Resistivity of 2D electrons with ν=1/2 in a zero magnetic field

The dependence of the resistivity of 2D electrons with Landau level filling factor ν=1/2 in a zero magnetic field is studied experimentally as a function of the carrier density. It is found that the ratio of the resistivity for B=0 and ν=1/2 is a linear function of the carrier density, as predicted by a theory based on the scattering of composite fermions by spatial fluctuations of the effective static magnetic field. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 154–158 (10 August 1997)     

Time evolution of <Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">μν</Emphasis></Subscript> and the cosmological constant problem

We study the cosmic time evolution of an effective quantum field theory energy-momentum tensor T _μν and show that, as a consequence of the effective nature of the theory, T _μν is such that the vacuum energy decreases with time. We find that the zero point energy at present time is washed out by the cosmological evolution. The implications of this finding for the cosmological constant problem are investigated.     

Form factors and branching ratio for the B→lνγ decay

Form factors parameterizing radiative leptonic decays of heavy mesons (B⁺→γl⁺ν_l) against photon energy are computed in the language of dispersion relations. The states contributing to the absorptive part in the dispersion relation are the multiparticle continuum, estimated by the quark triangle graph, and resonances with quantum numbers 1^- and 1⁺, which includes B^* and B_A ^* and their radial excitations, which model the higher state contributions. Constraints provided by the asymptotic behavior of the structure dependent amplitude, Ward identities and gauge invariance are used to provide useful information for the parameters needed. The couplings g_BB*γ and f_BBA*γ are predicted as we restrict ourselves to the first radial excitation; otherwise using these as an input the radiative decay coupling constants for the radial excitations are predicted. The value of the branching ratio for the process B⁺→γμ⁺ν_μ is found to be in the range 0.5×10^-6. A detailed comparison is given with other approaches.     

Anomalous light-induced drift of linear molecules

The sudden approximation in energy is used to derive analytic formulas that describe the anomalous light-induced drift (LID) of linear molecules absorbing radiation in the rovibrational transition nJ _i −mJ _f (n and m are the ground and excited vibrational states, and J _α is the rotational quantum number in the vibrational state α=m, n). It is shown that for all linear molecules with moderate values B≲1 cm⁻¹ of the rotational constant, anomalous LID can always by observed under the proper experimental conditions; temperature T, rotational quantum number J _i , and type of transition (P or R). The parameter γ=B[J _i (J _i +1)−J _f (J _f +1)] ν _n /2k _BT (ν _m −ν _n ) is used to derive a condition for observing anomalous LID: γ∼1 (k _B is the Boltzmann constant and ν _α is the transport rate of collisions of molecules in the vibrational state α and buffer particles at moderate molecular velocities , where is the most probable velocity of the buffer particles). For ν _m >ν _n anomalous LID can be observed only in P-transitions, while for ν _m <ν _n it can be observed only in R-transitions. It is shown that anomalous LID is possible for all ratios β=M _b /M of the masses of the buffer particles (M _b ) and of the resonant particles (M) and any absorption-line broadening (Doppler or homogeneous). The optimum conditions for observing anomalous LID are realized when the absorption line is Doppler-broadened in an atmosphere of medium-weight (β∼1) and heavy (β≫1) buffer particles. In this case, anomalous LID can be observed in the same transition within a broad temperature interval ΔT∼T. If the buffer particles are light (β≪1) or if the broadening of the absorption line is homogeneous, anomalous LID in the same transition can be observed only within a narrow temperature range ΔT≪T. Zh. éksp. Teor. Fiz. 115, 1664–1679 (May 1999)     

Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001     

The Boltzmann Equation for Driven Systems of Inelastic Soft Spheres

We study a generic class of inelastic soft sphere models with a binary collision rate g^ν that depends on the relative velocity g. This includes previously studied inelastic hard spheres (ν = 1) and inelastic Maxwell molecules (ν = 0). We develop a new asymptotic method for analyzing large deviations from Gaussian behavior for the velocity distribution function f(c). The framework is that of the spatially uniform nonlinear Boltzmann equation and special emphasis is put on the situation where the system is driven by white noise. Depending on the value of exponent ν, three different situations are reported. For ν < −2, the non-equilibrium steady state is a repelling fixed point of the dynamics. For ν > −2, it becomes an attractive fixed point, with velocity distributions f(c) having stretched exponential behavior at large c. The corresponding dominant behavior of f(c) is computed together with sub-leading corrections. In the marginally stable case ν = −2, the high energy tail of f(c) is of power law type and the associated exponents are calculated. Our analytical predictions are confronted with Monte Carlo simulations, with a remarkably good agreement.     

Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems, as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order l≥ 3 contribute to an exponential which corresponds to a mean-field energy involving the second operator U₂, instead of the potential itself as usual - in other words, the mean-field correction is expressed in terms of a modification of a local Boltzmann equilibrium. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator U_n with n≥ 3 contains a “tree-reducible part”, which groups naturally with U₂ through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics. Received 18 October 2001     

ESR in the Earth’s magnetic field as a cause of dislocation motion in NaCl crystals

The resonance displacements of the dislocations, l ∼ 100 μm, in NaCl crystals placed in the crossed Earth’s magnetic field B _Earth and the ac field $ \tilde B $ \tilde B ≈ 3 μT of the variable frequency ν ∼ 10⁶ Hz have been discovered in the absence of any other impact on the crystals. Two peaks of the mean dislocation path l(ν) with the maxima at ν₁ = 1.3 MHz and ν₂ = 3 MHz have been observed for the field $ \tilde B $ \tilde B oriented along the vertical and horizontal components of B _Earth, respectively. The effect is explained by the depinning of the dislocations from the impurity centers after their structural transformation due to the ESR in the dislocation-impurity system in the crossed fields. The subsequent motion of the dislocations proceeds under the action of internal stress in the crystals. A physical model has been proposed to explain the strong anisotropy of the effect with respect to the mutual orientation of the dislocation lines and magnetic fields.     

Semilinear PDEs on Self-Similar Fractals

A Laplacian may be defined on self-similar fractal domains in terms of a suitable self-similar Dirichlet form, enabling discussion of elliptic PDEs on such domains. In this context it is shown that that semilinear equations such as Δu+u ^p = 0, with zero Dirichlet boundary conditions, have non-trivial non-negative solutions if 0<ν≤ 2 and p>1, or if ν >2 and 1<p< (ν+ 2)/(ν− 2), where ν is the “intrinsic dimension” or “spectral dimension” of the system. Thus the intrinsic dimension takes the r\^{o}le of the Euclidean dimension in the classical case in determining critical exponents of semilinear problems. Received: 11 December 1998 / Accepted: 22 March 1999     

Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory

No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures ρ on Ω having zero mean value and dispersion σ²(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ²(ρ) = hⁿ (for n = 2 we obtain the conventional quantum formalism).     

On the possible existence of a neutrino pulsar

If the neutrino has a magnetic moment in the interval 10⁻¹³μ_B < μ _ν < 10⁻¹² μ_B and if a magnetic field of strength about 10¹⁴ G exists in the supernova envelope, the effect of a pulsation of a neutrino signal from a supernova may arise owing to a ν _L → ν _R resonance transition in the envelope magnetic field.     

From macroscopic to atomic motions in liquid metals

Summary In the present review of liquid dynamics studies on liquid metals are reported. Particularly the case of liquid lead is reviewed because this case was carefully studied by neutron scattering technique,S(Q,ω) being determined at two widely different temperaturesT=623 K andT=1170 K and therefore different densities. In addition extensive supplementary MD simulations were made using a 16 384-particle system. The simulations ranged from a determination of an effective pair potential for lead to simulation of the density correlation functionsF(Q,t) andF _s(Q,t), as well as the longitudinal and transversal current correlation functionsJ ₁(Q,t) andJ _T(Q,t). The MD simulation ?calibrated? via the experimentalS(Q) andS(Q,ω) was used to prolong the range of neutron data to draw conclusions regarding such quantities as dispersion relations for the current correlationsJ ₁(Q,t) andJ _T(Q,t), the generalized viscosity functions ν₁(Q,t), ν₁(Q) and ν_s(Q). Information regarding bulk viscosity ν_B(Q) is also gained. Conclusions are drawn regarding the relative importance of the derived pair potential form by comparison to corresponding hard-sphere data. The general framework of linearized hydrodynamic equations for the macroscopic situation transforming to visco-elastic equations of motion for finite wave-length and high frequency works well also for the case of a continuous potential. The region of transition from simple visco-elastic to hydrodynamic behaviour is occurring at wavelengths in the range (12÷20) ? for the cases studied. The spatial properties of the viscosity functions ν₁(r), ν_s(r) and ν_B(r) are found to correlate well with the range of the radial distribution function for the liquid. The general results for liquid lead probably have wide range of applicability to other simple liquids with similarS(Q) andg(r) properties. The authors have agreed not to receive proofs for correction.     

Far-infrared s→p ± interexciton transitions in InGaAs/GaAs coupled double quantum wells

We consider s→p ^± interexciton far-infrared (FIR) magnetooptical transitions in coupled double quantum wells (DQWs). Spatially direct (intrawell) and indirect (interwell) excitons in strained In_xGa_1−x As/GaAs symmetric DQWs with a simple valence band are considered. The evolution of the transition energies and oscillator strengths as functions of the transverse magnetic field B in different regimes is studied: we consider the direct regime (zero and low transverse electric field ℰ), the indirect regime (high ℰ), and the indirect-direct crossover (induced by increasing B at intermediate ℰ). Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 198–202 (10 August 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Suppression of the equilibrium tunneling current between slightly disordered two-dimensional electron systems with different electron concentrations in a high magnetic field

Tunneling between parallel two-dimensional electron gases (2DEG) in accumulation layers formed on both sides of the single doped AlGaAs barrier are examined in both zero and high magnetic field. Accumulation layers are separated from highly n-doped contact regions which freely supply electrons to the 2DEGs via 80 nm thick lightly n-doped spacer layers. Strongly oscillating current with magnetic field along the 2DEGs is absent in this arrangement. Without magnetic field resonant tunneling between 2DEGs with different as grown electron concentration could be settle by application of external voltage bias. High magnetic fields (ν<1) shift resonant tunneling to zero external bias and suppresses tunneling current, creating wide gap in the tunneling density of states at the Fermi level arisen from the in-plane Coulomb interaction in the 2DEGs. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 236–241 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Magnetoplastic effect in irradiated NaCl and LiF crystals

The effect of low x-ray irradiation doses (≈10² rad) on the magnetoplastic effect — the detachment of dislocations from paramagnetic centers under the action of an external magnetic field B — in alkali-halide crystals has been investigated. The measurements were performed on LiF crystals and three types of NaCl crystals, differing in impurity content. The dependence of the mean free path l of the dislocations on the rotational frequency ν of a sample in a magnetic field was especially sensitive to low irradiation doses. In unirradiated crystals this dependence is a single-step dependence and is characterized by a critical frequency ν _c ∝B ² above which the magnetoplastic effect is not observed. The frequency ν _c depends only on the type of paramagnetic centers, and not on their density. Even the lowest irradiation dose employed (<100 rad) leads to a sharp restructuring of the dependence l(ν), converting it into a two-step dependence (for edge dislocations) with an additional critical frequency ν _c2, that is insensitive to the irradiation dose, and that corresponds to the appearance of magnetically sensitive stoppers of a new type under irradiation. The initial critical frequency ν _c1, as a rule, also varies with the dose, reflecting the change in state of the impurity complexes (Ca in NaCl and Mg in LiF). Specifically, it is shown for NaCl(Ca) crystals that as the irradiation dose increases, the frequency ν _c1 increases, gradually approaching the value ν _c2, so that by the time the dose is ≈300 rad, the dependence l(ν) once again becomes a single-step dependence, dropping sharply only for ν⩾ν _c2. It is shown that the addition of a small number of Ni atoms to a NaCl crystal makes the Ca complexes radiation resistant, and the critical frequency ν _c1 corresponding to them initially equals ν _c2 for crystals with no Ni. The recombination kinetics of radiation defects in the case in which the samples are irradiated under a tungsten lamp was investigated. A possible physical model of the observed dependences is discussed. Zh. éksp. Teor. Fiz. 111, 615–626 (February 1997)     

Noncolliding Squared Bessel Processes

We consider a particle system of the squared Bessel processes with index ν>−1 conditioned never to collide with each other, in which if −1<ν<0 the origin is assumed to be reflecting. When the number of particles is finite, we prove for any fixed initial configuration that this noncolliding diffusion process is determinantal in the sense that any multitime correlation function is given by a determinant with a continuous kernel called the correlation kernel. When the number of particles is infinite, we give sufficient conditions for initial configurations so that the system is well defined. There the process with an infinite number of particles is determinantal and the correlation kernel is expressed using an entire function represented by the Weierstrass canonical product, whose zeros on the positive part of the real axis are given by the particle-positions in the initial configuration. From the class of infinite-particle initial configurations satisfying our conditions, we report one example in detail, which is a fixed configuration such that every point of the square of positive zero of the Bessel function J _ν is occupied by one particle. The process starting from this initial configuration shows a relaxation phenomenon converging to the stationary process, which is determinantal with the extended Bessel kernel, in the long-term limit.     

Exciton magnetotransport in two-dimensional systems: Weak-localization effects

The paper considers the effect of a magnetic field B on the transport of neutral composite particles, namely excitons, in weakly disordered two-dimensional (2D) systems. In the case of classical transport (when the interference of different paths is neglected), the magnetic field suppresses exciton transport, and the static diffusion constant D(B) monotonically drops with B. When quantum-mechanical corrections due to weak localization are taken into account, D(B) becomes a nonmonotonic function of B. In weak magnetic fields, where the magnetic length is much larger than the exciton Bohr radius, ℓ_B=(ℏc/eB)^1/2≫a _B =ε ℏ²/μe ²,a positive magnetodiffusion effect is predicted, i.e., the exciton mobility should increase with B. Zh. éksp. Teor. Fiz. 114, 359–378 (July 1998)     

Energy gaps at neutrality point in bilayer graphene in a magnetic field

Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the ν = 0 quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane ($ \bar \Delta _0 $ \bar \Delta _0 , B), where $ \bar \Delta _0 $ \bar \Delta _0 is a top-bottom gates voltage imbalance, is described. It is shown that the energy gap scales linearly, ΔE ∼ 14B [T] K, with magnetic field.