arXiv subjects

Er'el Granot

Publications and source records attributed to Er'el Granot.

29 records · Page 2Linked to original sources

arXiv2006

Universal potential barrier penetration by initially confined wavepackets

The dynamics of an initially sharp-boundary wavepacket in the presence of an arbitrary potential barrier are investigated. It is shown that the penetration through the barrier is universal in the sense that it depends only on the values of the wavefunction and its derivatives at the boundary. The dependence on the derivatives vanishes at long distances from the barrier, where the dynamics are governed solely by the initial value of the wavefunction at the boundary.

quant-ph↗

arXiv2006

Potential Barrier Classification by Short-Time Measurement

We investigate the short-time dynamics of a delta-function potential barrier on an initially confined wave-packet. There are mainly two conclusions: A) At short times the probability density of the first particles that passed through the barrier is unaffected by it. B) When the barrier is absorptive (i.e., its potential is imaginary) it affects the transmitted wave function at shorter times than a real potential barrier. Therefore, it is possible to distinguish between an imaginary and a real potential barrier by measuring its effect at short times only on the transmitting wavefunction.

quant-ph↗

arXiv2005

Shearing a fermionic gas and quantized friction

The frictional forces in sheared fermionic gas are investigated. The gas is sheared by two sliding surfaces. Except for a small imperfection (bulge) on one of them, the surfaces are totally smooth. We show that when the bulge is extremely small, and the gas is also confined in the lateral dimension, the frictional force (F) is quantized. That is, F=m*mu*v, where v is the sliding velocity with respect to the lubricant gas, m is an integer, and mu is the friction coefficient. It is also shown that mu is proportional to the Planck constant h and depends only on the bulge's properties (it does not depend on either the gas properties or the sliding velocity).

cond-mat.other↗

arXiv2005

Generic Short-Time Propagation of Sharp-Boundaries Wave Packets

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wavefunction is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can be written as an expression that depends only on the values of the function (and its derivatives) at the boundaries. In particular, it is shown that at short times ($t\ll2mx^2/\hbar$, where $x$ is the distance to the boundaries) the wavefunction propagation depends only on the wavefunction's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wavefunction (i.e., for wavepackets with finite-width boundaries) and suggest an experimental verification.

quant-ph↗

arXiv2004

Point scatterers in low number of dimensions

It is well known that in 1D the cross section of a point scatterer increases along with the scatterer's strength (potential). In this paper we show that this is an exceptional case, and in all the other cases, where a point defect has a physical meaning, i.e., 0<d<1 and 1<d<=2 (d is the dimensions number), the cross section does not increase monotonically with the scatterer's strength. In fact, the cross section exhibits a resonance dependence on the scatterer's strength, and in the singular 2D case it gets its maximum value for an infinitely weak strength. We use this fact to show that two totally different generalized functions can describe exactly the same physical entity (the same scatterer).

cond-mat.mes-hall↗

arXiv2003

Scatterer that leaves "footprints" but no "fingerprints"

We calculate the exact transmission coefficient of a quantum wire in the presence of a single point defect at the wire's cut-off frequencies. We show that while the conductance pattern (i.e., the scattering) is strongly affected by the presence of the defect, the pattern is totally independent of the defect's characteristics (i.e., the defect that caused the scattering cannot be identified from that pattern).

quant-ph↗

arXiv2003

Universal conductance reduction in a quantum wire

Even a single point defect in a quantum wire causes a conductance reduction. In this paper we prove (without any approximations) that for any point impurity this conductance reduction in all the sub-bands is exactly 2e^2/h. Moreover, it is shown that in the case of a surface defect, not only is the conductance minimum independent of the defect characteristics, but the transmission matrix also converges to universal (defect-independent) values. We also discuss particle confinement between two arbitrarily weak point defects.

cond-mat.mes-hall↗

arXiv2002

Narrow Spectral Response of a Brillouin Amplifier transmission channel

We investigate the spectral response of a Brillouin amplifier in the frequency regime within the SBS bandwidth. This is done by amplitude modulating the pump with a low frequency, and therefore, unlike previous studies, the spectrum of the modulated pump is, in all cases, smaller than the SBS bandwidth. We show both theoretically and experimentally that unlike phase modulation, which was reported in the literature, the amplitude modulation increases the Brillouin amplifier gain, and that this effect has a very narrow bandwidth. Only modulation frequencies that are lower than a certain cut-off frequency increase the gain. This cut-off frequency is inversely proportional to the fiber's length, and can therefore be arbitrarily small.

physics.optics↗

arXiv2002

Limitations to bit-rate and spatial capacity of an optical data transmission channel

The maximum bit-rate of a slab waveguide is ultimately determined by the waveguide dispersion. We show that while the maximum bit rate in a waveguide is inversely proportional to the waveguide's width, bit rate per unit width (i.e., spatial capacity) decreases, and in the limit of a zero-width waveguide it converges to a value, which is independent of the waveguide's refractive indices. This value is qualitatively equivalent to the transmission rate per unit of width in free space. We also show that in a 3D waveguide (e.g., fibers), unlike free space, the spatial capacity vanishes in the same limit.

physics.optics↗

arXiv2002

Forbidden activation levels in a non-stationary tunneling process

Tunneling in the presence of an opaque barrier, part of which varies in time, is investigated numerically and analytically in one dimension. Clearly, due to the varying barrier a tunneling particle experiences spectral widening. However, in the case of strong perturbations, the particles' activation to certain energies is avoided. We show that this effect occurs only when the perturbation decays faster than 1/t^2.

cond-mat↗

arXiv2001

Selected elevation in quantum tunneling

The tunneling through an opaque barrier with a strong oscillating component is investigated. It is shown, that in the strong perturbations regime (in contrast to the weak one), higher perturbations rate does not necessarily improve the activation. In fact, in this regime two rival factors play a role, and as a consequence, this tunneling system behaves like a sensitive frequency-shifter device: for most incident particles' energies activation occurs and the particles are energetically elevated, while for specific energies activation is depressed and the transmission is very low. This effect is unique to the strong perturbation regime, and it is totally absent in the weak perturbation case. Moreover, it cannot be deduced even in the adiabatic regime. It is conjectured that this mechanism can be used as a frequency-dependent transistor, in which the device's transmission is governed by the external field frequency.

quant-ph↗