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QUANTUM GENERALIZATION OF THE THOMAS  FERMI APPROACH : EXACTLY SOLVABLE EXAMPLE
Correct allowing for the interparticle interaction in manybody systems faces considerable mathematical difficulties. The most frequently used approximation in such problems is the mean field approximation (MFA) which neglects fluctuations and the particles are considered as a continuous medium of inhomogeneous density. If , moreover, the system is described by the classical distribution function ( the statistics can be a quantum one) we obtain the well known Thomas  Fermi approach .However there are situations when at least some of the degrees of freedom of the system have to be treated in accord with quantum mechanics. Such examples are electrons in quantum wells or dipolar excitons in an electrostatic trap. In such cases the density of particles appearing in MFA is to be expressed via wave functions of a particle in the effective potential. The latter, in its turn, depends on the wave functions and occupation numbers, so one has to solve a selfconsistent problem. In case of a shortrange interparticle pair potential (2D gas of dipolar excitons) a nonlinear wave equation arises while for the longrange ( Coulomb) pair interaction the corresponding equation becomes integrodifferential (nonlocal effects). Two different systems are considered: bose  gas of dipolar excitons in a ring shape trap and fermigas of electrons in a quantum well of a MOSstructure. The trapped excitons are described by the GrossPitaevskyi nonlinear equation and for the very simple case of the rectangular potential of the “empty” trap the exact analytical solution is found. The most interesting result of this problem is criterion for existence of bound state in the effective potential ( in the one particle problem a 1D symmetric potential well always contains at least one bound state) . Methodologically instructive is the way of obtaining the eigenvalue of the GrossPitaevskyi equation: the ground state energy is found from the normalization condition. In case of electrons in a quantum well one deals with nonlinear integrodifferential equation for which the exact solution is unknown. The direct variational method was used to find the frequency of the intersubband transition. This frequency turned out to be scaled with the electron concentration N as $N^{2/3}$.
Chaplik A.V. JETP Letters 105 (9) (2017) Toward a selfconsistent theory of Fermi systems with flat bands
A model of fermion condensation, advanced more than 25 years ago, still remains the subject of hot debates, due to the fact that within its frameworks, nonFermiliquid (NFL) behavior, ubiquitously exhibited by strongly correlated Fermi systems, including electron systems of solids, is properly elucidated. The model is derived with the aid of the same Landau postulate that the ground state energy $E$ is a functional of its quasiparticle momentum distribution $n$, giving rise to the conventional Landau state. However, the model discussed deals with completely different solutions, emergent beyond a critical point, at which the topological stability of the Landau state breaks down, and therefore relevant solutions of the problem are found from the wellknown variational condition of mathematical physics $\delta E(n)/\delta n({\bf p})=\mu$ where $\mu$ is the chemical potential. Since the left side of this condition is nothing but the quasiparticle energy $\epsilon({\bf p})$, the variational condition does imply formation of the flat band or, in different words, a fermion condensate (FC). In fact, variational condition furnishes an opportunity to find solely the FC quasiparticle momentum distribution $n_*({\bf p}\in \Omega)$. New allotropes of carbon based in the C60 and C20 fullerenes with outstanding mechanical properties
Materials harder than diamond are always attract great attention from the scientists all over the world. Many attempts were made towards the synthesis especially of carbon material harder than diamond, which is the hardest possible material nowadays. A special interest belongs to materials called as fullerites. There are several experimental and theoretical works, where the synthesis and investigation of superhard fullerite were carried out. [1]–[4] Such materials reveal outstanding mechanical properties with the bulk modulus of several times higher than that of diamond. In this case the computational approaches and methods allow the theoretical investigations and prediction of a new materials with desired properties without using very expensive experimental equipment. Here we used the stateoftheart theoretical methods of computational predictions to predict new carbon phases based on the fullerene molecules of different sizes (C_{60} and C_{20}). Using the evolutionary algorithm, implemented in USPEX package, [5] we considered more than 3000 possible crystal structures to find the most stable ones. The important point, that predicted phases are based on the polymerized fullerites, displaying the superior mechanical properties. We defined the crystal structure of predicted 4 stable allotropes by simulating the XRD patterns. All predicted structures are highly symmetric. The mechanical properties were studied in details in terms of elastic tensor, bulk and shear moduli and velocities of acoustic waves. All predicted structures display elastic constants and bulk modulus very close to diamond, which allows to say that we indeed predict new superhard phases. The possible way of synthesis of such phases was proposed consisting in the cold compression of a mixture of graphite and C_{60} fullerenes. The important feature of predicted phases (besides the mechanical properties) is that they have relatively small band gap ~2.5 eV, while the cI24 phase has the direct gap of 0.53 eV. All obtained data allows the conclusion that predicted superhard semiconducting phases based on the polymerized fullerenes reveal necessary properties for applications in the electronic as basic elements.
[1] V.D. Blank, S.G. Buga, G.A. Dubitsky, N. R Serebryanaya, M.Y. Popov, and B. Sundqvist, Carbon 36, 319 (1998). [2] M. Popov, V. Mordkovich, S. Perfilov, A. Kirichenko, B. Kulnitskiy, I. Perezhogin, and V. Blank, Carbon 76, 250 (2014). [3] Y.A. Kvashnina, A.G. Kvashnin, M.Y. Popov, B.A. Kulnitskiy, I.A. Perezhogin, E.V. Tyukalova, L.A. Chernozatonskii, P.B. Sorokin, and V.D. Blank, J. Phys. Chem. Lett. 6, 2147 (2015). [4] Y.A. Kvashnina, A.G. Kvashnin, L.A. Chernozatonskii, and P.B. Sorokin, Carbon 115, 546 (2017). [5] C.W. Glass, A.R. Oganov, and N. Hansen, Comput. Phys. Commun. 175, 713 (2006).
Kvashnina Yu.A., Kvashnin D.G., Kvashnin A.G., Sorokin P.B. JETP Letters 105 ( 7) (2017)
Stochastic clustering of materials by plasma  surface interaction
Recently stochastic clustering with statistical selfsimilarity (fractality) has been found on material surface exposed under extreme plasma thermal loads in fusion devices (see [1]). In such devices, multiple processes of erosion and redeposition of the eroded material, surface melting and motion of the surface layers lead to a stochastic surface growth on the scales from tens of nanometers to hundreds of micrometers. The moving of eroded material species during redeposition from plasma and agglomeration on the surface is governed by stochastic electric fields generated by the hightemperature plasma. The specific property of the nearwall plasma in fusion device is the nonGaussian statistics of electric field fluctuations with longrange correlations [2]. It leads to the stochastic agglomerate growth with a selfsimilar structure (hierarchical granularity  fractality) of nonGaussian statistics contrary to a trivial roughness observed in ordinary processes of stochastic agglomeration. The dominant factor in such process in fusion device is the collective effect during stochastic clustering rather than the chemical element composition and physical characteristics of the solid material. In support of this view it is reported in this Letter, that such similar stochastic fractal structure with hierarchical granularity and selfsimilarity is formed on various materials, such as tungsten, carbon materials and stainless steel exposed to hightemperature plasma in fusion devices. In the literature it is discussed hypotheses of universal scalings of stochastic objects and processes with multiscale invariance property (statistical selfsimilarity), see e.g. [3]. The kinetic models propose the describing of the stochastic clustering with a selfsimilar structure and considering the power law solutions for the number N of agglomerating clusters with mass m (see e.g. [4]), N(m)=Cm^{(3+}^{h}^{)/2}, where h is a selfsimilarity exponent of the agglomeration kinetic model, C is a constant factor. It is surprisingly found in this Letter that such the power laws (with power exponents from 2.4 to 2.8) describing the roughness of the test specimens from fusion devices are strictly deviated from that of the reference samples formed in a trivial agglomeration process forming Brownianlike rough surface (such as samples exposed to lowtemperature glow discharge plasma and rough steel casting with the power law exponent in the range of 1.97 to 2.2). Statistics of stochastic clustering samples from fusion devices is typically nonGaussian and has a "heavy" tails of probability distribution functions (PDF) of stochastic surface heights (of the Hurst exponent from 0.68 to 0.86). It is contrary to the Gaussian PDF of the reference samples with trivial stochastic surface. Stochastic clustering of materials from fusion devices is characterised by multifractal statistics. Quantitative characteristics of statistical inhomogeneity of such material structure, including multifractal spectrum with broadening of 0.5 ¾ 1.2, are in the range observed for typical multifractal objects and processes in nature. This may indicate a universal mechanism of stochastic clustering of materials under the influence of hightemperature plasma.
1. V.P. Budaev et al., JETP Letters vol. 95, 2, 78 (2012). 2. V.P. Budaev, S.P. Savin, L.M. Zelenyi, PhysicsUspekhi 54 (9), 875 (2011) 3. A. L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge Univ. Press, Cambridge, 1995). 4. C. Connaughton, R. Rajesh, O. Zaboronski, PRL 94 (19), 194503 (2005).
V.P. Budaev, JETP Letters vol. 105, issue 5 (2017) Fluctuational shift of nematic  isotropic phase transition temperature
Modern physics of liquid crystals is much younger than its traditional condensed matter material counterparts. Therefore the field is not yet completely elaborated and exhausted, and one may still expect discoveries of new mesogen materials exhibiting of new types of liquidcrystalline ordering. A few years ago such a discovery of socalled bentcore or dimer mesogens which can form short pitch heliconical nematic state (also known as twistbend nematics, $N_{TB}$) [1, 2], attracted a lot of interest to this new state of matter with nanoscale orientational modulation. First, to understand the nature of the phase, basically different from conventional uniform nematics and from modulated in mass density smectics (see e.g., Landau theory approach, [3,4]). Second, to exploit potentially very perspective applications of the $N_{TB}$ liquid crystals. Along this way, very recently S.M.Saliti, M.G.Tamba, S.N. Sprunt, C.Welch, G.H.Mehl, A.Jakli, J.T.Gleeson [5] observed of the unprecedentedly large magnetic field induced shift $\Delta T_c(H)$ of the nematic  isotropic transition temperature. What is even more surprising $\Delta T_c(H)$ does not follow the thermodynamics textbook wisdom prediction $H^2$ scaling. Our interpretation of such a behavior is based on singular longitudinal fluctuations of the nematic order parameter. Since these fluctuations are governed by the Goldstone director fluctuations they exist only in the nematic state. External magnetic field suppresses the singular longitudinal fluctuations of the order parameter. The reduction of the fluctuations changes the equilibrium value of the modulus of the order parameter in the nematic state, and leads to additional (with respect to the mean field contribution) fluctuational shift of the nematic  isotropic transition temperature. The mechanism works for any nematic liquid crystals, however the magnitude of the fluctuational shift increases with decrease of the Frank elastic moduli. Since some of these moduli supposed to be anomalously small for the bentcore or dimer mesogen formed nematic liquid crystals, just these liquid crystals are promising candidates for the observation of the predicted fluctuational shift of the phase transition temperature. Paradox of photons disconnected trajectories being located by means of "weak measurements" in the nested MaxZehnder interferometer
In a recent letter A. Danan et al. [A. Danan, D. Farfurnik, S. BarAd et al., Phys. Rev. Lett. 111, 240402 (2013)] have experimentally demonstrated an intriguing behavior of photons in an interferometer. Simplified layout of the experimental setup represents a nested MachZehnder interferometer (MZI) and is shown below. The surprising result is obtained when the inner MZI is tuned to destructive interference of the light propagating toward mirror F. In that case the power spectrum shows not only peak at the frequency of mirror C but two more peaks at the frequencies of mirrors A and B, and no peaks at the frequencies of mirrors E and F. From these results authors conclude that the path of the photons is not represented by connected trajectories, because the photons are registered inside the inner MZI and not registered outside it. These unusual results have raised an active discussion. Nevertheless, until now there was no comprehensive and clear analysis of the experiment within the framework of the classical electromagnetic waves approach. In this letter, we calculate the signal power spectrum at the output of the nested MZI, based on traditional concept of the classical electromagnetic waves (or quantum mechanics). This concept imply the continuity of the wave (photon) trajectories. We give intuitive clear and comprehensive explanation of paradoxical results. So, there is no necessity for a new concept of disconnected trajectories.
Simplified experimental setup with two nested MachZehnder interferometers. A, B, C, E, and F stands for mirrors; BS1 and BS2, and PBS1 and PBS2 stands for ordinary and polarized beam splitters respectively. The elements BS1, A, B, and BS2 form an inner MZI whereas the elements PBS1, C, E, F and PBS2 form an outer MZI. Various mirrors inside the MZI vibrate with different frequencies. The rotation of a mirror causes a vertical shift of the light beam reflected off that mirror. The shift is measured by a quadcell photodetector QCD. When the vibration frequency of a certain mirror appears in the power spectrum, authors conclude that photons have been near that particular mirror
G.N.Nikolaev JETP Letters 105 (3) (2017) Dark matter from dark energy in qtheory
The dynamics of the quantum vacuum is one of the major unsolved problems of relativistic quantum field theory and cosmology. The reason is that relativistic quantum field theory and general relativity describe processes well below the Planck energy scale, while the deep ultraviolet quantum vacuum at or above the Planck energy scale remains unknown. Following the condensed matter experience we develop a special macroscopic approach called qtheory, which incorporates the ultraviolet degrees of freedom of the quantum vacuum into an effective theory and allows us to study the dynamics of the quantum vacuum and its influence on the evolution of the Universe. The vacuum in our approach is considered as the Lorentzinvariant analog of a condensedmatter system (liquid or solid) which is stable in free space. The variable q is the Lorentzinvariant analog of the particle number density, whose conservation regulates the thermodynamics and dynamics of manybody systems. This approach is universal in the sense that the same results are obtained using different formulations of the qfield. In the paper, we choose the qfield in terms of a 4form field strength, which has, in particular, been used by Hawking for discussion of the main cosmological constant problem  why is the observed value of the cosmological constant many orders of magnitude smaller than follows from naive estimates of the vacuum energy as the energy of zeropoint motion. In qtheory, the huge zeropoint energy is naturally cancelled by the microscopic (transPlanckian) degrees of freedom, as follows from the GibbsDuhem identity, which is applicable to any equilibrium ground state including the one of the physical vacuum. In the paper, we consider a further extension of qtheory. We demonstrate that, in an expanding Universe, the variable effectively splits into two components. The smooth part of the relaxing vacuum field is responsible for dark energy, while the rapidly oscillating component behaves as cold dark matter. In this way, qtheory provides a combined solution to the missingmass problem and the cosmological constant problem. If this scenario is correct, the implication would be that direct searches for darkmatter particles remain unsuccessful in the foreseeable future. F.R. Klinkhamer and G.E. Volovik, JETP Letters 105, issue 1 (2017) NEW METHOD OF INVESTIGATIONS
The ability to detect nonequilibrium spin accumulation (imbalance) by all electrical means is one of the key ingredients in spintronics . Transport detection typically relies on a nonlocal measurement of a contact potential difference induced by the spin imbalance by means of ferromagnetic contacts or spin resolving detectors . A drawback of these approaches lies in a difficulty to extract the absolute value of the spin imbalance without an independent calibration. An alternative concept of a spintocharge conversion via nonequilibrium shot noise was introduced and investigated in experiment recently . Here, the basic idea is that a nonequilibrium spin imbalance generates spontaneous current fluctuations, even in the absence of a net electric current. Being a primary approach , the shot noise based detection is potentially suitable for the absolute measurement of the spin imbalance. In addition, the noise measurement can be used for a local noninvasive sensing. In this letter, we calculate the impact of a spin relaxation on the spin imbalance generated shot noise in the absence of inelastic processes. We find that the spin relaxation increases the noise up to a factor of two, depending on the ratio of the conductor length and the spin relaxation length. The design of the system. A diffusive normal wire of the length L is attached to normal islands on both ends. Nonequilibrium energy distribution on the left hand side of the wire generates the shot noise at a zero net current. The spin imbalance on the lefthand side of the wire is due to the electric current flowing from one ferromagnetic lead (red) to another one with opposite magnetization (blue).
V.S. Khrapai and K.E. Nagaev JETP Letters 105, №1 (2017)
