On an exact hydrodynamic solution for the elliptic flow

Looking for the underlying hydrodynamic mechanisms determining the elliptic flow we show that for an expanding relativistic perfect fluid the transverse flow may derive from a solvable hydrodynamic potential, if the entropy is transversally conserved and the corresponding expansion "quasi-stationary", that is mainly governed by the temperature cooling. Exact solutions for the velocity flow coefficients $v_2$ and the temperature dependence of the spatial and momentum anisotropy are obtained and shown to be in agreement with the elliptic flow features of heavy-ion collisions.Comment: 10 pages, 4 figure

Nonequilibrium evolution thermodynamics

A new approach - nonequilibrium evolution thermodynamics, is compared with classical variant of Landau approachComment: 4 pages, 1 figur

Polarons in suspended carbon nanotubes

We prove theoretically the possibility of electric-field controlled polaron formation involving flexural (bending) modes in suspended carbon nanotubes. Upon increasing the field, the ground state of the system with a single extra electron undergoes a first order phase transition between an extended state and a localized polaron state. For a common experimental setup, the threshold electric field is only of order $\simeq 10^{-2}$ V/$\mu$m

Pulsars: Gigantic Nuclei

What is the real nature of pulsars? This is essentially a question of the fundamental strong interaction between quarks at low-energy scale and hence of the non-perturbative quantum chromo-dynamics, the solution of which would certainly be meaningful for us to understand one of the seven millennium prize problems (i.e., "Yang-Mills Theory") named by the Clay Mathematical Institute. After a historical note, it is argued here that a pulsar is very similar to an extremely big nucleus, but is a little bit different from the {\em gigantic nucleus} speculated 80 years ago by L. Landau. The paper demonstrates the similarity between pulsars and gigantic nuclei from both points of view: the different manifestations of compact stars and the general behavior of the strong interaction.Comment: 8 pages, 1 figures; Comments welcome

Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions

We develop the relativistic theory of hydrodynamic fluctuations for application to high energy heavy ion collisions. In particular, we investigate their effect on the expanding boost-invariant (Bjorken) solution of the hydrodynamic equations. We discover that correlations over a long rapidity range are induced by the propagation of the sound modes. Due to the expansion, the dispersion law for these modes is non-linear and attenuated even in the limit of zero viscosity. As a result, there is a non-dissipative wake behind the sound front which is generated by any instantaneous point-like fluctuation. We evaluate the two-particle correlators using the initial conditions and hydrodynamic parameters relevant for heavy-ion collisions at RHIC and LHC. In principle these correlators can be used to obtain information about the viscosities because the magnitudes of the fluctuations are directly proportional to them.Comment: 39 pages, 6 figures; references adde

Detection of spin injection into a double quantum dot: Violation of magnetic-field-inversion symmetry of nuclear polarization instabilities

In mesoscopic systems with spin-orbit coupling, spin-injection into quantum dots at zero magnetic field is expected under a wide range of conditions. However, up to now, a viable approach for experimentally identifying such injection has been lacking. We show that electron spin injection into a spin-blockaded double quantum dot is dramatically manifested in the breaking of magnetic- field-inversion symmetry of nuclear polarization instabilities. Over a wide range of parameters, the asymmetry between positive and negative instability fields is extremely sensitive to the injected electron spin polarization and allows for the detection of even very weak spin injection. This phenomenon may be used to investigate the mechanisms of spin transport, and may hold implications for spin-based information processing

Evaluation of specific heat for superfluid helium between 0 - 2.1 K based on nonlinear theory

The specific heat of liquid helium was calculated theoretically in the Landau theory. The results deviate from experimental data in the temperature region of 1.3 - 2.1 K. Many theorists subsequently improved the results of the Landau theory by applying temperature dependence of the elementary excitation energy. As well known, many-body system has a total energy of Galilean covariant form. Therefore, the total energy of liquid helium has a nonlinear form for the number distribution function. The function form can be determined using the excitation energy at zero temperature and the latent heat per helium atom at zero temperature. The nonlinear form produces new temperature dependence for the excitation energy from Bose condensate. We evaluate the specific heat using iteration method. The calculation results of the second iteration show good agreement with the experimental data in the temperature region of 0 - 2.1 K, where we have only used the elementary excitation energy at 1.1 K.Comment: 6 pages, 3 figures, submitted to Journal of Physics: Conference Serie

Critical phenomena and phase sequence in classical bilayer Wigner crystal at zero temperature

We study the ground-state properties of a system of identical classical Coulombic point particles, evenly distributed between two equivalently charged parallel plates at distance $d$; the system as a whole is electroneutral. It was previously shown that upon increasing d from 0 to infinity, five different structures of the bilayer Wigner crystal become energetically favored, starting from a hexagonal lattice (phase I, d=0) and ending at a staggered hexagonal lattice (phase V, d -> infinity). In this paper, we derive new series representations of the ground-state energy for all five bilayer structures. The derivation is based on a sequence of transformations for lattice sums of Coulomb two-particle potentials plus the neutralizing background, having their origin in the general theory of Jacobi theta functions. The new series provide convenient starting points for both analytical and numerical progress. Its convergence properties are indeed excellent: Truncation at the fourth term determines in general the energy correctly up to 17 decimal digits. The accurate series representations are used to improve the specification of transition points between the phases and to solve a controversy in previous studies. In particular, it is shown both analytically and numerically that the hexagonal phase I is stable only at d=0, and not in a finite interval of small distances between the plates as was anticipated before. The expansions of the structure energies around second-order transition points can be done analytically, which enables us to show that the critical behavior is of the Ginzburg-Landau type, with a mean-field critical index beta=1/2 for the growth of the order parameters

Exact solutions of classical scalar field equations

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.Comment: 7 pages, no figures. Added proof of existence of a zero mode and two more references. Accepted for publication in Journal of Nonlinear Mathematical Physic

A new collective mode in the fractional quantum Hall liquid

We apply the methods of continuum mechanics to the study of the collective modes of the fractional quantum Hall liquid. Our main result is that at long wavelength there are {\it two} distinct modes of oscillations, while previous theories predicted only {\it one}. The two modes are shown to arise from the internal dynamics of shear stresses created by the Coulomb interaction in the liquid. Our prediction is supported by recent light scattering experiments, which report the observation of two long-wavelength modes in a quantum Hall liquid.Comment: 4 pages, 1 Figur