A simple electrostatic model applicable to biomolecular recognition

An exact, analytic solution for a simple electrostatic model applicable to biomolecular recognition is presented. In the model, a layer of high dielectric constant material (representative of the solvent, water) whose thickness may vary separates two regions of low dielectric constant material (representative of proteins, DNA, RNA, or similar materials), in each of which is embedded a point charge. For identical charges, the presence of the screening layer always lowers the energy compared to the case of point charges in an infinite medium of low dielectric constant. Somewhat surprisingly, the presence of a sufficiently thick screening layer also lowers the energy compared to the case of point charges in an infinite medium of high dielectric constant. For charges of opposite sign, the screening layer always lowers the energy compared to the case of point charges in an infinite medium of either high or low dielectric constant. The behavior of the energy leads to a substantially increased repulsive force between charges of the same sign. The repulsive force between charges of opposite signs is weaker than in an infinite medium of low dielectric constant material but stronger than in an infinite medium of high dielectric constant material. The presence of this behavior, which we name asymmetric screening, in the simple system presented here confirms the generality of the behavior that was established in a more complicated system of an arbitrary number of charged dielectric spheres in an infinite solvent.Comment: 15 pages, 6 figure

Gravitational wave energy spectrum of a parabolic encounter

We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Matthews spectrum for eccentric orbits. This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity. We compare this weak-field result to strong-field calculations and find it is reasonably accurate (~10%) provided that the azimuthal and radial orbital frequencies do not differ by more than ~10%. For equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of rp > 20M. These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe, which could be detected by LISA.Comment: 5 pages, 3 figures. Minor changes to match published version; figure 1 corrected; references adde

Atom-dimer scattering length for fermions with different masses: analytical study of limiting cases

We consider the problem of obtaining the scattering length for a fermion colliding with a dimer, formed from a fermion identical to the incident one and another different fermion. This is done in the universal regime where the range of interactions is short enough so that the scattering length $a$ for non identical fermions is the only relevant quantity. This is the generalization to fermions with different masses of the problem solved long ago by Skorniakov and Ter-Martirosian for particles with equal masses. We solve this problem analytically in the two limiting cases where the mass of the solitary fermion is very large or very small compared to the mass of the two other identical fermions. This is done both for the value of the scattering length and for the function entering the Skorniakov-Ter-Martirosian integral equation, for which simple explicit expressions are obtained.Comment: Very simple form for the solution added; conclusion adde

Strong clustering of non-interacting, passive sliders driven by a Kardar-Parisi-Zhang surface

We study the clustering of passive, non-interacting particles moving under the influence of a fluctuating field and random noise, in one dimension. The fluctuating field in our case is provided by a surface governed by the Kardar-Parisi-Zhang (KPZ) equation and the sliding particles follow the local surface slope. As the KPZ equation can be mapped to the noisy Burgers equation, the problem translates to that of passive scalars in a Burgers fluid. We study the case of particles moving in the same direction as the surface, equivalent to advection in fluid language. Monte-Carlo simulations on a discrete lattice model reveal extreme clustering of the passive particles. The resulting Strong Clustering State is defined using the scaling properties of the two point density-density correlation function. Our simulations show that the state is robust against changing the ratio of update speeds of the surface and particles. In the equilibrium limit of a stationary surface and finite noise, one obtains the Sinai model for random walkers on a random landscape. In this limit, we obtain analytic results which allow closed form expressions to be found for the quantities of interest. Surprisingly, these results for the equilibrium problem show good agreement with the results in the non-equilibrium regime.Comment: 14 pages, 9 figure

Compressibility, zero sound, and effective mass of a fermionic dipolar gas at finite temperature

The compressibility, zero sound dispersion, and effective mass of a gas of fermionic dipolar molecules is calculated at finite temperature for one-, two-, and three-dimensional uniform systems, and in a multilayer quasi-two-dimensional system. The compressibility is nonmonotonic in the reduced temperature, $T/T_F$, exhibiting a maximum at finite temperature. This effect might be visible in a quasi-low-dimensional experiment, providing a clear signature of the onset of many-body quantum degeneracy effects. The collective mode dispersion and effective mass show similar nontrivial temperature and density dependence. In a quasi-low-dimensional system, the zero sound mode may propagate at experimentally attainable temperatures.Comment: 19 pages, 12 figures; substantially revised and expande

Limiting Laws of Linear Eigenvalue Statistics for Unitary Invariant Matrix Models

We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of statistics is smooth enough and using the asymptotic formulas by Deift et al for orthogonal polynomials with varying weights, we show first that if the support of the Density of States of the model consists of two or more intervals, then in the global regime the variance of statistics is a quasiperiodic function of n generically in the potential, determining the model. We show next that the exponent of the Laplace transform of the probability law is not in general 1/2variance, as it should be if the Central Limit Theorem would be valid, and we find the asymptotic form of the Laplace transform of the probability law in certain cases

Energy transfer in binary collisions of two gyrating charged particles in a magnetic field

Binary collisions of the gyrating charged particles in an external magnetic field are considered within a classical second-order perturbation theory, i.e., up to contributions which are quadratic in the binary interaction, starting from the unperturbed helical motion of the particles. The calculations are done with the help of a binary collisions treatment which is valid for any strength of the magnetic field and involves all harmonics of the particles cyclotron motion. The energy transfer is explicitly calculated for a regularized and screened potential which is both of finite range and nonsingular at the origin. The validity of the perturbation treatment is evaluated by comparing with classical trajectory Monte Carlo (CTMC) calculations which also allow to investigate the strong collisions with large energy and velocity transfer at low velocities. For large initial velocities on the other hand, only small velocity transfers occur. There the nonperturbative numerical CTMC results agree excellently with the predictions of the perturbative treatment.Comment: 12 pages, 4 figure

On the RKKY range function of a one dimensional non interacting electron gas

We show that the pitfalls encountered in earlier calculations of the RKKY range function for a non interacting one dimensional electron gas at zero temperature can be unraveled and successfully dealt with through a proper handling of the impurity potential.Comment: to appear in Phys. Re

Three-dimensional theory of stimulated Raman scattering

We present a three-dimensional theory of stimulated Raman scattering (SRS) or superradiance. In particular we address how the spatial and temporal properties of the generated SRS beam, or Stokes beam, of radiation depends on the spatial properties of the gain medium. Maxwell equations for the Stokes field operators and of the atomic operators are solved analytically and a correlation function for the Stokes field is derived. In the analysis we identify a superradiating part of the Stokes radiation that exhibit beam characteristics. We show how the intensity in this beam builds up in time and at some point largely dominates the total Stokes radiation of the gain medium. We show how the SRS depends on geometric factors such as the Fresnel number and the optical depth, and that in fact these two factors are the only factors describing the coherent radiation.Comment: 21 pages 14 figure

The long-term cyclotron dynamics of relativistic wave packets: spontaneous collapse and revival

In this work we study the effects of collapse and revival as well as {\it Zitterbewegung} (ZB) phenomenon, for the relativistic electron wave packets, which are a superposition of the states with quantum numbers sharply peaked around some level $n_0$ of the order of few tens. The probability densities as well as average velocities of the packet center and the average spin components were calculated analytically and visualized. Our computations demonstrate that due to dephasing of the states for times larger than the cyclotron period the initial wave packet (which includes the states with the positive energy only) loses the spatial localization so that the evolution can no longer be described classically. However, at the half-revival time $t=T_R/2$ its reshaping takes place firstly. The behavior of the wave packet containing the states of both energy bands (with $E_n>0$ and $E_n<0$) is more complicated. At short times of a few classical periods such packet splits into two parts which rotate with cyclotron frequency in the opposite directions and meet each other every one-half of the cyclotron period. At these moments their wave functions have significant overlap that leads to ZB. At the time of fractional revival each of two sub-packets is decomposed into few packets-fractions. However, at $t=T_R$ each of the two sub-packets (with positive or negative energy) restores at various points of the cyclotron orbit, that makes it impossible reshaping of initial wave packet entirely unlike the wave packet which consists of states with energies $E_n>0$ only. Obtained results can be useful for the description of electromagnetic radiation and absorption in relativistic plasma on astrophysics objects, where super high magnetic field has the value of the order $10^8-10^9$T, as well as for interpretation of experiments with trapped ions