Plateau transitions in fractional quantum Hall liquids

Effects of backward scattering between fractional quantum Hall (FQH) edge modes are studied. Based on the edge-state picture for hierarchical FQH liquids, we discuss the possibility of the transitions between different plateaux of the tunneling conductance G. We find a selection rule for the sequence which begins with a conductance (m: integer, p: even integer) in units of e ²/h. The shot-noise spectrum as well as the scaling behavior of the tunneling current is calculated explicitly. Received 5 October 1999 and Received in final form 19 November 1999     

Charge localization in organic conductors (TM)X: The influence of anion ordering

An investigation of the different contributions leading to charge localization in a 1/2 or 1/4 filled band 1D conductor has been conducted through a study of transport properties in the solid solution [(TMTSF)_1-x (TMTTF) _x]₂ReO₄. The existence of an ordering transition of the anions allows to identify two contributions to the electronic potential with wave vector 4k_F. A dominant on-site 4k_F potential besides the bond contribution is revealed when Umklapp scattering is pertinent via the weakening of the localization arising at the (0, 1/2, 1/2) anion ordering which is stabilized under pressure in the compound [(TMTSF) _0.5 (TMTTF)_0.5]₂ReO₄ at variance with the enhancement of localization observed in the homomolecular (TMTTF)₂ReO ₄ material. Received: 13 May 1998 / Revised: 8 July 1998 / Accepted: 9 July 1998     

A dynamic scattering approach for a gated interacting wire

A scattering approach for correlated one-dimensional systems is developed. The perfect contact to charge reservoirs is encoded in time-dependent boundary conditions. The conductance matrix for an arbitrary gated wire, respecting charge conservation, is expressed through a dynamic scattering matrix. Two applications are developed. First, it is shown that the dc conductance is equal to e ²/h for any model with conserved total left- and right-moving charges. Second, the ac conductance matrix is explicitly computated for the Tomonaga-Luttinger model (TLL). Received 31 August 1998     

Ionization of Rydberg atoms in THz-laser fields at the transition from low to high scaled frequencies

We have studied the ionization of Rydberg-excited xenon atoms in THz-laser fields and by quantum dynamical calculations. The experimental threshold laser field strength for 10% ionization probability follows an n^*-1.68 (1.04 THz) dependence (n^* effective principal quantum number) with additional weak resonance structures and shows that ionization does not occur by a Landau-Zener mechanism. At scaled frequencies of to 5.6 the simulated threshold fields for ionization in oscillatory fields show a dependence on the principal quantum number n of n^-4.1 to n^-1.35. Received: 17 February 1998 / Revised: 20 April 1998 / Accepted: 21 April 1998     

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures (T/J=10^-24) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given. Received: 12 February 1998 / Received in final form: 15 March 1998 / Accepted: 17 March 1998     

Spin correlations in the two-dimensional spin-5/2 Heisenberg antiferromagnet

We report a neutron scattering study of the instantaneous spin correlations in the two-dimensional spin S =5/2 square-lattice Heisenberg antiferromagnet Rb₂MnF₄. The measured correlation lengths are quantitatively described, with no adjustable parameters, by high-temperature series expansion results and by a theory based on the quantum self-consistent harmonic approximation. Conversely, we find that the data, which cover the range from about 1 to 50 lattice constants, are outside of the regime corresponding to renormalized classical behavior of the quantum non-linear model. In addition, we observe a crossover from Heisenberg to Ising critical behavior near the Néel temperature; this crossover is well described by a mean-field model with no adjustable parameters. Received: 3 March 1998 / Received in final form: 4 May 1998 / Accepted: 19 May 1998     

Hall effect plateaus and giant Shubnikov-de Haas oscillations in (BiSb)Telayered single crystals near the quantum limit

On bulk layered single crystals (Bi_0.25Sb_0.75)₂Te₃ with a hole concentration cm^-3 and a mobility cm²/Vs magnetoresistance and Hall effect investigations were performed in the temperature range T = 1.4 K ... 20 K in magnetic fields up to 18 T. For the magnetic field perpendicular to the layered structure giant Shubnikov-de Haas oscillations are measured; the positions of the maxima are triplets in the reciprocally scaled magnetic field. From the damping of the amplitudes with increasing temperature the cyclotron mass m _c = 0.12m ₀ is evaluated. Correlated with the SdH oscillations doublets of Hall effect plateaus (or kinks in low fields) are found. The weak well known Shubnikov-de Haas oscillations from the generally accepted multivallied highest valence band can be detected as a modulation on the giant oscillation. The high anisotropy of the SdH oscillations and their triplet structure in connection with the layered crystal structure lead us to suggest that the effects are caused by hole carrier pairing (mediated by the bipolaron mechanism) in quasi 2D sheets parallel to the crystal layer stacks. The measured Hall plateau resistances coincide with the quantum Hall effect values considering the number of layer stacks and the valley degeneracy of the 3D hole carrier reservoir. The ratio of spin splitting to Landau (cyclotron) splitting is observed to be . Received: 12 September 1997 / Revised: 8 January 1998 / Accepted: 22 January 1998     

Bias and temperature dependence of the noise in a single electron transistor

Models generalizing the su (2) XX spin-chain were recently introduced. These XXC models also have an underlying su (2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the A_m Lie algebras. Integrability of the new models is shown in the context of the quantum inverse scattering method. Their R-matrix is found and shown to yield a representation of the Hecke algebra. The diagonalization of the transfer matrices is carried out using the algebraic Bethe Ansatz. I comment on eventual generalizations and possible links to reaction-diffusion processes. Received: 24 June 1998 / Received in final form: 8 September 1998 / Accepted: 10 September 1998     

The new identity for the scattering matrix of exactly solvable models

We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one-dimensional Bose gas and XXZ Heisenberg quantum spin chain. Received: 4 December 1997 / Accepted: 17 March 1998     

Atomic Rayleigh scattering cross-sections and the associated anomalous dispersion in the X-ray regions

Elastic scattering cross-sections for Pd, Ag, Cd, In, Sn, Sb, Pt, Au and Pb are measured at an angle of 90 in the X-ray region 5.41 keV. These energies fall between the high-energy side of the L- and M-shell absorption edges of the atoms considered. The present atomic region is significant for solid X-rays to assess the contribution of resonance and solid-state environmental effects. Also it is the anomalous scattering region for many of the atoms of the periodic table. Experimental results are compared with theoretical calculations based on form factor formalisms including the anomalous corrections and available recent S-matrix values. Based on the experimental evidence, the present results indicate the influence of solid-state environmental effects, the importance of anomalous corrections nearer to absorption edges, the correctness of revised high-energy limit values, the superiority of S-matrix predictions over form factor values on measured elastic scattering cross-sections in the X-ray regime and also show the resonance behavior around K, L and M absorption edges. Received: 27 January 1998 / Received in final form: 4 January 1999     

Temporal coherent control induced by wave packet interferences in one and two photon atomic transitions

The interaction of a sequence of two identical ultrashort laser pulses with an atomic system results in quantum interferences as in Ramsey fringes experiments. These interferences allow achievement of temporal coherent control of the excitation probability. We present the results of a temporal coherent control experiment on two different atomic systems: one-photon absorption in K (4s-4p) and two-photon absorption in Cs (6s-7d). In K, the quantum interferences between the two excitation paths associated with the laser pulses are revealed through rapid oscillations of the excitation probability as a function of the time delay between the two pulses. These oscillations take place at the transition frequency (period T = 2.56 fs). The interferences are modulated by beats (at about 580 fs) resulting from the doublet structure of the excited state (4p (² P _1/2 , ² P _3/2 )). Three complementary interpretations of this experiment are presented: in terms of beats of quantum interferences, of variation in the spectrum intensity, and of wave packet interferences. Whenever the two laser pulses are temporally overlapped, optical interferences are superimposed on to the quantum interferences. The distinction between these two types of interference is clearly revealed in the two-photon excitation scheme performed on Cs (6s-7d (² D _3/2 , ² D _5/2 )) because quantum interferences occur at twice the frequency of the optical interferences. Received: 30 December 1997 / Revised: 28 February 1998 / Accepted: 4 March 1998     

Heat transport through a quantum dot with one-dimensional interacting leads under Coulomb blockade regime

The peculiarities of a low temperature heat transfer through a ballistic quantum dot (a double potential barrier) with interacting leads due to a long-range Coulomb interaction (in the geometrical capacitance approach) are considered. It is found that the thermal conductance K shows periodic peaks as a function of the electrostatic potential of a dot at low temperatures. At the peak maximum it is whereas near the minimum it is . Near the peak maximum the dependence K(T) is essentially nonmonotonic at the temperatures correspondent to the level spacing in the quantum dot. Received 20 October 1999 and Received in final form 20 January 2000     

Quantum scattering in the strip: From ballistic to localized regimes

Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined. Received: 28 January 1998 / Revised: 16 June 1998 / Accepted: 6 July 1998     

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k^-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level. Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998     

The smooth structural change in mesoscopic Peierls chains

We investigate the Peierls transition in finite chains by exact (Lanczos) diagonalization and within a seminumerical method based on the factorization of the electron-phonon wave function (Adiabatic Ansatz, AA). AA can be applied for mesoscopic chains up to micrometer sizes and its reliability can be checked self-consistently. Our study demonstrates the important role played for finite systems by the tunneling in the double well potential. The chains are dimerized only if their size N exceeds a critical value N_c which increases with increasing phonon frequency. Quantum phonon fluctuations yield a broad transition region. This smooth Peierls transition contrasts not only to the sharp mean field transition, but also with the sharp RPA soft mode instability, although RPA partially accounts for quantum phonon fluctuations. For weak coupling the dimerization disappears below micrometer sizes; therefore, this effect could be detected experimentally in mesoscopic systems. Received: 3 January 1998 / Revised: 13 March 1998 / Accepted: 3 April 1998     

Bound and scattering wave functions for a velocity-dependent Kisslinger potential for l > 0

Using formal scattering theory, the scattering wave functions are extrapolated to negative energies corresponding to bound-state poles. It is shown that the ratio of the normalized scattering and the corresponding bound-state wave functions, at a bound-state pole, is uniquely determined by the bound-state binding energy. This simple relation is proved analytically for an arbitrary angular momentum quantum number l > 0, in the presence of a velocity-dependent Kisslinger potential. The extrapolation relation is tested analytically by solving the Schr?dinger equation in the p-wave case exactly for the scattering and the corresponding bound-state wave functions when the Kisslinger potential has the form of a square well. A numerical resolution of the Schr?dinger equation in the p-wave case and of a square-well Kisslinger potential is carried out to investigate the range of validity of the extrapolated connection. It is found that the derived relation is satisfied best at low energies and short distances. Received: 17 October 2001 / Accepted: 4 January 2002     

How to get access to long range states of highly excited molecules

Due to competition between ionic and covalent dissociation, the excited potential curves of the alkali dimers display long range structures, leading in some cases to secondary wells. We discuss the possibility of populating the well (with a depth of 1614.8 cm^-1, located at R _e = 30.5a ₀ ) that is present in the Na₂ potential curve and propose detection schemes. Received: 28 May 1998 / Revised: 5 August 1998 / Accepted: 24 September 1998     

Cavitation in superfluid helium-4 at low temperature

We have studied the nucleation of bubbles in pure superfluid helium-4 at temperatures down to 65 mK. We have found that the nucleation is a stochastic process, and that at temperatures below 600 mK the nucleation rate is independent of temperature. These results are consistent with the assumption that the nucleation takes place via quantum tunneling. Received: 15 November 1997 / Received in final form: 19 December 1997 / Accepted: 22 January 1998     

Transition probabilities of forbidden lines in Pb I

Multiconfiguration Dirac-Fock as well as semiempirical calculations of decay rates of forbidden transitions within the ground 6s ² 6p ² configuration of neutral lead are reported and compared with relativistic Hartree-Fock results as well as with available experimental data. Received: 15 July 1998 / Received in final form: 15 October 1998