Surface polaritons in a dielectric at a boundary with a metal in a static electric field

The existence of surface polaritons in a dielectric at a boundary with an ideal metal or superconductor in a static electric field is predicted. The frequency regions in which polaritons exist are substantially different for opposite orientations of the electric field, so that a change in the direction of the field signifies “switching on” or “switching off” of surface polaritons with a fixed frequency. Pis'ma Zh. éksp. Teor. Fiz. 68, No. 12, 876–880 (25 December 1998)     

Dust particles in a thermophoretic trap in a plasma

The feasibility of confining dust particles in a plasma by thermophoretic forces was demonstrated. An extended dust structure in a positive glow discharge column was experimentally obtained at liquid nitrogen temperature. The dust structure was confined in an electrostatic-thermal trap, in which vertical stability was provided by the summed action of longitudinal electrostatic field and thermophoretic forces. Traps of this kind can be analyzed in terms of the general principles developed for confining particles in traps with the use of electric and magnetic multipole fields. We were able to change the shape and volume of the structure and even separate it into parts by varying temperature fields.     

Impurity diffusion in a gas flow in a channel

The impurity concentration N in a gas flow in a channel is approximately calculated. In a number of cases, the wall losses of impurities in the channel can be taken into account by introducing an effective lifetime τ that describes the diffusion drift of the impurity from the flow toward the walls.     

Chaotic mixing in a steady flow in a microchannel

We report experiments on mixing of a passively advected fluorescent dye in a low Reynolds number flow in a microscopic channel. The channel is a chain of repeating segments with a custom designed profile that generates a steady three-dimensional flow with stretching and folding, and chaotic mixing. A few statistical characteristics of mixing in the flow are studied and are all found to agree with theoretical and experimental results for the flows in the Batchelor regime of mixing that are chaotic in time. The proposed microchannel provides fast and efficient mixing and is simple to fabricate.     

Thermodynamics of a Charged Particle in a Noncommutative Plane in a Background Magnetic Field

Landau system in noncommutative space has been considered. To take into account the issue of gauge invariance in noncommutative space, we incorporate the Seiberg-Witten map in our analysis. Generalised Bopp-shift transformation is then used to map the noncommutative system to its commutative equivalent system. In particular we have computed the partition function of the system and from this we obtained the susceptibility of the Landau system and found that the result gets modified by the spatial noncommutative parameter θ. We also investigate the de Hass–van Alphen effect in noncommutative space and observe that the oscillation of the magnetization and the susceptibility gets noncommutative corrections. Interestingly, the susceptibility in the noncommutative scenario is non-zero in the range of the magnetic field greater than the threshold value which is in contrast to its commutative counterpart. The results obtained are valid upto all orders in the noncommutative parameter θ.     

Mean force on a small sphere in a sound field in a viscous fluid

A mean force exerted on a small rigid sphere by a sound wave in a viscous fluid is calculated. The force is expressed as a sum of drag force coming from the external steady flow existing in the absence of the sphere and contributions that are cross products of velocity and velocity derivatives of the incident field. Because of the drag force and an acoustic streaming generated near the sphere, the mean force does not coincide with the acoustic radiation pressure, i.e., the mean momentum flux carried by the sound field through any surface enclosing the sphere. If the sphere radius R is considerably smaller than the viscous wave penetration depth delta, the drag force can give the leading-order contribution (in powers of delta/R) to the mean force and the latter can then be directed against the radiation pressure. In another limit, delta< or =R, the drag force and acoustic streaming play a minor role, and the mean force reduces to the radiation pressure, which can be expressed through source strengths of the scattered sound field. The effect of viscosity can then be significant only if the incident wave is locally plane traveling.     

Transport through a constriction in a FQH-annulus

The flux periodicity of thermodynamic properties of an annulus in the fractional quantum Hall state with a constriction is considered. It is found that -periodicity is obtained due to transfer of fractionally charged particles or composite fermions between the edges of the annulus, respectively. The result for the finite magnitude of the persistent current across a very strong constriction is presented, as obtained with an extension of Wen’s edge state theory.     

Study of a soliton in a medium

The solution of the sine-Gordon equation for a medium is studied in a simplified “quasi-linear” approximation. Several aspects of this approximation are explored and compared with other approximate solutions for the sine-Gordon soliton.     

Drag on a sphere in a fluid

Summary The possible acceleration dependence of the drag on a sphere, executing a translatory motion in a fluid, is examined in detail. After revisiting the standard derivations of this dependence, it is pointed out that the result might be connected with the scheme of incompressible fluids. That the adoption of this scheme is crucial is made evident by showing that a striking contradiction would arise in compressible fluids. Next a procedure is applied which, in a suitable linear approximation, leads to an explicit expression for the drag in compressible fluids. The drag turns out to depend both on the present value and on the history of the speed of the sphere.

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Riassunto Si considera una sfera in moto traslatorio in un fluido e si esamina il problema dell’eventuale dipendenza della forza resistiva dall’accelerazione. Sulla base delle derivazioni classiche di tale dipendenza, si mette in evidenza che il risultato potrebbe essere conseguenza diretta dell’adozione del modello di fluido incomprimibile. Che tale modello sia realmente cruciale è provato anzitutto osservando che l’analoga trattazione, nel caso di fluidi comprimibili, conduce ad una contraddizione. Successivamente, seguendo un’opportuna approssimazione lineare, si perviene all’espressione esplicita della forza resistiva in un fluido comprimibile. Tale forza risulta dipendente sia dal valore attuale sia dalla storia della velocità della sfera.

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Резюме Рассматривается трансияционное движение сферы в жидкости и исследуется проблема эффективной зависимости силы сопротивления от ускорения. После анализа стандартных подходов для вывода этой зависимости отмечается, что исследуемый результат может быть связан с выбранной моделью несжимаемой жидкости. Тот факт, что выбор модели является сушественнум, иллюстрируется в случае сжимаемых жидкостей, где возникает противоречие. Затем развивается линейное приближение, которое приводит к явному выражению для сопротивления в сжимаемых жидкостях. Оказывается, что сопротивление зависит не только от скорости в данный момент, но и от истории скорости сферы.

     

Entropy of a needle in a haystack

In a quantum search algorithm, the initial state which is a linear superposition of all possible basis states is a separable state. At each iteration, the state becomes more and more entangled until eventually it disentangles and reverts to a separable state consisting of the marked state. It is therefore interesting to study how entanglement changes in a Grover search algorithm.     

Plasmons at a hole in a screen

The field distribution and the spectrum of plasma eigenmodes are determined for a circular hole in a screen having the form of a hyperboloid of revolution. The spectrum of plasmons is obtained for a planar screen with a circular hole. The symmetric mode with m=1 can be excited in the field of a dipole oriented along the screen plane, whereas the antisymmetric mode with m=0 can be excited by a dipole perpendicular to the screen plane.     

Relaxation of a dislocation in a nanocrystallite

Experimental studies of dislocations in nanoparticles are just beginning. The corresponding theoretical models are still lacking. In this context, the author analyzes relaxation of a dislocation in a nanoparticle. Mechanistically, this process is considered to occur primarily via dislocation drift induced by the stress-related image forces. Elementary dislocation displacements include the formation of a kink at one of the sides of the dislocation line, its diffusion along this line, and annihilation at the opposite side. For this mechanism, the dependence of the time of dislocation disappearance on the nanoparticle size has been identified.     

Antiferromagnets in a field and ferromagnets in a random field

A new mean field approach for antiferromagnets in a field is shown to be equivalent to a mean field treatment of ferromagnets in a random field. Phase diagrams of the two systems are analogous.     

Cyclotron resonance in a semiconductor in a steady electric field

The classical kinetic equation is solved to find the carrier distribution in the valence band for germanium in cyclotron resonance, the carriers being generated by the electric field. Negative power absorption is demonstrated.I am indebted to V. G. Veselago for proposing the topic and to Yu. M. Kagan for a discussion.     

Photo-magnetic phenomenon in a semi-conductor in a non-homogeneous magnetic field

The emf which is produced on illuminating a homogeneous semiconductor located in a non-homogeneous magnetic field is calculated. It is shown that this emf is composed of two parts — bulk and boundary. Further, there are given the results of experiments carried out on indium antimonide by means of which the conclusions of the theory were verified.