Quantum orientational melting and the phase diagram of a mesoscopic system

The “phase diagram” of a two-dimensional mesoscopic system of bosons is investigated. An example of such a system is a system of indirect magnetoexcitons in semiconductor double quantum dots. Quantum Monte Carlo calculations show the existence of quantum orientational melting. At zero (quite low) temperature, as quantum fluctuations of the particles intensify, two quantum disordering phenomena occur with increasing de Boer parameter q. First, at q≈10⁻³ the system passes to a radially ordered but orientationally disordered state, where different shells of a cluster rotate relative to one another. Then at q≈0.16 a transition to a superfluid state occurs. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 11, 817–822 (10 December 1998)     

The role of auto-ionization transitions in the formation of the extended fine structure of high-energy secondary electron spectra

Extended fine structure (EFS) of secondary electron (SE) spectra has been detected beyond the high-energy (∼720 and ∼840 eV) LVV Auger lines in iron and nickel. Two mechanisms of its formation are considered: 1) direct transitions of electrons to the final state p according to Fermi’s “golden rule” and 2) second-order processes of auto-ionization type, passing through excitation of a core electron to an intermediate state q of the continuum with subsequent filling of the hole formed during this process by a valence electron and transition of the electron from the intermediate state q to the final state p. Interference of the direct wave with the wave reflected from neighboring atoms generates the EFS both in the final (p) and in the intermediate (q) state with two different periods determined by the wave numbers p and q. Comparison of calculated extended fine structures with the experimentally observed ones leads to the conclusion that the structure is formed by second-order auto-ionization processes. Fiz. Tverd. Tela (St. Petersburg) 40, 1589–1594 (September 1998)     

Quadrupole interactions in MoCl5 intercalated in graphite

The time-differential perturbed angular correlation technique was used to investigate quadrupole interactions following the decay of⁹⁹Mo as a probe in the intercalation compound graphite-molybdenum pentachloride. Analysis of the 740-(44) 141 keV γ-γ correlation in⁹⁹Tc reveals the presence of two sites with static electric field gradient interactions, one of which corresponds to a moderately damped (δ∼16%), high-frequency interaction (v _q∼630 MHz), the other to a heavily damped (δ∼28%), low-frequency (v _q∼283 MHz) component.     

Thermal conductivity of nonlinear waves in disordered chains

We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity κ(T). We find indications for an asymptotic low-temperature κ ∼ T ⁴ and intermediate temperature κ ∼ T ² laws. These findings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (Laptyeva et al, Europhys. Lett. 91, 30001 (2010)).     

Quantum beats in excitons in Cu2O

A theoretical study is carried out of quantum beats (QB) in the time-dependent intensities of absorption of a test pulse and of spontaneous luminescence in a Cu₂O crystal under conditions of double optical resonance. It is assumed that pumping is effected by a CO₂-laser pulse which dynamically couples the exciton levels 1s(Γ ₅ ⁺ ) and 2p(Γ ₄ ⁻ ,Γ ₅ ⁻ ,Γ ₃ ⁻ Γ ₂ ⁻ ) and splits them into two or three pairs of quasi-energy levels. The frequency of the test pulse is in resonance with the frequency Γ ₅ ⁺ of the exciton. The corresponding intensities for various directions of the electric vector of the pump field E _L, the polarization vector ξ, and the wave vector q of the test pulse are obtained. The frequency of the quantum beats is twice the Rabi frequency, which for different values of E _L, ξ and q contains different sets of matrix elements of the dipole transitions between the levels 1s(Γ ₅ ⁺ ) and 2p(Γ ₄ ⁻ ,Γ ₅ ⁻ ,Γ ₃ ⁻ Γ ₂ ⁻ ). Thus, by measuring the period of the quantum beats it is possible to determine the unknown matrix elements of the indicated transitions. Fiz. Tverd. Tela (St. Petersburg) 39, 844–847 (May 1997)     

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     

Helicity modulus, quantum fluctuations, and superconducting transition in a Josephson junction, array

The effect of quantum fluctuations on a phase transition in a two-dimensional Josephson junction array is studied in terms of the two-dimensional XY model. A self-consistent harmonic approximation is used to calculate the linear response of the system to a perturbation by a uniform phase gradient (helicity modulus γ) as a function of dimensionless temperature Θ and of a quantum parameter q appearing due to the finite capacitance of each junction. Calculation of this quantity has permitted us to find the dependence of the Kosterlitz-Thouless transition temperature on q, which within a broad range of q variation is in agreement with the results of a quantum Monte Carlo simulation. Fiz. Tverd. Tela (St. Petersburg) 39, 818–822 (May 1997)     

DNA molecule as an elastic Heisenberg chain

A DNA molecule is simulated by an anisotropic elastic fiber which defines the configuration of the molecule central line and is supplemented with a chain of quantum two-level systems imitating hydrogen bonds between two polynucleotide chains in the DNA double helix. The system Hamiltonian consists of Kirchhoff’s classical elastic energy and the energy of a quantum anisotropic chain of “spins” 1/2. The two-level systems and macroscopic vector variables which determine the conformation of the central line are coupled by a classical vector field q, which is introduced to take into account the existence of two polynucleotide strands. Averaging over fast (microscopic) variables yields an effective potential U(q). In the approximation of weak coupling between the systems, the spectrum of elementary excitations and effective potential U(q) have been calculated in explicit form. The relation between elementary excitations in the “magnetic” subsystem and so-called breathing modes [C. Mandel, N. R. Kallenbach, and S. W. Englander, J. Mol. Biol. 135, 391 (1980); G. Manning, Biopolymers 22, 689 (1983)] corresponding to low-frequency excitations in DNA molecules is discussed. Zh. éksp. Teor. Fiz. 111, 1833–1844 (May 1997)     

Photogalvanic effect in an asymmetric system of three quantum wells in a strong magnetic field

The photogalvanic effect (PGE) in an asymmetric undoped system of three GaAs/AlGaAs quantum wells illuminated with white light of various intensities is investigated in magnetic fields up to 75 kOe at temperatures ranging from 4.2 K up to 300 K. A maximum of the spontaneous photogalvanic current J ^PGE as a function of the magnetic field predicted by A. A. Gorbatsevich et al., JETP Lett. 57, 580 (1993), is observed. Analysis of the experimental data shows that the main initial characteristic of the PGE is not the spontaneous current but rather the electromotive force E ^PGE arising in the direction perpendicular to the applied magnetic field. It is determined that this emf is independent of the intensity of the incident light, increases linearly with the size d of the illuminated region, and decreases slowly with temperature: E _max ^PGE ∼0.8 V at 300 K and ∼0.1 V at 4.2 K for d∼3 mm. The curve E ^PGE(H) at room temperature is determined with allowance for the strong transverse magnetoresistance of the nanostructure. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 197–202 (10 February 1996)     

Bistability of quantum magnetotransport in a multilayer Ge/p-Ge1−x Six heterostructure with wide potential wells

Two metastable states of a multilayer Ge/p-Ge_1−x Si_x heterosystem with wide (∼ 35 nm) potential wells (Ge) are observed in strong magnetic fields B at low temperatures. In the first state, the Hall resistivity exhibits an inflection near the value ρ_xy=h/e ² scaled to one Ge layer. The longitudinal magnetoresistivity ρ_xx(B) possesses a minimum in the range of fields where this inflection occurs. The temperature evolution of the inflection in ρ_xy(B), the minimum of ρ _xx(B), and the value of ρ_xy at the inflection indicates a weakly expressed state of the quantum Hall effect with a uniform current distribution over the layers. In the second metastable state, an unusually wide plateau near h/2e ² with a very weak field dependence is observed in ρ_xy(B). Estimates show that in these samples the Fermi level lies below but close to the top of the inflection in the bottom of the well. For this reason, the second state can be explained by separation of a hole gas in the Ge layers into two sublayers, and the saturation of ρ_xy(B) near h/2e ² can be explained by the formation of a quantum Hall insulator state. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 290–297 (25 August 1999)     

Vision of a fully laser-driven ${\sf n\gamma}{-}{\sf m\gamma}$ collider

The use is suggested of a laser-accelerated dense electron sheet with an energy of (E=[(g)\tilde] mc²E=\tilde{\gamma} mc^2) as a relativistic mirror to reflect coherently a second laser with photon energy ħω, generating by the Doppler boost high-energy γ photons with $ \hbar \omega ' = 4\tilde \gamma ^2 \hbar \omega $ \hbar \omega ' = 4\tilde \gamma ^2 \hbar \omega and short duration [A. Einstein, Annalen der Physik 17, 891 (1905); D. Habs et al., Appl. Phys. B 93, 349 (2008)]. Two of these counter-propagating γ beams are focused by the parabolically shaped electron sheets into the interaction region with small, close to diffraction-limited, spot size. Comparing the new nγ-mγ collider with former proposed γγ collider schemes we achieve the conversion of many photon-pairs in a small space-time volume to matter-antimatter particles, while in the other discussed setups only two isolated, much more high-energetic photons will be converted, reaching in the new approach much higher energy densities and temperatures. With a γ-field strength somewhat below the Schwinger limit we can reach this complete conversion of the γ bunch energy into e⁺e^- or quark-antiquark q[`(q)]q\bar{q}-plasmas. For a Bose-Einstein condensate (BEC) [A. Einstein, Physikalisch-mathematische Klasse (Berlin) 22, 261 (1924); A. Einstein, Physikalisch-mathematische Klasse (Berlin) 22, 3 (1925); A. Griffin, D.W. Snoke, S. Stringari, Bose-Einstein Condensation (Cambridge University Press, 1995)] final state or for the Cooper pair ground state at higher densities [A.J. Leggett, Quantum Liquids, Oxford Graduate Texts (Oxford University Press, 2006)] the strong induced transition into this coherent state is of special interest for single-cycle γ pulses. Due to annihilation these cold coherent states are very short-lived. For γ beams with photon energies of 1–10 keV the rather cold e<sup>+</sup>e<sup>-</sup>-plasma or e<sup>+</sup>e<sup>-</sup>-BEC expands to a cold dense aggregate of positronium (Ps) atoms, where the production of Ps molecules is discussed. For photon energies of 1–10 MeV we discuss the production of a cold induced π<sup>0</sup>-BEC followed by the formation of molecules. For the direct population of higher q[`(q)]q\bar{q} densities we can study condensates of color-neutral mesons with enhanced population. For a γγ collider with several-cycle laser pulses the following cycles heat up the fermion-antifermion f[`(f)]f\bar{f} system to a certain temperature. Thus we can reach high energy densities and temperatures of an e⁺e^-γ plasma, where the production of hadrons in general or the quark-gluon phase transition can be observed. Within the long-term goal of very high photon energies of about 1 GeV in the nγ-mγ-collider, even the electro-weak phase transition or SUSY phase transition could be reached.     

Dissipative curvature fluctuations in bilayer vesicles: Coexistence of pure-bending and hybrid curvature-compression modes

We have studied the relaxation dynamics of shape fluctuations in unilamellar lipid vesicles by neutron spin echo (NSE). The presence of a hybrid curvature-compression mode coexisting with the usual bending one has been revealed in the experimental relaxation functions at high q . Differently to the conventional relaxation ∼ q ³ typical for bending modes, the hybrid mode was found to relax as ∼ q ² , which is compatible with a dissipation mechanism arising from intermonolayer friction. Complementary data obtained from flickering spectroscopy (FS) in giant unilamellar vesicles confirm the existence of both modes coexisting together. By combining NSE and FS data we have depicted the experimental bimodal dispersion diagram, which is found compatible with theoretical predictions for reliable values of the material parameters. From the present data two conventional dynamical methods (NSE and FS) have been shown to be suitable for measuring intermonolayer friction coefficients in bilayer vesicles.     

Discovery of a narrow resonance state of the system K S K S at mass 1520 MeV

Data are presented which indicate the existence of a previously unknown narrow resonance near mass 1520 MeV, discovered while analyzing the system K _S K _S . The data were obtained at ITEP using the 6-m magnetic spectrometer in a beam of 40-GeV negative particles. The resonance is observed in π⁻ p and K ⁻ p interactions with a total statistical confidence of not less than 5 standard deviations. The width of this state is comparable to the mass resolution of the spectrometer (∼5 MeV). The mass is 1521.5±2.5 MeV. Estimates of the product σ·BR (K _S K _S ) give ∼5.0 nb in π⁻ p interactions and ∼250 nb in K ⁻ p interactions. From the fact that the production cross section of this resonance in the K ⁻ beam is approximately 50 times greater than the production cross section in the π⁻ beam, it can be concluded that this new state belongs to a system of mesons with hidden strangeness. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 242–246 (25 August 1999)     

Examples of gauged Laplacians on noncommutative spaces

We present two (classes of) examples of gauged Laplacian operators. The first one is a model of spin-Hall effect on a noncommutative four-sphere S _ϑ ⁴ with isospin degrees of freedom, coming from a noncommutative instanton, and invariant under the quantum group SO _ϑ (5). The second one, a Hall effect on a quantum 2-dimensional sphere S _q ², describes ‘excitations moving on the quantum sphere’ in the field of a magnetic monopole with symmetry coming from the quantum group SU _q (2). For both models, ample symmetries provide a complete diagonalization.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Geometrical Tools for Quantum Euclidean Spaces

We apply one of the formalisms of noncommutative geometry to ℝ ^N _q , the quantum space covariant under the quantum group SO _q (N). Over ℝ ^N _q there are two SO _q (N)-covariant differential calculi. For each we find a frame, a metric and two torsion-free covariant derivatives which are metric compatible up to a conformal factor and which have a vanishing linear curvature. This generalizes results found in a previous article for the case of ℝ³ _q . As in the case N=3, one has to slightly enlarge the algebra ℝ ^N _q ; for N odd one needs only one new generator whereas for N even one needs two. As in the particular case N=3 there is a conformal ambiguity in the natural metrics on the differential calculi over ℝ ^N _q . While in our previous article the frame was found “by hand”, here we disclose the crucial role of the quantum group covariance and exploit it in the construction. As an intermediate step, we find a homomorphism from the cross product of ℝ ^N _q with U _q so(N) into ℝ ^N _q , an interesting result in itself. Received: 4 March 2000 / Accepted: 11 October 2000     

Noncommutative Instantons on the 4-Sphere¶from Quantum Groups

We describe an approach to the noncommutative instantons on the 4-sphere based on quantum group theory. We quantize the Hopf bundle ?⁷→?⁴ making use of the concept of quantum coisotropic subgroups. The analysis of the semiclassical Poisson–Lie structure of U(4) shows that the diagonal SU(2) must be conjugated to be properly quantized. The quantum coisotropic subgroup we obtain is the standard SU _q (2); it determines a new deformation of the 4-sphere ∑⁴ _q as the algebra of coinvariants in ? _q ⁷. We show that the quantum vector bundle associated to the fundamental corepresentation of SU _q (2) is finitely generated and projective and we compute the explicit projector. We give the unitary representations of ∑⁴ _q , we define two 0-summable Fredholm modules and we compute the Chern–Connes pairing between the projector and their characters. It comes out that even the zero class in cyclic homology is non-trivial. Received: 3 January 2001 / Accepted: 14 November 2001     

Influence of antiferromagnetic ordering on the de Haas-van Alphen effect in a semimetal

The distinctive characteristics of the de Haas-van Alphen effect in semimetals with antiferromagnetic long-range order are investigated theoretically. It is shown that the transition of the subsystem of localized spins from the canted antiferromagnetic phase to the ferromagnetic phase is accompanied by an abrupt change in the “frequency” of the magnetization oscillations of band carriers M _∼. In the below-critical range of magnetic fields, M _∼ is not a function periodic in 1/H. Significantly, the additional contribution to the phase of the oscillatory factors is proportional to H ² and is determined entirely by quantum fluctuations in the antiferromagnetic subsystem. Fiz. Tverd. Tela (St. Petersburg) 39, 204–210 (February 1997)     

Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N _a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)_c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)_c=0.300±0.005, agrees with the value (t/U)_c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t _c)^−1/2]. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996)     

Swelling of two-dimensional polymer rings by trapped particles

The mean area of a two-dimensional Gaussian ring of N monomers is known to diverge when the ring is subject to a critical pressure differential, p _c ∼ N ^-1. In a recent publication (Eur. Phys. J. E 19, 461 (2006)) we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition from a crumpled state, where the mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N ². In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field theory, and Monte Carlo simulations. For a fixed number Q of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of an area constraint. In the Gaussian case the ring swells to such a mean area, 〈A〉 ∼ NQ, that the pressure exerted by the particles is at p _c for any Q. In the freely jointed model the mean area is such that the particle pressure is always higher than p _c, and 〈A〉 consequently follows a single scaling law, 〈A〉 ∼ N ² f (Q/N), for any Q. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained. Thus, the two ensembles are manifestly inequivalent in these systems. An erratum to this article is available at .