594 research outputs found
Separable Structure of Many-Body Ground-State Wave Function
We have investigated a general structure of the ground-state wave function
for the Schr\"odinger equation for identical interacting particles (bosons
or fermions) confined in a harmonic anisotropic trap in the limit of large .
It is shown that the ground-state wave function can be written in a separable
form. As an example of its applications, this form is used to obtain the
ground-state wave function describing collective dynamics for trapped
bosons interacting via contact forces.Comment: J. Phys. B: At. Mol. Opt. Phys. 33 (2000) (accepted for publication
Quantum cohomology of partial flag manifolds
We compute the quantum cohomology rings of the partial flag manifolds
F_{n_1\cdots n_k}=U(n)/(U(n_1)\times \cdots \times U(n_k)). The inductive
computation uses the idea of Givental and Kim. Also we define a notion of the
vertical quantum cohomology ring of the algebraic bundle. For the flag bundle
F_{n_1\cdots n_k}(E) associated with the vector bundle E this ring is found.Comment: 33 page
Purcell effect in Hyperbolic Metamaterial Resonators
The radiation dynamics of optical emitters can be manipulated by properly
designed material structures providing high local density of photonic states, a
phenomenon often referred to as the Purcell effect. Plasmonic nanorod
metamaterials with hyperbolic dispersion of electromagnetic modes are believed
to deliver a significant Purcell enhancement with both broadband and
non-resonant nature. Here, we have investigated finite-size cavities formed by
nanorod metamaterials and shown that the main mechanism of the Purcell effect
in these hyperbolic resonators originates from the cavity hyperbolic modes,
which in a microscopic description stem from the interacting cylindrical
surface plasmon modes of the finite number of nanorods forming the cavity. It
is found that emitters polarized perpendicular to the nanorods exhibit strong
decay rate enhancement, which is predominantly influenced by the rod length. We
demonstrate that this enhancement originates from Fabry-Perot modes of the
metamaterial cavity. The Purcell factors, delivered by those cavity modes,
reach several hundred, which is 4-5 times larger than those emerging at the
epsilon near zero transition frequencies. The effect of enhancement is less
pronounced for dipoles, polarized along the rods. Furthermore, it was shown
that the Purcell factor delivered by Fabry-Perot modes follows the dimension
parameters of the array, while the decay rate in the epsilon near-zero regime
is almost insensitive to geometry. The presented analysis shows a possibility
to engineer emitter properties in the structured metamaterials, addressing
their microscopic structure
Purcell effect in Hyperbolic Metamaterial Resonators
The radiation dynamics of optical emitters can be manipulated by properly
designed material structures providing high local density of photonic states, a
phenomenon often referred to as the Purcell effect. Plasmonic nanorod
metamaterials with hyperbolic dispersion of electromagnetic modes are believed
to deliver a significant Purcell enhancement with both broadband and
non-resonant nature. Here, we have investigated finite-size cavities formed by
nanorod metamaterials and shown that the main mechanism of the Purcell effect
in these hyperbolic resonators originates from the cavity hyperbolic modes,
which in a microscopic description stem from the interacting cylindrical
surface plasmon modes of the finite number of nanorods forming the cavity. It
is found that emitters polarized perpendicular to the nanorods exhibit strong
decay rate enhancement, which is predominantly influenced by the rod length. We
demonstrate that this enhancement originates from Fabry-Perot modes of the
metamaterial cavity. The Purcell factors, delivered by those cavity modes,
reach several hundred, which is 4-5 times larger than those emerging at the
epsilon near zero transition frequencies. The effect of enhancement is less
pronounced for dipoles, polarized along the rods. Furthermore, it was shown
that the Purcell factor delivered by Fabry-Perot modes follows the dimension
parameters of the array, while the decay rate in the epsilon near-zero regime
is almost insensitive to geometry. The presented analysis shows a possibility
to engineer emitter properties in the structured metamaterials, addressing
their microscopic structure
Cherenkov radiation in a gravitational wave background
A covariant criterion for the Cherenkov radiation emission in the field of a
non-linear gravitational wave is considered in the framework of exact
integrable models of particle dynamics and electromagnetic wave propagation. It
is shown that vacuum interacting with curvature can give rise to Cherenkov
radiation. The conically shaped spatial distribution of radiation is derived
and its basic properties are discussed.Comment: LaTeX file, no figures, 19 page
Superconductivity in a Mesoscopic Double Square Loop: Effect of Imperfections
We have generalized the network approach to include the effects of
short-range imperfections in order to analyze recent experiments on mesoscopic
superconducting double loops. The presence of weakly scattering imperfections
causes gaps in the phase boundary or for certain intervals of
, which depend on the magnetic flux penetrating each loop. This is
accompanied by a critical temperature , showing a smooth transition
between symmetric and antisymmetric states. When the scattering strength of
imperfections increases beyond a certain limit, gaps in the phase boundary
or appear for values of magnetic flux lying in intervals
around half-integer . The critical temperature corresponding to
these values of magnetic flux is determined mainly by imperfections in the
central branch. The calculated phase boundary is in good agreement with
experiment.Comment: 9 pages, 6 figure
Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate
A hydrodynamic description is used to study the normal modes of a vortex in a
zero-temperature Bose-Einstein condensate. In the Thomas-Fermi (TF) limit, the
circulating superfluid velocity far from the vortex core provides a small
perturbation that splits the originally degenerate normal modes of a
vortex-free condensate. The relative frequency shifts are small in all cases
considered (they vanish for the lowest dipole mode with |m|=1), suggesting that
the vortex is stable. The Bogoliubov equations serve to verify the existence of
helical waves, similar to those of a vortex line in an unbounded weakly
interacting Bose gas. In the large-condensate (small-core) limit, the
condensate wave function reduces to that of a straight vortex in an unbounded
condensate; the corresponding Bogoliubov equations have no bound-state
solutions that are uniform along the symmetry axis and decay exponentially far
from the vortex core.Comment: 15 pages, REVTEX, 2 Postscript figures, to appear in Phys. Rev. A. We
have altered the material in Secs. 3B and 4 in connection with the normal
modes that have |m|=1. Our present treatment satisfies the condition that the
fundamental dipole mode of a condensate with (or without) a vortex should
have the bare frequency $\omega_\perp
The ac magnetic response of mesoscopic type II superconductors
The response of mesoscopic superconductors to an ac magnetic field is
numerically investigated on the basis of the time-dependent Ginzburg-Landau
equations (TDGL). We study the dependence with frequency and dc
magnetic field of the linear ac susceptibility
in square samples with dimensions of the order of the London penetration depth.
At the behavior of as a function of agrees very well
with the two fluid model, and the imaginary part of the ac susceptibility,
, shows a dissipative a maximum at the frequency
. In the presence of a magnetic field a
second dissipation maximum appears at a frequency . The most
interesting behavior of mesoscopic superconductors can be observed in the
curves obtained at a fixed frequency. At a fixed number of
vortices, continuously increases with increasing . We
observe that the dissipation reaches a maximum for magnetic fields right below
the vortex penetration fields. Then, after each vortex penetration event, there
is a sudden suppression of the ac losses, showing discontinuities in
at several values of . We show that these
discontinuities are typical of the mesoscopic scale and disappear in
macroscopic samples, which have a continuos behavior of . We
argue that these discontinuities in are due to the effect of
{\it nascent vortices} which cause a large variation of the amplitude of the
order parameter near the surface before the entrance of vortices.Comment: 12 pages, 9 figures, RevTex
Broadening of Plasmonic Resonance Due to Electron Collisions with Nanoparticle Boundary: а Quantum Mechanical Consideration
We present a quantum mechanical approach to calculate broadening of plasmonic
resonances in metallic nanostructures due to collisions of electrons with the
surface of the structure. The approach is applicable if the characteristic size
of the structure is much larger than the de Broglie electron wavelength in the
metal. The approach can be used in studies of plasmonic properties of both
single nanoparticles and arrays of nanoparticles.Comment: 9 page
Ground State and Excited States of a Confined Bose Gas
The Bogoliubov approximation is used to study the ground state and low-lying
excited states of a dilute gas of atomic bosons held in an isotropic
harmonic potential characterized by frequency and oscillator length
. By assumption, the self-consistent condensate has a macroscopic
occupation number , with . For negative scattering
length , a simple variational trial function yields an estimate for the
critical condensate number at the
onset of collapse. For positive scattering length and large , the
spherical condensate has a well-defined radius , and the low-lying
excited states are compressional waves localized near the surface.
The frequencies of the lowest radial modes () for successive values of
orbital angular momentum form a rotational band , with
somewhat larger than .Comment: 11 pages, plainTEX, no figure
- …