-gluon plasma the thermodynamical potential is calculated with the g³-term taken into account. The equation of state of the hot quark-gluon plasma is found and its properties are discussed. The complete evolutional diagram of the hadronic matter is outlined. The phase curve asymptotics, which put bounds on the quark-gluon plasma domain, are found for the two limiting cases (μ = 0, T → T₀; T = 0, μ → μ₀). The phase transition of the hot quark-gluon plasma placed in external Abelian field is studied. The instability of such plasma has been found and the program of its stabilization is indicated. The infrared behaviour of the non-Abelian gauge theory is studied for finite temperatures when power divergencies are essential. The propagator of transverse gluons is shown to be singular for momenta |p| ˜ g²T and this cannot be avoided by summing the simplest bubble chains. The infrared asymptotic behaviour of the tree-gluon vertex is found and the results obtained are checked using the Slavnov-Taylor identities. The Green functions asymptotics found indicate either an instability of the quark-gluon plasma in the infrared momentum domain or the inconsistency of the perturbational methods. A non-perturbative approach to the infrared problem in QCD is developed within the axial gauge. The closed equations for the structure functions that determine the gluon polarization tensor are obtained by using the Slavnov-Taylor identities to found approximately the three-gluon vertex. It is shown that the solution of the equations obtained by iterations does not remove the infrared singularity from the temperature Green functions. The nonperturbative solution of such equations is discussed.     

Remnant Fermi surface in a pseudogap regime of the two-dimensional Hubbard model at finite temperature

A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the paramagnon theory (PT), and the two-particle self-consistent (TPSC) approach. In general, at finite temperature, the Fermi surface of the interacting electron systems is not sharply defined due to the broadening effects of the self-energy. In order to take account of those effects we consider the single-particle spectral function A(, 0) at the Fermi level, to describe the counterpart of the Fermi surface at T = 0. We find that the Fermi surface is destroyed close to the pseudogap regime due to the spin-fluctuation effects in both PT and TPSC approaches. Moreover, the top of the effective valence band is located around = (π/2,π/2) in agreement with earlier investigations on the single-hole motion in the antiferromagnetic background. A crossover behavior from the Fermi-liquid regime to the pseudogap regime is observed in the electron concentration dependence of the spectral function and the self-energy. Received 8 September 2000 and Received in final form 20 December 2000     

NMR Anomalies in Quasi-2D Organic Superconductors: Effects of Spin Fluctuations in a Fermi Liquid Approach

The -(BEDT-TTF)₂X organic superconductors are described by a two parameter 2D Fermi surface model, in which bandwidth and departure from perfect nesting can be varied. We have studied the spin fluctuations effect on the normal state properties in a Fermi liquid approach using the RPA approximation. The calculated NMR relaxation rate exhibits a peak in 1/(T ₁ T), which strongly decreases when the departure from perfect nesting of the Fermi surface and the bandwidth increase. These results are in good agreement with NMR experiments done in -(ET)₂X at least qualitatively. In conclusion, we have shown that, in the normal state and with a Fermi liquid approach, the spin fluctuations, which are present in the system due to an imperfect nesting property of the Fermi surface, can induce anomalies of the magnetic properties. Besides, we can restore the usual behaviour like the Korringa law by increasing the bandwidth or by considering a more imperfect nesting. Our calculation reproduces qualitatively the applied pressure relaxation rate experiment done in -(ET)₂X salt.     

Spectral densities of response functions for the O(3) symmetric Anderson and two channel Kondo models

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln divergence found in the low frequency behaviour of the T=0 dynamic susceptibility. Received 29 January 1999     

X-ray Photoelectron Spectroscopy of Sb2S3 Crystals

The paper presents the X-ray photoelectron spectra (XPS) of the valence band and core levels of semiconductor ferroelectric Sb₂S₃ single crystals, which show weak phase transitions and anomalies of various physical properties. The XPS were measured with monochromatized Al K _α radiation in the energy range 0-1450 eV and the temperature range 160-450 K. The valence band is located 0.8-7.5 eV below the Fermi level. Experimental results of the valence band and core levels are compared with the results of theoretical ab initio calculations of the molecular model of Sb₂S₃ crystal. The chemical shifts in Sb₂S₃ crystal for the Sb and S states are obtained. Results revealed that the small structural rearrangements at the phase transition T _c1 = 300 K shift the Fermi level and all electronic spectrum. Also, temperature dependence of a spontaneous polarisation shifts the electronic spectra of the valence band and core levels. Specific temperature-dependent excitations in Sb 3d core levels are also revealed.     

Fluctuations of Goldstone modes and the chiral transition in QCD

We provide evidence for the influence of thermal fluctuations of Goldstone modes on the chiral condensate at finite temperature. We show that at fixed temperature, T<T_c, in the vicinity of the chiral transition temperature this leads to a characteristic dependence of the chiral condensate on the square root of the light quark mass (m_l), which is expected for 3-dimensional models with broken O(N) symmetry. As a consequence the chiral susceptibility shows a strong quark mass dependence for all temperatures below T<T_c and diverges like in the chiral limit.     

Two-dimensional t-J model at moderate doping

Using the method which retains the rotation symmetry of spin components in the paramagnetic state and has no preset magnetic ordering, spectral and magnetic properties of the two-dimensional t-J model in the normal state are investigated for the ranges of hole concentrations 0 ⩽ x ⩽ 0.16 and temperatures 0.01t ⩽ T ⩽ 0.2t. The used hopping t and exchange J parameters of the model correspond to hole-doped cuprates. The obtained solutions are homogeneous which indicates that stripes and other types of phase separation are not connected with the strong electron correlations described by the model. A series of nearly equidistant maxima in the hole spectral function calculated for low T and x is connected with hole vibrations in the region of the perturbed short-range antiferromagnetic order. The hole spectrum has a pseudogap in the vicinity of (0,π) and (π, 0). For x ≈ 0.05 the shape of the hole Fermi surface is transformed from four small ellipses around (±π/2,±π/2) to two large rhombuses centered at (0, 0) and (π,π). The calculated temperature and concentration dependencies of the spin correlation length and the magnetic susceptibility are close to those observed in cuprate perovskites. These results offer explanations for the observed scaling of the static uniform susceptibility and for the changes in the spin-lattice relaxation and spin-echo decay rates in terms of the temperature and doping variations in the spin excitation spectrum of the model. Received 14 November 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: alexei@fi.tartu.ee     

Evolution of spin susceptibility from the Pauli to Curie-Weiss type in strongly correlated Fermi systems

The magnetic properties of strongly correlated Fermi systems are studied within the framework of the fermioncondensation model—phase transition associated with the rearrangement of the Landau quasiparticle distribution, resulting in the appearance of a plateau at T=0 exactly in the Fermi surface of the single-particle excitation spectrum. It is shown that the Curie-Weiss term ～T^?1 appears in the expression for the spin susceptibility χ_ac(T) of the system after the transition point at finite temperatures. The behavior of χ_ac(T, H) as a function of temperature and static magnetic field H in the region where the critical fermion-condensation temperature T _f is close to zero is discussed. The results are compared with the available experimental data.     

Bose condensation in strongly monideal systems

The possibility of the formation of a condensate with a finite absolute value of the momentum k₀ in a strongly nonideal Bose system is considered. Such a condensate comes into existence when the one-particle spectrum of a normal system touches zero in the point k₀ ≠ 0. The form of a correlation function below the condensation point shows the appearance of a long-range order, but not the infinite long-range one. In the case of liquid ⁴He estimates show that $\text{k}{}_0\text{? 1}\text{A}\text{?}{}^{\mathrm{?1}}$, and at the temperature T>₀ ～ 1 K this unusual condensate with a finite magnitude of the momentum turns into the conventional Bose-Einstein condensate with the zero momentum. The properties of correlation functions in the spaces of different dimensions are discussed.