Biomedical subjects

Almas F Sadreev

Publications and source records attributed to Almas F Sadreev.

8 recordsLinked to original sources

PubMed2006

Bound states in elastic waveguides.

We consider numerically the L-, T-, and X-shaped elastic waveguides with the Dirichlet boundary conditions for in-plane deformations (displacements) which obey the vectorial Navier-Cauchy equation. In the X-shaped waveguide we show the existence of a doubly degenerate bound state with frequency below the first symmetrical cutoff frequency, which belongs to the two-dimensional irreducible representation E of symmetry group C(4upsilon). Moreover the next bound state is below the next antisymmetric cutoff frequency. This bound state belongs to the irreducible representation A2. The T-shaped waveguide has only one bound state while the L-shaped one has no bound states.

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PubMed2005

Electric circuit networks equivalent to chaotic quantum billiards.

We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics.

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PubMed2004

Statistics of wave functions and currents induced by spin-orbit interaction in chaotic billiards.

We show that the wave function and current statistics in chaotic Robnik billiards crucially depend on the constant of the spin-orbit interaction (SOI). For small constant the current statistics is described by universal current distributions derived for slightly opened chaotic billiards [Saichev et al., J. Phys. A 35, L87 (2002)] although one of the components of the spinor eigenfunctions is not universal. For strong SOI both components of the spinor eigenstate are complex random Gaussian fields. This observation allows us to derive the distributions of spin-orbit persistent currents which well describe numerical statistics. For intermediate values of the statistics of the eigenstates and currents, both are deeply nonuniversal.

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PubMed2004

Current statistics for wave transmission through an open Sinai billiard: effects of net currents.

Transport through quantum and microwave cavities is studied by analytic and numerical techniques. In particular, we consider the statistics for a finite net probability current (Poynting vector) flowing through an open ballistic Sinai billiard to which two opposite leads/wave guides are attached. We show that if the net probability current is small, the scattering wave function inside the billiard is well approximated by a Gaussian random complex field. In this case, the current statistics are universal and obey simple analytic forms. For larger net currents, these forms still apply over several orders of magnitudes. However, small characteristic deviations appear in the tail regions. Although the focus is on electron and microwave billiards, the analysis is relevant also to other classical wave cavities as, for example, open planar acoustic reverberation rooms, elastic membranes, and water surface waves in irregularly shaped vessels.

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PubMed2004

Current statistics for transport through rectangular and circular billiards.

We consider the statistics of currents for electron (microwave) transmission through rectangular and circular billiards. For the resonant transmission the current distribution is describing by the universal distribution [J. Phys. A 35, L87 (2002)]]. For the more typical case of nonresonant transmission the current statistics reveals features of the current channeling (corridor effect) interior of the billiard. The numerical statistics is compared with analytical distributions.

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PubMed2004

Ground state and phase transitions in a system of arg-cysteamines self-assembled on a Au(111) crystal surface.

The translational and orientation order of arg-cysteamine molecules chemiabsorbed on the Au(111) crystal surface is considered. Couplings between carbon, nitrogen, and hydrogen atoms of the n-alkanethiols are approximated by the Lennard-Jones potential. Moreover, hydrogen bonds between oxygen and nitrogen and dipole-dipole interactions of the dipole moments of different atomic groups are taken into account. It is found that molecules are arranged in a 2 x 2 lattice and have the total symmetry C6 x Z2. The critical temperature of the phase transition to the tilted state Tc1, which breaks the symmetry C6, is estimated to be extremely high. The spontaneous breakdown of the remaining symmetry Z2 leads to the twisted state of the molecules and has the critical temperature Tc2=340 K.

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PubMed2003

Vortex phase diagram of F=1 spinor Bose-Einstein condensates.

We have calculated the F=1 ground state of a spinor Bose-Einstein condensate trapped harmonic potential with an applied Ioffe-Pitchard magnetic field. The vortex phase diagram is found in the plane spanned by perpendicular and longitudinal magnetic fields. The ferromagnetic condensate has two vortex phases which differ by winding number in the spinor components. The two vortices for the F(z)=-1 antiferromagnetic condensate are separated in space. Moreover, we considered an average local spin | >| to testify to what extent it is parallel to magnetic field (the nonadiabatic effects). We have shown that the effects are important at vortex cores.

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PubMed2002

Crossover from regular to irregular behavior in current flow through open billiards.

We discuss signatures of quantum chaos in terms of distributions of nodal points, saddle points, and streamlines for coherent electron transport through two-dimensional billiards, which are either nominally integrable or chaotic. As typical examples of the two cases we select rectangular and Sinai billiards. We have numerically evaluated distribution functions for nearest distances between nodal points and found that there is a generic form for open chaotic billiards through which a net current is passed. We have also evaluated the distribution functions for nodal points with specific vorticity (winding number) as well as for saddle points. The distributions may be used as signatures of quantum chaos in open systems. All distributions are well reproduced using random complex linear combinations of nearly monochromatic states in nominally closed billiards. In the case of rectangular billiards with simple sharp-cornered leads the distributions have characteristic features related to order among the nodal points. A flaring or rounding of the contact regions may, however, induce a crossover to nodal point distributions and current flow typical for quantum chaos. For an irregular arrangement of nodal points, as for example in the Sinai billiard, the quantum flow lines become very complex and volatile, recalling chaos among classical trajectories. Similarities with percolation are pointed out.

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