548 research outputs found
Quantum control by von Neumann measurements
A general scheme is presented for controlling quantum systems using evolution
driven by non-selective von Neumann measurements, with or without an additional
tailored electromagnetic field. As an example, a 2-level quantum system
controlled by non-selective quantum measurements is considered. The control
goal is to find optimal system observables such that consecutive non-selective
measurement of these observables transforms the system from a given initial
state into a state which maximizes the expected value of a target operator (the
objective). A complete analytical solution is found including explicit
expressions for the optimal measured observables and for the maximal objective
value given any target operator, any initial system density matrix, and any
number of measurements. As an illustration, upper bounds on measurement-induced
population transfer between the ground and the excited states for any number of
measurements are found. The anti-Zeno effect is recovered in the limit of an
infinite number of measurements. In this limit the system becomes completely
controllable. The results establish the degree of control attainable by a
finite number of measurements
Some generic aspects of bosonic excitations in disordered systems
We consider non-interacting bosonic excitations in disordered systems,
emphasising generic features of quadratic Hamiltonians in the absence of
Goldstone modes. We discuss relationships between such Hamiltonians and the
symmetry classes established for fermionic systems. We examine the density
\rho(\omega) of excitation frequencies \omega, showing how the universal
behavior \rho(\omega) ~ \omega^4 for small \omega can be obtained both from
general arguments and by detailed calculations for one-dimensional models
Existence and homogenization of the Rayleigh-B\'enard problem
The Navier-Stokes equation driven by heat conduction is studied. As a
prototype we consider Rayleigh-B\'enard convection, in the Boussinesq
approximation. Under a large aspect ratio assumption, which is the case in
Rayleigh-B\'enard experiments with Prandtl number close to one, we prove the
existence of a global strong solution to the 3D Navier-Stokes equation coupled
with a heat equation, and the existence of a maximal B-attractor. A rigorous
two-scale limit is obtained by homogenization theory. The mean velocity field
is obtained by averaging the two-scale limit over the unit torus in the local
variable
Anharmonic vs. relaxational sound damping in glasses: II. Vitreous silica
The temperature dependence of the frequency dispersion in the sound velocity
and damping of vitreous silica is reanalyzed. Thermally activated relaxation
accounts for the sound attenuation observed above 10 K at sonic and ultrasonic
frequencies. Its extrapolation to the hypersonic regime reveals that the
anharmonic coupling to the thermal bath becomes important in
Brillouin-scattering measurements. At 35 GHz and room temperature, the damping
due to this anharmonicity is found to be nearly twice that produced by
thermally activated relaxation. The analysis also reveals a sizeable velocity
increase with temperature which is not related with sound dispersion. This
suggests that silica experiences a gradual structural change that already
starts well below room temperature.Comment: 13 pages with 8 figure
Adhesive coatings based on aligned arrays of carbon nanostructures
This work was financially supported by Russian Foundation for Basic Research (projects 16-29-14023 and 18-32-00652) and Internal grant of the Southern Federal University (project VnGr-07/2017-26)
Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case
We study the asymptotic behavior of the solutions of a spectral problem for
the Laplacian in a domain with rapidly oscillating boundary. We consider the
case where the eigenvalue of the limit problem is multiple. We construct the
leading terms of the asymptotic expansions for the eigenelements and verify the
asymptotics
Comment: Superconducting transition in Nb nanowires fabricated using focused ion beam
In a recent paper Tettamanzi et al (2009 Nanotechnology \bf{20} 465302)
describe the fabrication of superconducting Nb nanowires using a focused ion
beam. They interpret their conductivity data in the framework of thermal and
quantum phase slips below . In the following we will argue that their
analysis is inappropriate and incomplete, leading to contradictory results.
Instead, we propose an interpretation of the data within a SN proximity model.Comment: 3 pages, 1 figure accepted in Nanotechnolog
Study of the dependence of Young's modulus of vertically aligned carbon nanotubes on their aspect ratio
The reported study was funded by RFBR according to the research projects No.16-29-14023 ofi_m, No.18-32-00652 and by grant of the Southern Federal University (project No. VnGr-07/2017-26)
Effects of Electron-Electron and Electron-Phonon Interactions in Weakly Disordered Conductors and Heterostuctures
We investigate quantum corrections to the conductivity due to the
interference of electron-electron (electron-phonon) scattering and elastic
electron scattering in weakly disordered conductors. The electron-electron
interaction results in a negative -correction in a 3D conductor. In
a quasi-two-dimensional conductor, ( is the thickness, is
the Fermi velocity), with 3D electron spectrum this correction is linear in
temperature and differs from that for 2D electrons (G. Zala et. al., Phys.
Rev.B {\bf 64}, 214204 (2001)) by a numerical factor. In a
quasi-one-dimensional conductor, temperature-dependent correction is
proportional to . The electron interaction via exchange of virtual phonons
also gives -correction. The contribution of thermal phonons interacting
with electrons via the screened deformation potential results in -term and
via unscreened deformation potential results in -term. The interference
contributions dominate over pure electron-phonon scattering in a wide
temperature range, which extends with increasing disorder.Comment: 6 pages, 2figure
Vibrational instability, two-level systems and Boson peak in glasses
We show that the same physical mechanism is fundamental for two seemingly
different phenomena such as the formation of two-level systems in glasses and
the Boson peak in the reduced density of low-frequency vibrational states
g(w)/w^2. This mechanism is the vibrational instability of weakly interacting
harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of
Debye frequency) the instability, controlled by the anharmonicity, creates a
new stable universal spectrum of harmonic vibrations with a Boson peak feature
as well as double-well potentials with a wide distribution of barrier heights.
Both are determined by the strength of the interaction I ~ w_c between the
oscillators. Our theory predicts in a natural way a small value for the
important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses.
We show that C ~ I^{-3} and decreases with increasing of the interaction
strength I. We show that the number of active two-level systems is very small,
less than one per ten million of oscillators, in a good agreement with
experiment. Within the unified approach developed in the present paper the
density of the tunneling states and the density of vibrational states at the
Boson peak frequency are interrelated.Comment: 28 pages, 3 figure
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