Screened perturbation theory at four loops

We study the thermodynamics of massless ⁴-theory using screened perturbation theory, which is a way to systematically reorganise the perturbative series. The free energy and pressure are calculated through four loops in a double expansion in powers of g² and m/T, where m is a thermal mass of order gT. The result is truncated at order g⁷. We find that the convergence properties are significantly improved compared to the weak-coupling expansion.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Quantum corrections to the energy density of a homogeneous Bose gas

Quantum corrections to the properties of a homogeneous interacting Bose gas at zero temperature can be calculated as a low-density expansion in powers of , where is the number density and a is the S-wave scattering length. We calculate the ground state energy density to second order in . The coefficient of the correction has a logarithmic term that was calculated in 1959. We present the first calculation of the constant under the logarithm. The constant depends not only on a, but also on an extra parameter that describes the low energy scattering of the bosons. In the case of alkali atoms, we argue that the second order quantum correction is dominated by the logarithmic term, where the argument of the logarithm is ,and is the length scale set by the van der Waals potential. Received 2 February 1999     

The internal energy and thermodynamic behaviour of a boson gas below the Bose-Einstein temperature

We have examined the issue of the kinetic energy of particles in the ground state of an ideal boson gas. By assuming that the particles, on dropping into the ground state, retain the kinetic energy they possess at the Bose-Einstein temperature TB, we obtain new expressions for the pressure and internal energy of the gas below TB, that are free of the difficulties associated with the corresponding expressions in current theory. Furthermore, these new equations yield a value for the maximum density temperature in liquid ⁴He that is very close to the measured value.     

Bose-Einstein condensation in a cavity

The effect of the physically correct boundary conditions and the nonvanishing ground state energy on Bose-Einstein condensation of quantum particles confined to a cubic volumeV=L ³ is evaluated. The transition point is shifted towards higher temperatures by the confinement, the specific heat below the onset of condensation is no longer proportional toT ^3/2, and the pressure does depend on the volume. Precise expressions for the modification of the ground state population and for the shift of the condensation temperature are derived, together with an expansion of the internal energy and of the specific heat. Numerical computations confirm the accuracy of our analytical approximations.Dedicated to Herbert Wagner, whose work on quantum Fermi liquids proved to be also very stimulating for quantum Bose liquids.     

Electron-electron interactions in the 2D electron system

In this paper, we report studies of the electron-electron interaction effects in 2D electron systems. The interaction manifests in renormalization of the effective spin susceptibility, effective mass, g^∗-factor, conductivity etc. By applying in-plane magnetic field, we tuned the effective interaction between the electrons and compared with theory the temperature dependence of the conductivity. We find a good agreement with interaction corrections calculated within the Fermi liquid theory. To address the question on the origin of the metal-insulator transition (MIT) in 2D, we explored transport and magnetotransport properties in the vicinity of the MIT and compared our data with solutions of two equations of the renormalization group (RG) theory, which describes temperature evolutions of the resistivity and interaction parameters for 2D electron system. We found a good agreement between the ρ(T,B_∥) data and the RG-theory in a wide range of the in-plane fields. These results support the Fermi liquid type origin of the metallic state and the interpretation of the observed 2D MIT as the true quantum phase transition.     

The measurement of the electronic g-factor in hydrogen-like ions --A promising tool for determining fundamental and nuclear constants

We describe a double-Penning-trap experiment suitable for testing QED in strong fields by determining the electronic g-factor of a single hydrogen-like ion in its ground state. Our measurements on ¹²C^{5 +} reach a relative accuracy of 2×10^-9, where the largest uncertainty results from the mass of the electron. Together with equally precise theoretical predictions therefore, it is possible to evaluate a new value for the electron's mass. The possibilities to obtain other fundamental constants and nuclear parameters are lined out. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: t.beier@gsi.de     

Nonlinear Hanle effect in Cs vapor under strong laser excitation

We report results of a theoretical and experimental study of the ground state nonlinear Hanle effect under strong laser excitation. It is shown that besides the well-known zero-magnetic field suppression of absorption on F _g = F→F _e = F - 1 transitions caused by population trapping, an optical pumping induced enhanced absorption occurs on F _g = F→F _e = F + 1 transitions for small B-fields. The latter effect becomes more pronounced for high F values. The experiment with atomic vapor of Cs (D₂ line, F _g = 4) confirms an increase of the spectrally unresolved fluorescence yield at zero magnetic field and 600 mW/cm² laser intensity by 9% or 42%, when excitation occurs with linearly or circularly polarized light, respectively. The results of the experiment agree with numerical simulation studies using equations of motion for a density matrix. Received 24 November 2001 / Received in final form 25 March 2002 Published online 24 September 2002     

Magnetism and phase separation in the ground state of the Hubbard model

We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilize a Néel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed. Received 9 January 2002 Published online 25 June 2002     

Crystal-field hamiltonian and spin-orbit interaction for d and d ions at low C3 symmetry sites: V:Al2O3 and Ni:LiNbO3

The experimental studies have provided evidence of the occurrence of transitions from the ³T_1g(³F) ground state to the crystal-field levels ³T_2g(³F), ³T_1g(³P) and ³A_2g(³F) for the V³⁺ centres in Al₂O₃ crystal; and from the ³A_2g(³F) ground state to the crystal-field levels ³T_2g(³F), ³T_1g(³F) and ³T_1g(³P) for the Ni²⁺ centres in LiNbO₃ crystal (levels are assigned to irreps of the O_h point symmetry group). Using the experimental spectroscopic data, theoretical calculations of the crystal-field levels of V³⁺:Al₂O₃ and Ni²⁺:LiNbO₃ are carried out based on the Racah theory. The observed crystalline-field splittings of the V³⁺ and Ni²⁺ terms were accounted for using a C₃ symmetry Hamiltonian. The spin-orbit interaction was taken into account in this work. The Racah, crystal-field and spin-orbit parameters, which fit experimental and theoretical energy levels, have been reliably obtained. A good agreement between the theoretical and experimental results for the energy levels of V³⁺:Al₂O₃ and Ni²⁺:LiNbO₃ has been obtained.     

Properties of ground state and anomalous quantum fluctuations in one-dimensional polaron-soliton systems—the effects of electron-two-phonon interaction and non-adiabatic quantum correlations

Based on the Holstein model Hamiltonian of one-dimensional molecular crystals, by making use of the expansion approach of the correlated squeezed-coherent states of phonon instead of the two-phonon coherent state expansion scheme, the properties of the ground state and the anomalous quantum fluctuations are investigated in a strongly coupled electron-phonon system with special consideration of the electron-two-phonon interaction. The effective renormalization (αi) of the displacement of the squeezed phonons with the effect of the squeezed-coherent states of phonon and both the electron-displaced phonon and the polaron-squeezed phonon correlations have been combined to obtain the anomalous quantum fluctuations for the corrections of the coherent state. Due to these non-adiabatic correlations, the effective displacement parameter αi is larger than the ordinary parameter α (0) i . In comparison with the electron-one-phonon interaction (g) corrected as αig, we have found the electron-two-phonon interaction (g1) corrected as αi2 g1 is enhanced significantly. For this reason, the ground state energy (E(2) 0 ) contributed by the electron-two-phonon interaction is more negative than the single-phonon case (E(1) 0 ) and the soliton solution is more stable. At the same time, the effects of the electron-two-phonon interaction greatly increase the polaron energy and the quantum fluctuations. Furthermore, in a deeper level, we have considered the effect of the polaron-squeezed phonon correlation (f-correlation). Since this correlation parameter f > 1, this effect will strengthen the electron-one and two-phonon interactions by fαig and f2αi2 g1, respectively. The final results show that the ground state energy and the polaron energy will appear more negative further and the quantum fluctuations will gain further improvement.     

一维分子晶体系统的极化子-孤子压缩态、系统基态性质和量子涨落

基于一维分子晶体系统的 Holstein 模型,采用压缩-相干态展开方法,计及电子-声子间量子关联和重整化平移修正,分析和研究电子-双声子相互作用对极化子-孤子系统基态性质和量子涨落的影响.推导了一维极化子-孤子系统的封闭形式非线性方程.应用非线性项展开方法,给出非线性方程的解析解和相关基态特性结果.研究表明,仅当电子-双声子耦合强度 g₁<0时非线性方程才有孤波解,此时声子量子涨落效应随着压缩的增加,极化子-孤子系统基态能量变得更负,孤子局域减少,孤子态更加稳定;另一方面,电子密度涨落〈Δ²n〉和声子坐标-动量的不确定量〈Δ²p〉〈Δ²q〉比无声子压缩效应的大,极化子结合能变得更负.特别是,当g₁<0时,双声子效应的量子涨落〈Δ²n〉与〈Δ²p〉〈Δ²q〉的值比单声子情况有明显增加. 关键词： 压缩-相干态展开 极化子-孤子态与量子涨落 电子-双声子相互作用 非线性薛定谔方程     

具有D4h对称性构型的C2+4分子的Jahn-Teller效应与能级分裂

依据量子理论与配位场理论,利用群论和对称性分析的方法探讨了C²⁺₄分子在具有D_4h对称性构型时,E×(b_1g+b_2g)系统的Jahn-Teller效应中的相关问题.研究了C²⁺₄分子的电子态与声子态的对称性及其活跃声子态,讨论了系统声子间的耦合与CG系数,构建了E×(b_1g+b_{2g 关键词： 2+4分子')" href="#">C²⁺4分子 对称性 能级分裂 Jahn-Teller畸变}     

Analytical potential energy functions for the ground and some excited states of N2

The analytical potential energy functions have been calculated for the ground state X¹Σ⁺_g and four excited electronic states a¹Π_g, A³Σ⁺_u, B′³Σ^?_u and B³Π_g of N₂ molecule using the algebraic and energy-consistent methods (AM-ECM). Based on our previously published full AM vibrational energies and spectroscopic constants, the low-lying force constants f_n, the expansion coefficients a_n and the variational parameters λ in the AM–ECM potentials are determined for these states. The computed AM–ECM potential energy curve of each state is in excellent agreement with the experimental data and better than other analytical potentials.     

Spin-Peierls and incommensurate states in layered S=1/2 system TiOCl

We demonstrate that TiOCl is a good model inorganic system to investigate spin-Peierls state. Our ³⁵Cl and ^47,49Ti NMR data show that a pseudo spin-gap behavior below T*=135 K precedes successive phase transitions at T_c=94 K and into a singlet spin-Peierls ground state with a large energy gap E_g/k_B=430 K.     

Electronic Raman scattering and phonon self-energy effects in the R-123 system: Signatures of gap and pseudogap

Using Raman spectroscopy and transport measurements we investigate thin epitaxial films of Y_1—x(Pr, Ca)_xBa₂Cu₃O_6+y. We explore the electronic Raman responses in A_1g, B_1g, and B_2g symmetry obtained after subtraction of phononic excitations, and especially, the 2Δ peaks that form out of the electronic background below T_c. We find that the energy of the B_1g 2Δ peak, which is a measure of the gap value, increases monotonically with decreasing doping until the peak becomes unresolvable. In contrast, the peak in A_1g symmetry follows T_c being still resolvable in the Pr-doped films. The B_2g response is weak and a 2Δ peak is only detected at the highest doping level. As a consequence of strong electron-phonon coupling, the B_1g phonon at ∼340 cm^—1 exhibits a pronounced Fano-type line shape. We use a phenomenological model to describe the line shape that takes into account real and imaginary part of the electronic response. It allows us to obtain the self-energy corrections and the mass-enhancement factor λ as a measure of the coupling. In the normal state we find λ = 0.015 around optimal doping and decreasing values with decreasing doping. The electron-phonon coupling increases strongly below T_c in overdoped samples in which the B_1g 2Δ peaks appear in the vicinity of the phonon. Self-energy effects observed in the superconducting state can only partly be assigned to the redistributing electronic response. Anomalies with respect to frequency, linewidth, and intensity remain. They appear at increasing temperatures with decreasing doping and we provide evidence that they are connected to the presence of the pseudogap. We supplement our study by a comparison with single crystal data and investigate the influence of site-substitutional disorder on the electronic response and the electron-phonon interaction.     

Leptodermous expansion of nuclear ground state energies and the anomaly in the nuclear curvature energy

The leptodermous expansion of the total ground state energy of a nucleus into volume, surface, curvature and gauss curvature contributions has been studied starting from a semi-classical energy density formalism of extended Thomas Fermi type. A numerical procedure was used to obtain the surface energy and curvature energy contributions from surface moments of energy density profilesH(r) for a sequence of nuclei withN=Z and neglecting the coulomb interaction for the three Skyrme forces. A transition to the liquid drop model type expansion in increasing powers ofA ^−1/3 is then made, taking into account the dependence of the central density and the surface structure on the mass of the nucleus. It is found that there is no inconsistency between the curvature contribution to the total energy in the leptodermous expansion and theA ^−1/3 term contribution in the liquid drop model expansion. It has been shown that the earlier apparent anomaly between the above two methods arises due to the use of semi-infinite approximation and the mass dependence of the central density and the surface structure of finite nuclei.     

Electron-doping versus hole-doping in the 2D t-t' Hubbard model

We compare the one-loop renormalization group flow to strong coupling of the electronic interactions in the two-dimensional t-t'-Hubbard model with t' = - 0.3t for band fillings smaller and larger than half-filling. Using a numerical N-patch scheme ( N = 32, ..., 96) we show that in the electron-doped case with decreasing electron density there is a rapid transition from a d _{x2 - y2}-wave superconducting regime with small characteristic energy scale to an approximate nesting regime with strong antiferromagnetic tendencies and higher energy scales. This contrasts with the hole-doped side discussed recently which exhibits a broad parameter region where the renormalization group flow suggests a truncation of the Fermi surface at the saddle points. We compare the quasiparticle scattering rates obtained from the renormalization group calculation which further emphasize the differences between the two cases. Received 19 December 2000 and Received in final form 28 February 2001     

Structure of the superconducting state of superconductors near the critical field Hc2 for values of the Ginzburg-Landau parameter kclose to unity

It is shown that near the transition temperature T _c the coefficients of the second and third terms in the expansion of the free energy in powers of H _c2−B (B is the magnetic field induction inside the superconductor) go to zero simultaneously for a value of κ=1 for the Ginzburg-Landau parameter. Thereby the structure of the mixed state near H _c2 for a value of the parameter κ close to unity is determined by the temperature correction to the coefficient for the third power and the coefficient for the fourth power in the expansion of the free energy in powers of H _c2−B. The values of these coefficients depend on the type of vortex lattice. Zh. éksp. Teor. Fiz. 112, 1499–1509 (October 1997)