127 research outputs found
Four-dimensional photonic lattices and discrete tesseract solitons
We theoretically study discrete photonic lattices in more than three
dimensions and point out that such systems can exist in continuous
three-dimensional (3D) space. We study discrete diffraction in the linear
regime, and predict the existence of four-dimensional (4D) tesseract solitons
in nonlinear 4D periodic photonic lattices. Finally, we propose a design
towards a potential realization of such periodic 4D lattices in experiments.Comment: Submitted to PRL on 14 May 201
Ground state properties of a one-dimensional strongly-interacting Bose-Fermi mixture in a double-well potential
We calculate the reduced single-particle density matrix (RSPDM), momentum
distributions, natural orbitals and their occupancies, for a strongly
interacting one-dimensional Bose-Fermi mixture in a double-well potential with
a large central barrier. For mesoscopic systems, we find that the ground state
properties qualitatively differ for mixtures with even number of particles
(both odd-odd and even-even mixtures) in comparison to mixtures with odd
particle numbers (odd-even and even-odd mixtures). For even mixtures the
momentum distribution is smooth, whereas the momentum distribution of odd
mixtures possesses distinct modulations; the differences are observed also in
the off-diagonal correlations of the RSPDM, and in the occupancies of natural
orbitals. The calculation is based on a derived formula which enables efficient
calculation of the RSPDM for mesoscopic mixtures in various potentials.Comment: 10 figure
The matrix of a linear operator in a pair of ordered bases
In the lecture it is shown how to represent a linear operator by a matrix.
This representation allows us to define an operation with matrices
The problem of the initial approximation for a special nonlinear least squares problem
In [6] the existence theorem for the best least squares approximation of parameters for the exponential function is proved.
In this paper we consider the problem of choosing a good initial approximation of these parameters
The existence theorem for the solution of a nonlinear least squares problem
In this paper we prove a theorem which gives necessary and sufficient conditions which guarantee the existence of the global minimum for a continuous real valued function bounded from below, which is defined on a non-compact set.
The use of the theorem is illustrated by an example of the least squares problem
Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions
The asymptotic form of the wave functions describing a freely expanding
Lieb-Liniger gas is derived by using a Fermi-Bose transformation for
time-dependent states, and the stationary phase approximation. We find that
asymptotically the wave functions approach the Tonks-Girardeau (TG) structure
as they vanish when any two of the particle coordinates coincide. We point out
that the properties of these asymptotic states can significantly differ from
the properties of a TG gas in a ground state of an external potential. The
dependence of the asymptotic wave function on the initial state is discussed.
The analysis encompasses a large class of initial conditions, including the
ground states of a Lieb-Liniger gas in physically realistic external
potentials. It is also demonstrated that the interaction energy asymptotically
decays as a universal power law with time, .Comment: Section VI added to v2; published versio
Lieb-Liniger gas in a constant force potential
We use Gaudin's Fermi-Bose mapping operator to calculate exact solutions for
the Lieb-Liniger model in a linear (constant force) potential (the constructed
exact stationary solutions are referred to as the Lieb-Liniger-Airy wave
functions). The ground state properties of the gas in the wedge-like trapping
potential are calculated in the strongly interacting regime by using
Girardeau's Fermi-Bose mapping and the pseudopotential approach in the
-approximation ( denotes the strength of the interaction). We point out
that quantum dynamics of Lieb-Liniger wave packets in the linear potential can
be calculated by employing an -dimensional Fourier transform as in the case
of free expansion
Synthetic Lorentz force in classical atomic gases via Doppler effect and radiation pressure
We theoretically predict a novel type of synthetic Lorentz force for
classical (cold) atomic gases, which is based on the Doppler effect and
radiation pressure. A fairly uniform and strong force can be constructed for
gases in macroscopic volumes of several cubic millimeters and more. This opens
the possibility to mimic classical charged gases in magnetic fields, such as
those in a tokamak, in cold atom experiments.Comment: are welcom
Momentum distribution of a freely expanding Lieb-Liniger gas
We numerically study free expansion of a few Lieb-Liniger bosons, which are
initially in the ground state of an infinitely deep hard-wall trap. Numerical
calculation is carried out by employing a standard Fourier transform, as
follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger
gas. We study the evolution of the momentum distribution, the real-space
single-particle density, and the occupancies of natural orbitals. Our numerical
calculation allows us to explore the behavior of these observables in the
transient regime of the expansion, where they are non-trivially affected by the
particle interactions. We derive analytically (by using the stationary phase
approximation) the formula which connects the asymptotic shape of the momentum
distribution and the initial state. For sufficiently large times the momentum
distribution coincides (up to a simple scaling transformation) with the shape
of the real-space single-particle density (the expansion is asymptotically
ballistic). Our analytical and numerical results are in good agreement.Comment: small changes; references correcte
Analysis of solution of the least squares problem
For the given data , we consider the
existence problem of the best parameter approximation of the exponential model function in the sense of ordinary least squares and total least squares.
Results related to that problem which have been obtained and published by the authors so far are given in the paper, as well as some new results on nonuniqueness of the best parameter approximation
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